TSTP Solution File: SWB038+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB038+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 08:32:05 EDT 2022
% Result : Theorem 3.70s 2.68s
% Output : Proof 3.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWB038+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n026.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Sep 3 20:15:24 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.34 Usage: tptp [options] [-file:]file
% 0.11/0.34 -h, -? prints this message.
% 0.11/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.34 -m, -model generate model.
% 0.11/0.34 -p, -proof generate proof.
% 0.11/0.34 -c, -core generate unsat core of named formulas.
% 0.11/0.34 -st, -statistics display statistics.
% 0.11/0.34 -t:timeout set timeout (in second).
% 0.11/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.34 -<param>:<value> configuration parameter and value.
% 0.11/0.34 -o:<output-file> file to place output in.
% 3.70/2.68 % SZS status Theorem
% 3.70/2.68 % SZS output start Proof
% 3.70/2.68 tff(icext_type, type, (
% 3.70/2.68 icext: ( $i * $i ) > $o)).
% 3.70/2.68 tff(tptp_fun_X_67_type, type, (
% 3.70/2.68 tptp_fun_X_67: ( $i * $i ) > $i)).
% 3.70/2.68 tff(uri_ex_c1_type, type, (
% 3.70/2.68 uri_ex_c1: $i)).
% 3.70/2.68 tff(uri_ex_c2_type, type, (
% 3.70/2.68 uri_ex_c2: $i)).
% 3.70/2.68 tff(uri_ex_y_type, type, (
% 3.70/2.68 uri_ex_y: $i)).
% 3.70/2.68 tff(uri_ex_x_type, type, (
% 3.70/2.68 uri_ex_x: $i)).
% 3.70/2.68 tff(tptp_fun_X6_140_type, type, (
% 3.70/2.68 tptp_fun_X6_140: $i)).
% 3.70/2.68 tff(tptp_fun_X1_146_type, type, (
% 3.70/2.68 tptp_fun_X1_146: $i)).
% 3.70/2.68 tff(tptp_fun_X5_142_type, type, (
% 3.70/2.68 tptp_fun_X5_142: $i)).
% 3.70/2.68 tff(ic_type, type, (
% 3.70/2.68 ic: $i > $o)).
% 3.70/2.68 tff(iext_type, type, (
% 3.70/2.68 iext: ( $i * $i * $i ) > $o)).
% 3.70/2.68 tff(uri_owl_equivalentClass_type, type, (
% 3.70/2.68 uri_owl_equivalentClass: $i)).
% 3.70/2.68 tff(tptp_fun_X0_144_type, type, (
% 3.70/2.68 tptp_fun_X0_144: $i)).
% 3.70/2.68 tff(uri_rdf_List_type, type, (
% 3.70/2.68 uri_rdf_List: $i)).
% 3.70/2.68 tff(uri_owl_intersectionOf_type, type, (
% 3.70/2.68 uri_owl_intersectionOf: $i)).
% 3.70/2.68 tff(uri_rdf_nil_type, type, (
% 3.70/2.68 uri_rdf_nil: $i)).
% 3.70/2.68 tff(tptp_fun_X2_143_type, type, (
% 3.70/2.68 tptp_fun_X2_143: $i)).
% 3.70/2.68 tff(uri_rdf_rest_type, type, (
% 3.70/2.68 uri_rdf_rest: $i)).
% 3.70/2.68 tff(uri_rdf_first_type, type, (
% 3.70/2.68 uri_rdf_first: $i)).
% 3.70/2.68 tff(tptp_fun_X3_141_type, type, (
% 3.70/2.68 tptp_fun_X3_141: $i)).
% 3.70/2.68 tff(uri_owl_unionOf_type, type, (
% 3.70/2.68 uri_owl_unionOf: $i)).
% 3.70/2.68 tff(tptp_fun_X4_145_type, type, (
% 3.70/2.68 tptp_fun_X4_145: $i)).
% 3.70/2.68 tff(uri_owl_complementOf_type, type, (
% 3.70/2.68 uri_owl_complementOf: $i)).
% 3.70/2.68 tff(tptp_fun_X_3_type, type, (
% 3.70/2.68 tptp_fun_X_3: ( $i * $i * $i ) > $i)).
% 3.70/2.68 tff(tptp_fun_X_6_type, type, (
% 3.70/2.68 tptp_fun_X_6: ( $i * $i * $i ) > $i)).
% 3.70/2.68 tff(1,assumption,(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))), introduced(assumption)).
% 3.70/2.68 tff(2,plain,
% 3.70/2.68 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))))))),
% 3.70/2.68 inference(bind,[status(th)],[])).
% 3.70/2.68 tff(3,plain,
% 3.70/2.68 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 3.70/2.68 inference(quant_intro,[status(thm)],[2])).
% 3.70/2.68 tff(4,plain,
% 3.70/2.68 (^[C1: $i, C2: $i] : refl((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 3.70/2.68 inference(bind,[status(th)],[])).
% 3.70/2.68 tff(5,plain,
% 3.70/2.68 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 3.70/2.68 inference(quant_intro,[status(thm)],[4])).
% 3.70/2.68 tff(6,plain,
% 3.70/2.68 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))))))),
% 3.70/2.68 inference(bind,[status(th)],[])).
% 3.70/2.68 tff(7,plain,
% 3.70/2.68 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 3.70/2.68 inference(quant_intro,[status(thm)],[6])).
% 3.70/2.68 tff(8,plain,
% 3.70/2.68 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 3.70/2.68 inference(transitivity,[status(thm)],[7, 5])).
% 3.70/2.68 tff(9,plain,
% 3.70/2.68 (^[C1: $i, C2: $i] : trans(monotonicity(rewrite(((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))), rewrite((iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1)))) <=> (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))), ((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))))), rewrite((((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))), ((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))))),
% 3.84/2.68 inference(bind,[status(th)],[])).
% 3.84/2.68 tff(10,plain,
% 3.84/2.68 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 3.84/2.68 inference(quant_intro,[status(thm)],[9])).
% 3.84/2.68 tff(11,plain,
% 3.84/2.68 (^[C1: $i, C2: $i] : rewrite((((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))))),
% 3.84/2.68 inference(bind,[status(th)],[])).
% 3.84/2.68 tff(12,plain,
% 3.84/2.68 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1))))))) <=> ![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1)))))),
% 3.84/2.68 inference(quant_intro,[status(thm)],[11])).
% 3.84/2.68 tff(13,plain,
% 3.84/2.68 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 3.84/2.68 inference(rewrite,[status(thm)],[])).
% 3.84/2.68 tff(14,plain,
% 3.84/2.68 (^[C1: $i, C2: $i] : rewrite((iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))))),
% 3.84/2.68 inference(bind,[status(th)],[])).
% 3.84/2.68 tff(15,plain,
% 3.84/2.68 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 3.84/2.68 inference(quant_intro,[status(thm)],[14])).
% 3.84/2.68 tff(16,axiom,(![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_eqdis_equivalentclass')).
% 3.84/2.68 tff(17,plain,
% 3.84/2.68 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 3.84/2.68 inference(modus_ponens,[status(thm)],[16, 15])).
% 3.84/2.68 tff(18,plain,
% 3.84/2.68 (![C1: $i, C2: $i] : (iext(uri_owl_equivalentClass, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X))))),
% 3.84/2.68 inference(modus_ponens,[status(thm)],[17, 13])).
% 3.84/2.68 tff(19,plain,(
% 3.84/2.68 ![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~(icext(C1, tptp_fun_X_67(C2, C1)) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 3.84/2.68 inference(skolemize,[status(sab)],[18])).
% 3.84/2.68 tff(20,plain,
% 3.84/2.68 (![C1: $i, C2: $i] : (((~iext(uri_owl_equivalentClass, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (icext(C1, X) <=> icext(C2, X)))) & (iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1)))))),
% 3.84/2.68 inference(modus_ponens,[status(thm)],[19, 12])).
% 3.84/2.68 tff(21,plain,
% 3.84/2.68 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 3.84/2.68 inference(modus_ponens,[status(thm)],[20, 10])).
% 3.84/2.68 tff(22,plain,
% 3.84/2.68 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X))))))) | (~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1)))))))),
% 3.84/2.68 inference(modus_ponens,[status(thm)],[21, 8])).
% 3.84/2.68 tff(23,plain,
% 3.84/2.68 (![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))),
% 3.84/2.68 inference(modus_ponens,[status(thm)],[22, 3])).
% 3.84/2.68 tff(24,plain,
% 3.84/2.68 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_equivalentClass, C1, C2) | (~ic(C2)) | (~ic(C1)) | ((~icext(C1, tptp_fun_X_67(C2, C1))) <=> icext(C2, tptp_fun_X_67(C2, C1))))) | (~((~iext(uri_owl_equivalentClass, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : (icext(C1, X) <=> icext(C2, X)))))))))) | (~((~(iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X)))))))))),
% 3.84/2.68 inference(quant_inst,[status(thm)],[])).
% 3.84/2.68 tff(25,plain,
% 3.84/2.68 (~((~(iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X))))))))),
% 3.84/2.68 inference(unit_resolution,[status(thm)],[24, 23])).
% 3.84/2.68 tff(26,plain,
% 3.84/2.68 (((~(iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> icext(uri_ex_c2, X)))))))) | (iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 3.84/2.68 inference(tautology,[status(thm)],[])).
% 3.84/2.68 tff(27,plain,
% 3.84/2.68 (iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.84/2.68 inference(unit_resolution,[status(thm)],[26, 25])).
% 3.84/2.68 tff(28,plain,
% 3.84/2.68 (?[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> ?[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 3.84/2.68 inference(rewrite,[status(thm)],[])).
% 3.84/2.68 tff(29,plain,
% 3.84/2.68 (^[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1))), ((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2))), ((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2)))), (((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x))), (((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x)))), ((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4))), ((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4)))), (((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y))), (((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y)))), ((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6))), ((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6)))), (((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y))), (((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y)))), ((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil))), ((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil)))), (((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3))), (((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3)))), ((((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5))), ((((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5)))), (((((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> ((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5)) & iext(uri_rdf_rest, X2, uri_rdf_nil)))), rewrite(((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5) & iext(uri_rdf_rest, X2, uri_rdf_nil))), (((((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5) & iext(uri_rdf_rest, X2, uri_rdf_nil))))),
% 3.85/2.69 inference(bind,[status(th)],[])).
% 3.85/2.69 tff(30,plain,
% 3.85/2.69 (?[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : ((((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> ?[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 3.85/2.69 inference(quant_intro,[status(thm)],[29])).
% 3.85/2.69 tff(31,axiom,(?[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : ((((((((((((iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x)) & iext(uri_rdf_first, X0, X1)) & iext(uri_rdf_rest, X0, X2)) & iext(uri_rdf_first, X3, uri_ex_x)) & iext(uri_rdf_rest, X3, X4)) & iext(uri_owl_complementOf, X5, uri_ex_y)) & iext(uri_owl_complementOf, uri_ex_c1, X6)) & iext(uri_rdf_first, X4, uri_ex_y)) & iext(uri_rdf_rest, X4, uri_rdf_nil)) & iext(uri_owl_unionOf, X6, X3)) & iext(uri_rdf_first, X2, X5)) & iext(uri_rdf_rest, X2, uri_rdf_nil))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','premise_rdfbased_sem_bool_demorgan')).
% 3.85/2.69 tff(32,plain,
% 3.85/2.69 (?[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[31, 30])).
% 3.85/2.69 tff(33,plain,
% 3.85/2.69 (?[X1: $i, X4: $i, X0: $i, X2: $i, X5: $i, X3: $i, X6: $i] : (iext(uri_owl_intersectionOf, uri_ex_c2, X0) & iext(uri_owl_complementOf, X1, uri_ex_x) & iext(uri_rdf_first, X0, X1) & iext(uri_rdf_rest, X0, X2) & iext(uri_rdf_first, X3, uri_ex_x) & iext(uri_rdf_rest, X3, X4) & iext(uri_owl_complementOf, X5, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6) & iext(uri_rdf_first, X4, uri_ex_y) & iext(uri_rdf_rest, X4, uri_rdf_nil) & iext(uri_owl_unionOf, X6, X3) & iext(uri_rdf_first, X2, X5) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[32, 28])).
% 3.85/2.69 tff(34,plain,(
% 3.85/2.69 iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) & iext(uri_owl_complementOf, X1!146, uri_ex_x) & iext(uri_rdf_first, X0!144, X1!146) & iext(uri_rdf_rest, X0!144, X2!143) & iext(uri_rdf_first, X3!141, uri_ex_x) & iext(uri_rdf_rest, X3!141, X4!145) & iext(uri_owl_complementOf, X5!142, uri_ex_y) & iext(uri_owl_complementOf, uri_ex_c1, X6!140) & iext(uri_rdf_first, X4!145, uri_ex_y) & iext(uri_rdf_rest, X4!145, uri_rdf_nil) & iext(uri_owl_unionOf, X6!140, X3!141) & iext(uri_rdf_first, X2!143, X5!142) & iext(uri_rdf_rest, X2!143, uri_rdf_nil)),
% 3.85/2.69 inference(skolemize,[status(sab)],[33])).
% 3.85/2.69 tff(35,plain,
% 3.85/2.69 (iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)),
% 3.85/2.69 inference(and_elim,[status(thm)],[34])).
% 3.85/2.69 tff(36,plain,
% 3.85/2.69 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))) <=> ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))))),
% 3.85/2.69 inference(bind,[status(th)],[])).
% 3.85/2.69 tff(37,plain,
% 3.85/2.69 (![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 3.85/2.69 inference(quant_intro,[status(thm)],[36])).
% 3.85/2.69 tff(38,plain,
% 3.85/2.69 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))))),
% 3.85/2.69 inference(bind,[status(th)],[])).
% 3.85/2.69 tff(39,plain,
% 3.85/2.69 (![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 3.85/2.69 inference(quant_intro,[status(thm)],[38])).
% 3.85/2.69 tff(40,plain,
% 3.85/2.69 (![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 3.85/2.69 inference(rewrite,[status(thm)],[])).
% 3.85/2.69 tff(41,plain,
% 3.85/2.69 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_intersectionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))))),
% 3.85/2.69 inference(bind,[status(th)],[])).
% 3.85/2.69 tff(42,plain,
% 3.85/2.69 (![X: $i, Y: $i] : (iext(uri_owl_intersectionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 3.85/2.69 inference(quant_intro,[status(thm)],[41])).
% 3.85/2.69 tff(43,axiom,(![X: $i, Y: $i] : (iext(uri_owl_intersectionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_prop_intersectionof_ext')).
% 3.85/2.69 tff(44,plain,
% 3.85/2.69 (![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[43, 42])).
% 3.85/2.69 tff(45,plain,
% 3.85/2.69 (![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[44, 40])).
% 3.85/2.69 tff(46,plain,(
% 3.85/2.69 ![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 3.85/2.69 inference(skolemize,[status(sab)],[45])).
% 3.85/2.69 tff(47,plain,
% 3.85/2.69 (![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[46, 39])).
% 3.85/2.69 tff(48,plain,
% 3.85/2.69 (![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[47, 37])).
% 3.85/2.69 tff(49,plain,
% 3.85/2.69 (((~![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!144)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!144)))))),
% 3.85/2.69 inference(rewrite,[status(thm)],[])).
% 3.85/2.69 tff(50,plain,
% 3.85/2.69 ((~![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!144)))))),
% 3.85/2.69 inference(quant_inst,[status(thm)],[])).
% 3.85/2.69 tff(51,plain,
% 3.85/2.69 ((~![X: $i, Y: $i] : ((~iext(uri_owl_intersectionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!144))))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[50, 49])).
% 3.85/2.69 tff(52,plain,
% 3.85/2.69 (~((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!144)))),
% 3.85/2.69 inference(unit_resolution,[status(thm)],[51, 48, 35])).
% 3.85/2.69 tff(53,plain,
% 3.85/2.69 (((~ic(uri_ex_c2)) | (~icext(uri_rdf_List, X0!144))) | ic(uri_ex_c2)),
% 3.85/2.69 inference(tautology,[status(thm)],[])).
% 3.85/2.69 tff(54,plain,
% 3.85/2.69 (ic(uri_ex_c2)),
% 3.85/2.69 inference(unit_resolution,[status(thm)],[53, 52])).
% 3.85/2.69 tff(55,plain,
% 3.85/2.69 (iext(uri_owl_complementOf, uri_ex_c1, X6!140)),
% 3.85/2.69 inference(and_elim,[status(thm)],[34])).
% 3.85/2.69 tff(56,plain,
% 3.85/2.69 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X))))) <=> ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X))))))),
% 3.85/2.69 inference(bind,[status(th)],[])).
% 3.85/2.69 tff(57,plain,
% 3.85/2.69 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 3.85/2.69 inference(quant_intro,[status(thm)],[56])).
% 3.85/2.69 tff(58,plain,
% 3.85/2.69 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y))) <=> ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X))))))),
% 3.85/2.69 inference(bind,[status(th)],[])).
% 3.85/2.69 tff(59,plain,
% 3.85/2.69 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 3.85/2.69 inference(quant_intro,[status(thm)],[58])).
% 3.85/2.69 tff(60,plain,
% 3.85/2.69 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 3.85/2.69 inference(rewrite,[status(thm)],[])).
% 3.85/2.69 tff(61,plain,
% 3.85/2.69 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_complementOf, X, Y) => (ic(X) & ic(Y))) <=> ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y))))),
% 3.85/2.69 inference(bind,[status(th)],[])).
% 3.85/2.69 tff(62,plain,
% 3.85/2.69 (![X: $i, Y: $i] : (iext(uri_owl_complementOf, X, Y) => (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 3.85/2.69 inference(quant_intro,[status(thm)],[61])).
% 3.85/2.69 tff(63,axiom,(![X: $i, Y: $i] : (iext(uri_owl_complementOf, X, Y) => (ic(X) & ic(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_prop_complementof_ext')).
% 3.85/2.69 tff(64,plain,
% 3.85/2.69 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[63, 62])).
% 3.85/2.69 tff(65,plain,
% 3.85/2.69 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[64, 60])).
% 3.85/2.69 tff(66,plain,(
% 3.85/2.69 ![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (ic(X) & ic(Y)))),
% 3.85/2.69 inference(skolemize,[status(sab)],[65])).
% 3.85/2.69 tff(67,plain,
% 3.85/2.69 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[66, 59])).
% 3.85/2.69 tff(68,plain,
% 3.85/2.69 (![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[67, 57])).
% 3.85/2.69 tff(69,plain,
% 3.85/2.69 (((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_complementOf, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_complementOf, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1)))))),
% 3.85/2.69 inference(rewrite,[status(thm)],[])).
% 3.85/2.69 tff(70,plain,
% 3.85/2.69 ((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_complementOf, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1)))))),
% 3.85/2.69 inference(quant_inst,[status(thm)],[])).
% 3.85/2.69 tff(71,plain,
% 3.85/2.69 ((~![X: $i, Y: $i] : ((~iext(uri_owl_complementOf, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_complementOf, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1))))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[70, 69])).
% 3.85/2.69 tff(72,plain,
% 3.85/2.69 (~((~ic(X6!140)) | (~ic(uri_ex_c1)))),
% 3.85/2.69 inference(unit_resolution,[status(thm)],[71, 68, 55])).
% 3.85/2.69 tff(73,plain,
% 3.85/2.69 (((~ic(X6!140)) | (~ic(uri_ex_c1))) | ic(uri_ex_c1)),
% 3.85/2.69 inference(tautology,[status(thm)],[])).
% 3.85/2.69 tff(74,plain,
% 3.85/2.69 (ic(uri_ex_c1)),
% 3.85/2.69 inference(unit_resolution,[status(thm)],[73, 72])).
% 3.85/2.69 tff(75,plain,
% 3.85/2.69 ((~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)) <=> (~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2))),
% 3.85/2.69 inference(rewrite,[status(thm)],[])).
% 3.85/2.69 tff(76,axiom,(~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conclusion_rdfbased_sem_bool_demorgan')).
% 3.85/2.69 tff(77,plain,
% 3.85/2.69 (~iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2)),
% 3.85/2.70 inference(modus_ponens,[status(thm)],[76, 75])).
% 3.85/2.70 tff(78,plain,
% 3.85/2.70 ((~(iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.85/2.70 inference(tautology,[status(thm)],[])).
% 3.85/2.70 tff(79,plain,
% 3.85/2.70 ((~(iext(uri_owl_equivalentClass, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.85/2.70 inference(unit_resolution,[status(thm)],[78, 77])).
% 3.85/2.70 tff(80,plain,
% 3.85/2.70 ((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.85/2.70 inference(unit_resolution,[status(thm)],[79, 74, 54, 27])).
% 3.85/2.70 tff(81,plain,
% 3.85/2.70 ((~((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))) | (~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.85/2.70 inference(tautology,[status(thm)],[])).
% 3.85/2.70 tff(82,plain,
% 3.85/2.70 ((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.85/2.70 inference(unit_resolution,[status(thm)],[81, 80])).
% 3.85/2.70 tff(83,plain,
% 3.85/2.70 (~icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.85/2.70 inference(unit_resolution,[status(thm)],[82, 1])).
% 3.85/2.70 tff(84,plain,
% 3.85/2.70 (iext(uri_rdf_rest, X2!143, uri_rdf_nil)),
% 3.85/2.70 inference(and_elim,[status(thm)],[34])).
% 3.85/2.70 tff(85,plain,
% 3.85/2.70 (iext(uri_rdf_first, X2!143, X5!142)),
% 3.85/2.70 inference(and_elim,[status(thm)],[34])).
% 3.85/2.70 tff(86,plain,
% 3.85/2.70 (iext(uri_rdf_rest, X0!144, X2!143)),
% 3.85/2.70 inference(and_elim,[status(thm)],[34])).
% 3.85/2.70 tff(87,plain,
% 3.85/2.70 (iext(uri_rdf_first, X0!144, X1!146)),
% 3.85/2.70 inference(and_elim,[status(thm)],[34])).
% 3.85/2.70 tff(88,plain,
% 3.85/2.70 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))) <=> (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X))))))))))))), (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X))))))))))))))), rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X))))))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))), (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))))),
% 3.85/2.70 inference(bind,[status(th)],[])).
% 3.85/2.70 tff(89,plain,
% 3.85/2.70 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))),
% 3.85/2.70 inference(quant_intro,[status(thm)],[88])).
% 3.85/2.70 tff(90,plain,
% 3.85/2.70 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : refl(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))))),
% 3.85/2.70 inference(bind,[status(th)],[])).
% 3.85/2.70 tff(91,plain,
% 3.85/2.70 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))),
% 3.85/2.70 inference(quant_intro,[status(thm)],[90])).
% 3.85/2.70 tff(92,plain,
% 3.85/2.70 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))))),
% 3.85/2.70 inference(bind,[status(th)],[])).
% 3.85/2.70 tff(93,plain,
% 3.85/2.70 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))),
% 3.85/2.70 inference(quant_intro,[status(thm)],[92])).
% 3.85/2.70 tff(94,plain,
% 3.85/2.70 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))),
% 3.85/2.70 inference(transitivity,[status(thm)],[93, 91])).
% 3.85/2.70 tff(95,plain,
% 3.85/2.70 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) <=> ((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))), trans(monotonicity(trans(monotonicity(rewrite((icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))) <=> (~((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))), (((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (~((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))), rewrite(((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (~((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))) <=> (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))), (((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))), ((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))), rewrite((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))), ((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))), ((((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))))) <=> (((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X))))))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))), rewrite((((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X))))))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))), ((((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))))) <=> (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))))) <=> (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))))), rewrite((((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))))),
% 3.85/2.70 inference(bind,[status(th)],[])).
% 3.85/2.70 tff(96,plain,
% 3.85/2.70 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))),
% 3.85/2.70 inference(quant_intro,[status(thm)],[95])).
% 3.85/2.70 tff(97,plain,
% 3.85/2.70 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))))))),
% 3.85/2.70 inference(bind,[status(th)],[])).
% 3.85/2.70 tff(98,plain,
% 3.85/2.70 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))))))),
% 3.87/2.70 inference(quant_intro,[status(thm)],[97])).
% 3.87/2.70 tff(99,plain,
% 3.87/2.70 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))),
% 3.87/2.70 inference(rewrite,[status(thm)],[])).
% 3.87/2.70 tff(100,plain,
% 3.87/2.70 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite((iext(uri_owl_intersectionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) <=> (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X)))))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X)))))) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X)))))))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))))),
% 3.87/2.70 inference(bind,[status(th)],[])).
% 3.87/2.70 tff(101,plain,
% 3.87/2.70 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))),
% 3.87/2.70 inference(quant_intro,[status(thm)],[100])).
% 3.87/2.70 tff(102,axiom,(![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_bool_intersectionof_class_002')).
% 3.87/2.70 tff(103,plain,
% 3.87/2.70 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))),
% 3.87/2.70 inference(modus_ponens,[status(thm)],[102, 101])).
% 3.87/2.70 tff(104,plain,
% 3.87/2.70 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))),
% 3.87/2.70 inference(modus_ponens,[status(thm)],[103, 99])).
% 3.87/2.70 tff(105,plain,(
% 3.87/2.70 ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))),
% 3.87/2.70 inference(skolemize,[status(sab)],[104])).
% 3.87/2.70 tff(106,plain,
% 3.87/2.70 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))))))),
% 3.87/2.70 inference(modus_ponens,[status(thm)],[105, 98])).
% 3.87/2.70 tff(107,plain,
% 3.87/2.70 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))),
% 3.87/2.70 inference(modus_ponens,[status(thm)],[106, 96])).
% 3.87/2.70 tff(108,plain,
% 3.87/2.70 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))),
% 3.87/2.71 inference(modus_ponens,[status(thm)],[107, 94])).
% 3.87/2.71 tff(109,plain,
% 3.87/2.71 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))),
% 3.87/2.71 inference(modus_ponens,[status(thm)],[108, 89])).
% 3.87/2.71 tff(110,plain,
% 3.87/2.71 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | ((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | (~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))))))))),
% 3.87/2.71 inference(rewrite,[status(thm)],[])).
% 3.87/2.71 tff(111,plain,
% 3.87/2.71 (((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X))))))))))))) <=> ((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))))))))),
% 3.87/2.71 inference(rewrite,[status(thm)],[])).
% 3.87/2.71 tff(112,plain,
% 3.87/2.71 ((~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))))))) <=> (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X))))))))))))),
% 3.87/2.71 inference(rewrite,[status(thm)],[])).
% 3.87/2.71 tff(113,plain,
% 3.87/2.71 (((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X))))))))))))) <=> ((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))))))))),
% 3.87/2.71 inference(monotonicity,[status(thm)],[112])).
% 3.87/2.71 tff(114,plain,
% 3.87/2.71 (((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X))))))))))))) <=> ((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))))))))),
% 3.87/2.71 inference(transitivity,[status(thm)],[113, 111])).
% 3.87/2.71 tff(115,plain,
% 3.87/2.71 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | ((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | ((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X))))))))))))))),
% 3.87/2.71 inference(monotonicity,[status(thm)],[114])).
% 3.87/2.71 tff(116,plain,
% 3.87/2.71 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | ((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | (~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))))))))),
% 3.87/2.71 inference(transitivity,[status(thm)],[115, 110])).
% 3.87/2.71 tff(117,plain,
% 3.87/2.71 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | ((~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(X5!142)) | (~ic(X1!146)) | (~ic(uri_ex_c2)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))))))))),
% 3.87/2.71 inference(quant_inst,[status(thm)],[])).
% 3.87/2.71 tff(118,plain,
% 3.87/2.71 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | (~iext(uri_rdf_first, X0!144, X1!146)) | (~iext(uri_rdf_rest, X0!144, X2!143)) | (~iext(uri_rdf_first, X2!143, X5!142)) | (~iext(uri_rdf_rest, X2!143, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X))))))))))))),
% 3.87/2.71 inference(modus_ponens,[status(thm)],[117, 116])).
% 3.88/2.71 tff(119,plain,
% 3.88/2.71 (~((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))))))),
% 3.88/2.71 inference(unit_resolution,[status(thm)],[118, 109, 87, 86, 85, 84])).
% 3.88/2.71 tff(120,plain,
% 3.88/2.71 (((~(iext(uri_owl_intersectionOf, uri_ex_c2, X0!144) | (~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (icext(uri_ex_c2, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2)) <=> ((~icext(X1!146, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))) | (~icext(X5!142, tptp_fun_X_3(X5!142, X1!146, uri_ex_c2))))))) | (~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X))))))))))) | ((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))))),
% 3.88/2.71 inference(tautology,[status(thm)],[])).
% 3.88/2.71 tff(121,plain,
% 3.88/2.71 ((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X))))))))),
% 3.88/2.71 inference(unit_resolution,[status(thm)],[120, 119])).
% 3.88/2.71 tff(122,plain,
% 3.88/2.71 ((~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))))) | (~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X))))))))),
% 3.88/2.71 inference(tautology,[status(thm)],[])).
% 3.88/2.71 tff(123,plain,
% 3.88/2.71 ((~((~iext(uri_owl_intersectionOf, uri_ex_c2, X0!144)) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))))) | (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X))))))))),
% 3.88/2.71 inference(unit_resolution,[status(thm)],[122, 35])).
% 3.88/2.71 tff(124,plain,
% 3.88/2.71 (~((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))))),
% 3.88/2.71 inference(unit_resolution,[status(thm)],[123, 121])).
% 3.88/2.71 tff(125,plain,
% 3.88/2.71 (((~ic(uri_ex_c2)) | (~ic(X1!146)) | (~ic(X5!142)) | (~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X))))))) | ![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))),
% 3.88/2.71 inference(tautology,[status(thm)],[])).
% 3.88/2.71 tff(126,plain,
% 3.88/2.71 (![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))),
% 3.88/2.71 inference(unit_resolution,[status(thm)],[125, 124])).
% 3.88/2.71 tff(127,plain,
% 3.88/2.71 ((~![X: $i] : (icext(uri_ex_c2, X) <=> (~((~icext(X5!142, X)) | (~icext(X1!146, X)))))) | (icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))))),
% 3.88/2.71 inference(quant_inst,[status(thm)],[])).
% 3.88/2.71 tff(128,plain,
% 3.88/2.71 (icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))),
% 3.88/2.71 inference(unit_resolution,[status(thm)],[127, 126])).
% 3.88/2.71 tff(129,plain,
% 3.88/2.71 ((~(icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))))) | icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | ((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 3.88/2.72 inference(tautology,[status(thm)],[])).
% 3.88/2.72 tff(130,plain,
% 3.88/2.72 (icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | ((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[129, 128])).
% 3.88/2.72 tff(131,plain,
% 3.88/2.72 ((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[130, 83])).
% 3.88/2.72 tff(132,plain,
% 3.88/2.72 (iext(uri_owl_complementOf, X5!142, uri_ex_y)),
% 3.88/2.72 inference(and_elim,[status(thm)],[34])).
% 3.88/2.72 tff(133,plain,
% 3.88/2.72 (^[Z: $i, C: $i] : refl(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(134,plain,
% 3.88/2.72 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[133])).
% 3.88/2.72 tff(135,plain,
% 3.88/2.72 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(136,plain,
% 3.88/2.72 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[135])).
% 3.88/2.72 tff(137,plain,
% 3.88/2.72 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 3.88/2.72 inference(transitivity,[status(thm)],[136, 134])).
% 3.88/2.72 tff(138,plain,
% 3.88/2.72 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(139,plain,
% 3.88/2.72 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[138])).
% 3.88/2.72 tff(140,plain,
% 3.88/2.72 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(141,plain,
% 3.88/2.72 (^[Z: $i, C: $i] : trans(monotonicity(rewrite(((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))) <=> (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))), ((iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> (iext(uri_owl_complementOf, Z, C) => (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))), rewrite((iext(uri_owl_complementOf, Z, C) => (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))), ((iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(142,plain,
% 3.88/2.72 (![Z: $i, C: $i] : (iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[141])).
% 3.88/2.72 tff(143,axiom,(![Z: $i, C: $i] : (iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_bool_complementof_class')).
% 3.88/2.72 tff(144,plain,
% 3.88/2.72 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[143, 142])).
% 3.88/2.72 tff(145,plain,
% 3.88/2.72 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[144, 140])).
% 3.88/2.72 tff(146,plain,(
% 3.88/2.72 ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))),
% 3.88/2.72 inference(skolemize,[status(sab)],[145])).
% 3.88/2.72 tff(147,plain,
% 3.88/2.72 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[146, 139])).
% 3.88/2.72 tff(148,plain,
% 3.88/2.72 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[147, 137])).
% 3.88/2.72 tff(149,plain,
% 3.88/2.72 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, X5!142, uri_ex_y)) | (~((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | (~iext(uri_owl_complementOf, X5!142, uri_ex_y)) | (~((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X)))))))),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(150,plain,
% 3.88/2.72 (((~iext(uri_owl_complementOf, X5!142, uri_ex_y)) | (~((~ic(uri_ex_y)) | (~ic(X5!142)) | (~![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X))))))) <=> ((~iext(uri_owl_complementOf, X5!142, uri_ex_y)) | (~((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X)))))))),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(151,plain,
% 3.88/2.72 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, X5!142, uri_ex_y)) | (~((~ic(uri_ex_y)) | (~ic(X5!142)) | (~![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, X5!142, uri_ex_y)) | (~((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X))))))))),
% 3.88/2.72 inference(monotonicity,[status(thm)],[150])).
% 3.88/2.72 tff(152,plain,
% 3.88/2.72 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, X5!142, uri_ex_y)) | (~((~ic(uri_ex_y)) | (~ic(X5!142)) | (~![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | (~iext(uri_owl_complementOf, X5!142, uri_ex_y)) | (~((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X)))))))),
% 3.88/2.72 inference(transitivity,[status(thm)],[151, 149])).
% 3.88/2.72 tff(153,plain,
% 3.88/2.72 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, X5!142, uri_ex_y)) | (~((~ic(uri_ex_y)) | (~ic(X5!142)) | (~![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X)))))))),
% 3.88/2.72 inference(quant_inst,[status(thm)],[])).
% 3.88/2.72 tff(154,plain,
% 3.88/2.72 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | (~iext(uri_owl_complementOf, X5!142, uri_ex_y)) | (~((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X))))))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[153, 152])).
% 3.88/2.72 tff(155,plain,
% 3.88/2.72 (~((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X)))))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[154, 148, 132])).
% 3.88/2.72 tff(156,plain,
% 3.88/2.72 (((~ic(X5!142)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X))))) | ![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X)))),
% 3.88/2.72 inference(tautology,[status(thm)],[])).
% 3.88/2.72 tff(157,plain,
% 3.88/2.72 (![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X)))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[156, 155])).
% 3.88/2.72 tff(158,plain,
% 3.88/2.72 ((~![X: $i] : (icext(X5!142, X) <=> (~icext(uri_ex_y, X)))) | (icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 3.88/2.72 inference(quant_inst,[status(thm)],[])).
% 3.88/2.72 tff(159,plain,
% 3.88/2.72 (icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[158, 157])).
% 3.88/2.72 tff(160,plain,
% 3.88/2.72 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (~icext(X6!140, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | (~iext(uri_owl_complementOf, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (~icext(X6!140, X)))))))),
% 3.88/2.72 inference(rewrite,[status(thm)],[])).
% 3.88/2.72 tff(161,plain,
% 3.88/2.72 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (~icext(X6!140, X)))))))),
% 3.88/2.72 inference(quant_inst,[status(thm)],[])).
% 3.88/2.72 tff(162,plain,
% 3.88/2.72 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | (~iext(uri_owl_complementOf, uri_ex_c1, X6!140)) | (~((~ic(X6!140)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (~icext(X6!140, X))))))),
% 3.88/2.72 inference(modus_ponens,[status(thm)],[161, 160])).
% 3.88/2.72 tff(163,plain,
% 3.88/2.72 (~((~ic(X6!140)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (~icext(X6!140, X)))))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[162, 148, 55])).
% 3.88/2.72 tff(164,plain,
% 3.88/2.72 (((~ic(X6!140)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c1, X) <=> (~icext(X6!140, X))))) | ![X: $i] : (icext(uri_ex_c1, X) <=> (~icext(X6!140, X)))),
% 3.88/2.72 inference(tautology,[status(thm)],[])).
% 3.88/2.72 tff(165,plain,
% 3.88/2.72 (![X: $i] : (icext(uri_ex_c1, X) <=> (~icext(X6!140, X)))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[164, 163])).
% 3.88/2.72 tff(166,plain,
% 3.88/2.72 ((~![X: $i] : (icext(uri_ex_c1, X) <=> (~icext(X6!140, X)))) | (icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 3.88/2.72 inference(quant_inst,[status(thm)],[])).
% 3.88/2.72 tff(167,plain,
% 3.88/2.72 (icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[166, 165])).
% 3.88/2.72 tff(168,plain,
% 3.88/2.72 ((~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.72 inference(tautology,[status(thm)],[])).
% 3.88/2.72 tff(169,plain,
% 3.88/2.72 ((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[168, 167])).
% 3.88/2.72 tff(170,plain,
% 3.88/2.72 (~icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.72 inference(unit_resolution,[status(thm)],[169, 1])).
% 3.88/2.72 tff(171,plain,
% 3.88/2.72 (iext(uri_rdf_rest, X4!145, uri_rdf_nil)),
% 3.88/2.72 inference(and_elim,[status(thm)],[34])).
% 3.88/2.72 tff(172,plain,
% 3.88/2.72 (iext(uri_rdf_first, X4!145, uri_ex_y)),
% 3.88/2.72 inference(and_elim,[status(thm)],[34])).
% 3.88/2.72 tff(173,plain,
% 3.88/2.72 (iext(uri_rdf_rest, X3!141, X4!145)),
% 3.88/2.72 inference(and_elim,[status(thm)],[34])).
% 3.88/2.72 tff(174,plain,
% 3.88/2.72 (iext(uri_rdf_first, X3!141, uri_ex_x)),
% 3.88/2.72 inference(and_elim,[status(thm)],[34])).
% 3.88/2.72 tff(175,plain,
% 3.88/2.72 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))) <=> (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))))), (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))))))), rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))), (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(176,plain,
% 3.88/2.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[175])).
% 3.88/2.72 tff(177,plain,
% 3.88/2.72 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : refl(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(178,plain,
% 3.88/2.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[177])).
% 3.88/2.72 tff(179,plain,
% 3.88/2.72 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 3.88/2.72 inference(bind,[status(th)],[])).
% 3.88/2.72 tff(180,plain,
% 3.88/2.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 3.88/2.72 inference(quant_intro,[status(thm)],[179])).
% 3.88/2.72 tff(181,plain,
% 3.88/2.72 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 3.88/2.72 inference(transitivity,[status(thm)],[180, 178])).
% 3.88/2.72 tff(182,plain,
% 3.88/2.72 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) <=> ((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))), rewrite((iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))), ((((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))), rewrite((((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))), ((((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))), rewrite((((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))))),
% 3.88/2.73 inference(bind,[status(th)],[])).
% 3.88/2.73 tff(183,plain,
% 3.88/2.73 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 3.88/2.73 inference(quant_intro,[status(thm)],[182])).
% 3.88/2.73 tff(184,plain,
% 3.88/2.73 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))),
% 3.88/2.73 inference(bind,[status(th)],[])).
% 3.88/2.73 tff(185,plain,
% 3.88/2.73 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))),
% 3.88/2.73 inference(quant_intro,[status(thm)],[184])).
% 3.88/2.73 tff(186,plain,
% 3.88/2.73 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 3.88/2.73 inference(rewrite,[status(thm)],[])).
% 3.88/2.73 tff(187,plain,
% 3.88/2.73 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite((iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X))))) <=> (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X)))))) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))),
% 3.88/2.73 inference(bind,[status(th)],[])).
% 3.88/2.73 tff(188,plain,
% 3.88/2.73 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 3.88/2.73 inference(quant_intro,[status(thm)],[187])).
% 3.88/2.73 tff(189,axiom,(![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_bool_unionof_class_002')).
% 3.88/2.73 tff(190,plain,
% 3.88/2.73 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 3.88/2.73 inference(modus_ponens,[status(thm)],[189, 188])).
% 3.88/2.73 tff(191,plain,
% 3.88/2.73 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 3.88/2.73 inference(modus_ponens,[status(thm)],[190, 186])).
% 3.88/2.73 tff(192,plain,(
% 3.88/2.73 ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 3.88/2.73 inference(skolemize,[status(sab)],[191])).
% 3.88/2.73 tff(193,plain,
% 3.88/2.73 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))),
% 3.88/2.73 inference(modus_ponens,[status(thm)],[192, 185])).
% 3.88/2.73 tff(194,plain,
% 3.88/2.73 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 3.88/2.73 inference(modus_ponens,[status(thm)],[193, 183])).
% 3.88/2.73 tff(195,plain,
% 3.88/2.73 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 3.88/2.73 inference(modus_ponens,[status(thm)],[194, 181])).
% 3.88/2.73 tff(196,plain,
% 3.88/2.73 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))),
% 3.88/2.73 inference(modus_ponens,[status(thm)],[195, 176])).
% 3.88/2.73 tff(197,plain,
% 3.88/2.73 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))))))),
% 3.88/2.73 inference(rewrite,[status(thm)],[])).
% 3.88/2.73 tff(198,plain,
% 3.88/2.73 (((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))))))) <=> ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))))))),
% 3.88/2.73 inference(rewrite,[status(thm)],[])).
% 3.88/2.73 tff(199,plain,
% 3.88/2.73 ((~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_y, X) | icext(uri_ex_x, X)))))))))) <=> (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))))))),
% 3.88/2.73 inference(rewrite,[status(thm)],[])).
% 3.88/2.73 tff(200,plain,
% 3.88/2.73 (((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_y, X) | icext(uri_ex_x, X))))))))))) <=> ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))))))),
% 3.88/2.73 inference(monotonicity,[status(thm)],[199])).
% 3.88/2.73 tff(201,plain,
% 3.88/2.73 (((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_y, X) | icext(uri_ex_x, X))))))))))) <=> ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))))))),
% 3.88/2.74 inference(transitivity,[status(thm)],[200, 198])).
% 3.88/2.74 tff(202,plain,
% 3.88/2.74 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_y, X) | icext(uri_ex_x, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))))))))),
% 3.88/2.74 inference(monotonicity,[status(thm)],[201])).
% 3.88/2.74 tff(203,plain,
% 3.88/2.74 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_y, X) | icext(uri_ex_x, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))))))),
% 3.88/2.74 inference(transitivity,[status(thm)],[202, 197])).
% 3.88/2.74 tff(204,plain,
% 3.88/2.74 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_y)) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_y, X) | icext(uri_ex_x, X)))))))))))),
% 3.88/2.74 inference(quant_inst,[status(thm)],[])).
% 3.88/2.74 tff(205,plain,
% 3.88/2.74 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_6(C2, C1, Z))) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, X3!141, uri_ex_x)) | (~iext(uri_rdf_rest, X3!141, X4!145)) | (~iext(uri_rdf_first, X4!145, uri_ex_y)) | (~iext(uri_rdf_rest, X4!145, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))))))),
% 3.88/2.74 inference(modus_ponens,[status(thm)],[204, 203])).
% 3.88/2.74 tff(206,plain,
% 3.88/2.74 (~((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[205, 196, 174, 173, 172, 171])).
% 3.88/2.74 tff(207,plain,
% 3.88/2.74 (((~(iext(uri_owl_unionOf, X6!140, X3!141) | (~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | ((~icext(X6!140, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140))) <=> (icext(uri_ex_y, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)) | icext(uri_ex_x, tptp_fun_X_6(uri_ex_y, uri_ex_x, X6!140)))))) | (~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))))) | ((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(208,plain,
% 3.88/2.74 ((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[207, 206])).
% 3.88/2.74 tff(209,plain,
% 3.88/2.74 (iext(uri_owl_unionOf, X6!140, X3!141)),
% 3.88/2.74 inference(and_elim,[status(thm)],[34])).
% 3.88/2.74 tff(210,plain,
% 3.88/2.74 ((~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))) | (~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(211,plain,
% 3.88/2.74 ((~((~iext(uri_owl_unionOf, X6!140, X3!141)) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))))) | (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[210, 209])).
% 3.88/2.74 tff(212,plain,
% 3.88/2.74 (~((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[211, 208])).
% 3.88/2.74 tff(213,plain,
% 3.88/2.74 (((~ic(uri_ex_x)) | (~ic(X6!140)) | (~ic(uri_ex_y)) | (~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X))))) | ![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(214,plain,
% 3.88/2.74 (![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[213, 212])).
% 3.88/2.74 tff(215,plain,
% 3.88/2.74 ((~![X: $i] : (icext(X6!140, X) <=> (icext(uri_ex_x, X) | icext(uri_ex_y, X)))) | (icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 3.88/2.74 inference(quant_inst,[status(thm)],[])).
% 3.88/2.74 tff(216,plain,
% 3.88/2.74 (icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[215, 214])).
% 3.88/2.74 tff(217,plain,
% 3.88/2.74 ((~(icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | (~(icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(218,plain,
% 3.88/2.74 (icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | (~(icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[217, 216])).
% 3.88/2.74 tff(219,plain,
% 3.88/2.74 (~(icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[218, 170])).
% 3.88/2.74 tff(220,plain,
% 3.88/2.74 ((icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(221,plain,
% 3.88/2.74 (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[220, 219])).
% 3.88/2.74 tff(222,plain,
% 3.88/2.74 ((~(icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(223,plain,
% 3.88/2.74 ((~(icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[222, 221])).
% 3.88/2.74 tff(224,plain,
% 3.88/2.74 (icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[223, 159])).
% 3.88/2.74 tff(225,plain,
% 3.88/2.74 (iext(uri_owl_complementOf, X1!146, uri_ex_x)),
% 3.88/2.74 inference(and_elim,[status(thm)],[34])).
% 3.88/2.74 tff(226,plain,
% 3.88/2.74 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, X1!146, uri_ex_x)) | (~((~ic(uri_ex_x)) | (~ic(X1!146)) | (~![X: $i] : (icext(X1!146, X) <=> (~icext(uri_ex_x, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | (~iext(uri_owl_complementOf, X1!146, uri_ex_x)) | (~((~ic(uri_ex_x)) | (~ic(X1!146)) | (~![X: $i] : (icext(X1!146, X) <=> (~icext(uri_ex_x, X)))))))),
% 3.88/2.74 inference(rewrite,[status(thm)],[])).
% 3.88/2.74 tff(227,plain,
% 3.88/2.74 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, X1!146, uri_ex_x)) | (~((~ic(uri_ex_x)) | (~ic(X1!146)) | (~![X: $i] : (icext(X1!146, X) <=> (~icext(uri_ex_x, X)))))))),
% 3.88/2.74 inference(quant_inst,[status(thm)],[])).
% 3.88/2.74 tff(228,plain,
% 3.88/2.74 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | (~iext(uri_owl_complementOf, X1!146, uri_ex_x)) | (~((~ic(uri_ex_x)) | (~ic(X1!146)) | (~![X: $i] : (icext(X1!146, X) <=> (~icext(uri_ex_x, X))))))),
% 3.88/2.74 inference(modus_ponens,[status(thm)],[227, 226])).
% 3.88/2.74 tff(229,plain,
% 3.88/2.74 (~((~ic(uri_ex_x)) | (~ic(X1!146)) | (~![X: $i] : (icext(X1!146, X) <=> (~icext(uri_ex_x, X)))))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[228, 148, 225])).
% 3.88/2.74 tff(230,plain,
% 3.88/2.74 (((~ic(uri_ex_x)) | (~ic(X1!146)) | (~![X: $i] : (icext(X1!146, X) <=> (~icext(uri_ex_x, X))))) | ![X: $i] : (icext(X1!146, X) <=> (~icext(uri_ex_x, X)))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(231,plain,
% 3.88/2.74 (![X: $i] : (icext(X1!146, X) <=> (~icext(uri_ex_x, X)))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[230, 229])).
% 3.88/2.74 tff(232,plain,
% 3.88/2.74 ((~![X: $i] : (icext(X1!146, X) <=> (~icext(uri_ex_x, X)))) | (icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 3.88/2.74 inference(quant_inst,[status(thm)],[])).
% 3.88/2.74 tff(233,plain,
% 3.88/2.74 (icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[232, 231])).
% 3.88/2.74 tff(234,plain,
% 3.88/2.74 ((icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(235,plain,
% 3.88/2.74 (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[234, 219])).
% 3.88/2.74 tff(236,plain,
% 3.88/2.74 ((~(icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(237,plain,
% 3.88/2.74 ((~(icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[236, 235])).
% 3.88/2.74 tff(238,plain,
% 3.88/2.74 (icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[237, 233])).
% 3.88/2.74 tff(239,plain,
% 3.88/2.74 ((~((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(240,plain,
% 3.88/2.74 ($false),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[239, 238, 224, 131])).
% 3.88/2.74 tff(241,plain,(~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))), inference(lemma,lemma(discharge,[]))).
% 3.88/2.74 tff(242,plain,
% 3.88/2.74 ((~(icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(243,plain,
% 3.88/2.74 (icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[242, 167])).
% 3.88/2.74 tff(244,plain,
% 3.88/2.74 (icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[243, 241])).
% 3.88/2.74 tff(245,plain,
% 3.88/2.74 ((~(icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(246,plain,
% 3.88/2.74 ((~icext(X6!140, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[245, 216])).
% 3.88/2.74 tff(247,plain,
% 3.88/2.74 (icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[246, 244])).
% 3.88/2.74 tff(248,plain,
% 3.88/2.74 ((~((~icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) <=> icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))) | icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(249,plain,
% 3.88/2.74 (icext(uri_ex_c1, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[248, 80])).
% 3.88/2.74 tff(250,plain,
% 3.88/2.74 (icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[249, 241])).
% 3.88/2.74 tff(251,plain,
% 3.88/2.74 ((~(icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))))) | (~icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(252,plain,
% 3.88/2.74 ((~icext(uri_ex_c2, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[251, 128])).
% 3.88/2.74 tff(253,plain,
% 3.88/2.74 (~((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[252, 250])).
% 3.88/2.74 tff(254,plain,
% 3.88/2.74 (((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))) | icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(tautology,[status(thm)],[])).
% 3.88/2.74 tff(255,plain,
% 3.88/2.74 (icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.74 inference(unit_resolution,[status(thm)],[254, 253])).
% 3.88/2.74 tff(256,plain,
% 3.88/2.74 ((~(icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.78 inference(tautology,[status(thm)],[])).
% 3.88/2.78 tff(257,plain,
% 3.88/2.78 ((~(icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.78 inference(unit_resolution,[status(thm)],[256, 255])).
% 3.88/2.78 tff(258,plain,
% 3.88/2.78 (~icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.78 inference(unit_resolution,[status(thm)],[257, 233])).
% 3.88/2.78 tff(259,plain,
% 3.88/2.78 (((~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(X1!146, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))) | icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.78 inference(tautology,[status(thm)],[])).
% 3.88/2.78 tff(260,plain,
% 3.88/2.78 (icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.78 inference(unit_resolution,[status(thm)],[259, 253])).
% 3.88/2.78 tff(261,plain,
% 3.88/2.78 ((~(icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.78 inference(tautology,[status(thm)],[])).
% 3.88/2.78 tff(262,plain,
% 3.88/2.78 ((~(icext(X5!142, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) <=> (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))))) | (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))),
% 3.88/2.78 inference(unit_resolution,[status(thm)],[261, 260])).
% 3.88/2.78 tff(263,plain,
% 3.88/2.78 (~icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.78 inference(unit_resolution,[status(thm)],[262, 159])).
% 3.88/2.78 tff(264,plain,
% 3.88/2.78 ((~(icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)))) | icext(uri_ex_x, tptp_fun_X_67(uri_ex_c2, uri_ex_c1)) | icext(uri_ex_y, tptp_fun_X_67(uri_ex_c2, uri_ex_c1))),
% 3.88/2.78 inference(tautology,[status(thm)],[])).
% 3.88/2.78 tff(265,plain,
% 3.88/2.78 ($false),
% 3.88/2.78 inference(unit_resolution,[status(thm)],[264, 263, 258, 247])).
% 3.88/2.78 % SZS output end Proof
%------------------------------------------------------------------------------