TSTP Solution File: SWB068+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB068+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 08:32:10 EDT 2022
% Result : Theorem 0.69s 0.72s
% Output : Proof 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWB068+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 20:17:35 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.69/0.72 % SZS status Theorem
% 0.69/0.72 % SZS output start Proof
% 0.69/0.72 tff(icext_type, type, (
% 0.69/0.72 icext: ( $i * $i ) > $o)).
% 0.69/0.72 tff(tptp_fun_Z_79_type, type, (
% 0.69/0.72 tptp_fun_Z_79: $i > $i)).
% 0.69/0.72 tff(tptp_fun_X2_141_type, type, (
% 0.69/0.72 tptp_fun_X2_141: $i)).
% 0.69/0.72 tff(uri_owl_AllDifferent_type, type, (
% 0.69/0.72 uri_owl_AllDifferent: $i)).
% 0.69/0.72 tff(iext_type, type, (
% 0.69/0.72 iext: ( $i * $i * $i ) > $o)).
% 0.69/0.72 tff(uri_rdf_type_type, type, (
% 0.69/0.72 uri_rdf_type: $i)).
% 0.69/0.72 tff(uri_owl_members_type, type, (
% 0.69/0.72 uri_owl_members: $i)).
% 0.69/0.72 tff(uri_ex_w2_type, type, (
% 0.69/0.72 uri_ex_w2: $i)).
% 0.69/0.72 tff(uri_ex_w1_type, type, (
% 0.69/0.72 uri_ex_w1: $i)).
% 0.69/0.72 tff(uri_owl_differentFrom_type, type, (
% 0.69/0.72 uri_owl_differentFrom: $i)).
% 0.69/0.72 tff(tptp_fun_X1_140_type, type, (
% 0.69/0.72 tptp_fun_X1_140: $i)).
% 0.69/0.72 tff(uri_rdf_rest_type, type, (
% 0.69/0.72 uri_rdf_rest: $i)).
% 0.69/0.72 tff(uri_rdf_first_type, type, (
% 0.69/0.72 uri_rdf_first: $i)).
% 0.69/0.72 tff(tptp_fun_X0_142_type, type, (
% 0.69/0.72 tptp_fun_X0_142: $i)).
% 0.69/0.72 tff(uri_ex_w3_type, type, (
% 0.69/0.72 uri_ex_w3: $i)).
% 0.69/0.72 tff(uri_rdf_nil_type, type, (
% 0.69/0.72 uri_rdf_nil: $i)).
% 0.69/0.72 tff(1,plain,
% 0.69/0.72 (^[X: $i, C: $i] : refl((iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> (iext(uri_rdf_type, X, C) <=> icext(C, X)))),
% 0.69/0.72 inference(bind,[status(th)],[])).
% 0.69/0.72 tff(2,plain,
% 0.69/0.72 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.69/0.72 inference(quant_intro,[status(thm)],[1])).
% 0.69/0.72 tff(3,plain,
% 0.69/0.72 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X)) <=> ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(4,axiom,(![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','rdfs_cext_def')).
% 0.69/0.72 tff(5,plain,
% 0.69/0.72 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.69/0.72 tff(6,plain,(
% 0.69/0.72 ![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.69/0.72 inference(skolemize,[status(sab)],[5])).
% 0.69/0.72 tff(7,plain,
% 0.69/0.72 (![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.69/0.72 tff(8,plain,
% 0.69/0.72 ((~![X: $i, C: $i] : (iext(uri_rdf_type, X, C) <=> icext(C, X))) | (iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent) <=> icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141)))),
% 0.69/0.72 inference(quant_inst,[status(thm)],[])).
% 0.69/0.72 tff(9,plain,
% 0.69/0.72 (iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent) <=> icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.69/0.72 tff(10,plain,
% 0.69/0.72 (^[X: $i, Y: $i] : refl((iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y))) <=> (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y))))),
% 0.69/0.72 inference(bind,[status(th)],[])).
% 0.69/0.72 tff(11,plain,
% 0.69/0.72 (![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y))) <=> ![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))),
% 0.69/0.72 inference(quant_intro,[status(thm)],[10])).
% 0.69/0.72 tff(12,plain,
% 0.69/0.72 (![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y))) <=> ![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(13,axiom,(![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_eqdis_differentfrom')).
% 0.69/0.72 tff(14,plain,
% 0.69/0.72 (![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.69/0.72 tff(15,plain,(
% 0.69/0.72 ![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))),
% 0.69/0.72 inference(skolemize,[status(sab)],[14])).
% 0.69/0.72 tff(16,plain,
% 0.69/0.72 (![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))),
% 0.69/0.72 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.69/0.72 tff(17,plain,
% 0.69/0.72 ((~![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))) | (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) <=> (~(uri_ex_w1 = uri_ex_w2)))),
% 0.69/0.72 inference(quant_inst,[status(thm)],[])).
% 0.69/0.72 tff(18,plain,
% 0.69/0.72 (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) <=> (~(uri_ex_w1 = uri_ex_w2))),
% 0.69/0.72 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.69/0.72 tff(19,plain,
% 0.69/0.72 (?[X0: $i, X2: $i, X1: $i] : (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0) & iext(uri_rdf_first, X2, uri_ex_w1) & iext(uri_rdf_rest, X2, X1)) <=> ?[X0: $i, X2: $i, X1: $i] : (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0) & iext(uri_rdf_first, X2, uri_ex_w1) & iext(uri_rdf_rest, X2, X1))),
% 0.69/0.72 inference(rewrite,[status(thm)],[])).
% 0.69/0.72 tff(20,plain,
% 0.69/0.72 (^[X0: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) <=> (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3))), ((((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) <=> ((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)))), rewrite(((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) <=> (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil))), ((((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) <=> (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil)))), (((((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) <=> ((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)))), rewrite(((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) <=> (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3))), (((((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) <=> (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)))), ((((((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) & iext(uri_rdf_first, X1, uri_ex_w2)) <=> ((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) & iext(uri_rdf_first, X1, uri_ex_w2)))), rewrite(((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) & iext(uri_rdf_first, X1, uri_ex_w2)) <=> (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2))), ((((((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) & iext(uri_rdf_first, X1, uri_ex_w2)) <=> (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2)))), (((((((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) & iext(uri_rdf_first, X1, uri_ex_w2)) & iext(uri_rdf_rest, X1, X0)) <=> ((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2)) & iext(uri_rdf_rest, X1, X0)))), rewrite(((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2)) & iext(uri_rdf_rest, X1, X0)) <=> (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0))), (((((((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) & iext(uri_rdf_first, X1, uri_ex_w2)) & iext(uri_rdf_rest, X1, X0)) <=> (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0)))), ((((((((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) & iext(uri_rdf_first, X1, uri_ex_w2)) & iext(uri_rdf_rest, X1, X0)) & iext(uri_rdf_first, X2, uri_ex_w1)) <=> ((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0)) & iext(uri_rdf_first, X2, uri_ex_w1)))), rewrite(((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0)) & iext(uri_rdf_first, X2, uri_ex_w1)) <=> (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0) & iext(uri_rdf_first, X2, uri_ex_w1))), ((((((((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) & iext(uri_rdf_first, X1, uri_ex_w2)) & iext(uri_rdf_rest, X1, X0)) & iext(uri_rdf_first, X2, uri_ex_w1)) <=> (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0) & iext(uri_rdf_first, X2, uri_ex_w1)))), (((((((((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) & iext(uri_rdf_first, X1, uri_ex_w2)) & iext(uri_rdf_rest, X1, X0)) & iext(uri_rdf_first, X2, uri_ex_w1)) & iext(uri_rdf_rest, X2, X1)) <=> ((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0) & iext(uri_rdf_first, X2, uri_ex_w1)) & iext(uri_rdf_rest, X2, X1)))), rewrite(((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0) & iext(uri_rdf_first, X2, uri_ex_w1)) & iext(uri_rdf_rest, X2, X1)) <=> (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0) & iext(uri_rdf_first, X2, uri_ex_w1) & iext(uri_rdf_rest, X2, X1))), (((((((((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) & iext(uri_rdf_first, X1, uri_ex_w2)) & iext(uri_rdf_rest, X1, X0)) & iext(uri_rdf_first, X2, uri_ex_w1)) & iext(uri_rdf_rest, X2, X1)) <=> (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0) & iext(uri_rdf_first, X2, uri_ex_w1) & iext(uri_rdf_rest, X2, X1))))),
% 0.69/0.73 inference(bind,[status(th)],[])).
% 0.69/0.73 tff(21,plain,
% 0.69/0.73 (?[X0: $i, X2: $i, X1: $i] : ((((((((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) & iext(uri_rdf_first, X1, uri_ex_w2)) & iext(uri_rdf_rest, X1, X0)) & iext(uri_rdf_first, X2, uri_ex_w1)) & iext(uri_rdf_rest, X2, X1)) <=> ?[X0: $i, X2: $i, X1: $i] : (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0) & iext(uri_rdf_first, X2, uri_ex_w1) & iext(uri_rdf_rest, X2, X1))),
% 0.69/0.73 inference(quant_intro,[status(thm)],[20])).
% 0.69/0.73 tff(22,axiom,(?[X0: $i, X2: $i, X1: $i] : ((((((((iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) & iext(uri_rdf_first, X0, uri_ex_w3)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) & iext(uri_rdf_first, X1, uri_ex_w2)) & iext(uri_rdf_rest, X1, X0)) & iext(uri_rdf_first, X2, uri_ex_w1)) & iext(uri_rdf_rest, X2, X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','premise_rdfbased_sem_ndis_alldifferent_bw')).
% 0.69/0.73 tff(23,plain,
% 0.69/0.73 (?[X0: $i, X2: $i, X1: $i] : (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0) & iext(uri_rdf_first, X2, uri_ex_w1) & iext(uri_rdf_rest, X2, X1))),
% 0.69/0.73 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.69/0.73 tff(24,plain,
% 0.69/0.73 (?[X0: $i, X2: $i, X1: $i] : (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0, uri_ex_w3) & iext(uri_rdf_rest, X0, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X0) & iext(uri_rdf_first, X2, uri_ex_w1) & iext(uri_rdf_rest, X2, X1))),
% 0.69/0.73 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.69/0.73 tff(25,plain,(
% 0.69/0.73 iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) & iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) & iext(uri_rdf_first, X0!142, uri_ex_w3) & iext(uri_rdf_rest, X0!142, uri_rdf_nil) & iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) & iext(uri_rdf_first, X1!140, uri_ex_w2) & iext(uri_rdf_rest, X1!140, X0!142) & iext(uri_rdf_first, X2!141, uri_ex_w1) & iext(uri_rdf_rest, X2!141, X1!140)),
% 0.69/0.73 inference(skolemize,[status(sab)],[24])).
% 0.69/0.73 tff(26,plain,
% 0.69/0.73 (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2)),
% 0.69/0.73 inference(and_elim,[status(thm)],[25])).
% 0.69/0.73 tff(27,plain,
% 0.69/0.73 ((~(iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) <=> (~(uri_ex_w1 = uri_ex_w2)))) | (~iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2)) | (~(uri_ex_w1 = uri_ex_w2))),
% 0.69/0.73 inference(tautology,[status(thm)],[])).
% 0.69/0.73 tff(28,plain,
% 0.69/0.73 ((~(iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w2) <=> (~(uri_ex_w1 = uri_ex_w2)))) | (~(uri_ex_w1 = uri_ex_w2))),
% 0.69/0.73 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.69/0.73 tff(29,plain,
% 0.69/0.73 (~(uri_ex_w1 = uri_ex_w2)),
% 0.69/0.73 inference(unit_resolution,[status(thm)],[28, 18])).
% 0.69/0.73 tff(30,plain,
% 0.69/0.73 ((~![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))) | (iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) <=> (~(uri_ex_w2 = uri_ex_w3)))),
% 0.69/0.73 inference(quant_inst,[status(thm)],[])).
% 0.69/0.73 tff(31,plain,
% 0.69/0.73 (iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) <=> (~(uri_ex_w2 = uri_ex_w3))),
% 0.69/0.73 inference(unit_resolution,[status(thm)],[30, 16])).
% 0.69/0.73 tff(32,plain,
% 0.69/0.73 (iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)),
% 0.69/0.73 inference(and_elim,[status(thm)],[25])).
% 0.69/0.73 tff(33,plain,
% 0.69/0.73 ((~(iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) <=> (~(uri_ex_w2 = uri_ex_w3)))) | (~iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3)) | (~(uri_ex_w2 = uri_ex_w3))),
% 0.69/0.73 inference(tautology,[status(thm)],[])).
% 0.69/0.73 tff(34,plain,
% 0.69/0.73 ((~(iext(uri_owl_differentFrom, uri_ex_w2, uri_ex_w3) <=> (~(uri_ex_w2 = uri_ex_w3)))) | (~(uri_ex_w2 = uri_ex_w3))),
% 0.69/0.73 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.69/0.73 tff(35,plain,
% 0.69/0.73 (~(uri_ex_w2 = uri_ex_w3)),
% 0.69/0.73 inference(unit_resolution,[status(thm)],[34, 31])).
% 0.69/0.73 tff(36,plain,
% 0.69/0.73 ((~![X: $i, Y: $i] : (iext(uri_owl_differentFrom, X, Y) <=> (~(X = Y)))) | (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) <=> (~(uri_ex_w1 = uri_ex_w3)))),
% 0.69/0.73 inference(quant_inst,[status(thm)],[])).
% 0.69/0.73 tff(37,plain,
% 0.69/0.73 (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) <=> (~(uri_ex_w1 = uri_ex_w3))),
% 0.69/0.73 inference(unit_resolution,[status(thm)],[36, 16])).
% 0.69/0.73 tff(38,plain,
% 0.69/0.73 (iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)),
% 0.69/0.73 inference(and_elim,[status(thm)],[25])).
% 0.69/0.73 tff(39,plain,
% 0.69/0.73 ((~(iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) <=> (~(uri_ex_w1 = uri_ex_w3)))) | (~iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3)) | (~(uri_ex_w1 = uri_ex_w3))),
% 0.69/0.73 inference(tautology,[status(thm)],[])).
% 0.69/0.73 tff(40,plain,
% 0.69/0.73 ((~(iext(uri_owl_differentFrom, uri_ex_w1, uri_ex_w3) <=> (~(uri_ex_w1 = uri_ex_w3)))) | (~(uri_ex_w1 = uri_ex_w3))),
% 0.69/0.73 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.69/0.73 tff(41,plain,
% 0.69/0.73 (~(uri_ex_w1 = uri_ex_w3)),
% 0.69/0.73 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.69/0.73 tff(42,plain,
% 0.69/0.73 (iext(uri_rdf_rest, X2!141, X1!140)),
% 0.69/0.73 inference(and_elim,[status(thm)],[25])).
% 0.69/0.73 tff(43,plain,
% 0.69/0.73 (iext(uri_rdf_first, X2!141, uri_ex_w1)),
% 0.69/0.73 inference(and_elim,[status(thm)],[25])).
% 0.69/0.73 tff(44,plain,
% 0.69/0.73 (iext(uri_rdf_rest, X1!140, X0!142)),
% 0.69/0.73 inference(and_elim,[status(thm)],[25])).
% 0.69/0.73 tff(45,plain,
% 0.69/0.73 (iext(uri_rdf_first, X1!140, uri_ex_w2)),
% 0.69/0.73 inference(and_elim,[status(thm)],[25])).
% 0.69/0.73 tff(46,plain,
% 0.69/0.73 (iext(uri_rdf_rest, X0!142, uri_rdf_nil)),
% 0.69/0.73 inference(and_elim,[status(thm)],[25])).
% 0.69/0.73 tff(47,plain,
% 0.69/0.73 (iext(uri_rdf_first, X0!142, uri_ex_w3)),
% 0.69/0.73 inference(and_elim,[status(thm)],[25])).
% 0.69/0.73 tff(48,plain,
% 0.69/0.73 (^[S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : refl(((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1))))) <=> ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1))))))),
% 0.69/0.73 inference(bind,[status(th)],[])).
% 0.69/0.73 tff(49,plain,
% 0.69/0.73 (![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1))))) <=> ![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))))),
% 0.69/0.73 inference(quant_intro,[status(thm)],[48])).
% 0.69/0.73 tff(50,plain,
% 0.69/0.73 (^[S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3))) <=> (~((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2))))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3)))) <=> (~(~((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2))))))), rewrite((~(~((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2))))) <=> ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)))), ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3)))) <=> ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2))))), rewrite((icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1)) & iext(uri_owl_members, tptp_fun_Z_79(S1), S1)) <=> (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3)))) | (icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1)) & iext(uri_owl_members, tptp_fun_Z_79(S1), S1))) <=> (((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2))) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1))))))), rewrite((((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2))) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1))))) <=> ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))))), (((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3)))) | (icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1)) & iext(uri_owl_members, tptp_fun_Z_79(S1), S1))) <=> ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))))))),
% 0.69/0.73 inference(bind,[status(th)],[])).
% 0.69/0.73 tff(51,plain,
% 0.69/0.73 (![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3)))) | (icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1)) & iext(uri_owl_members, tptp_fun_Z_79(S1), S1))) <=> ![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))))),
% 0.69/0.73 inference(quant_intro,[status(thm)],[50])).
% 0.69/0.73 tff(52,plain,
% 0.69/0.73 (![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3)))) | ?[Z: $i] : (icext(uri_owl_AllDifferent, Z) & iext(uri_owl_members, Z, S1))) <=> ![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3)))) | ?[Z: $i] : (icext(uri_owl_AllDifferent, Z) & iext(uri_owl_members, Z, S1)))),
% 0.69/0.73 inference(rewrite,[status(thm)],[])).
% 0.69/0.73 tff(53,plain,
% 0.69/0.73 (^[S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2))), ((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3))), ((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3)))), (((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3))), (((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3)))), ((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil))), ((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil)))), (((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) & (~(A1 = A2))) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) & (~(A1 = A2))))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) & (~(A1 = A2))) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)))), (((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) & (~(A1 = A2))) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2))))), ((((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) & (~(A1 = A2))) & (~(A1 = A3))) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2))) & (~(A1 = A3))))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2))) & (~(A1 = A3))) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)))), ((((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) & (~(A1 = A2))) & (~(A1 = A3))) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3))))), (((((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) & (~(A1 = A2))) & (~(A1 = A3))) & (~(A2 = A3))) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3))) & (~(A2 = A3))))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3))) & (~(A2 = A3))) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3)))), (((((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) & (~(A1 = A2))) & (~(A1 = A3))) & (~(A2 = A3))) <=> (iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3))))), ((((((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) & (~(A1 = A2))) & (~(A1 = A3))) & (~(A2 = A3))) => ?[Z: $i] : (icext(uri_owl_AllDifferent, Z) & iext(uri_owl_members, Z, S1))) <=> ((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3))) => ?[Z: $i] : (icext(uri_owl_AllDifferent, Z) & iext(uri_owl_members, Z, S1))))), rewrite(((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3))) => ?[Z: $i] : (icext(uri_owl_AllDifferent, Z) & iext(uri_owl_members, Z, S1))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3)))) | ?[Z: $i] : (icext(uri_owl_AllDifferent, Z) & iext(uri_owl_members, Z, S1)))), ((((((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) & (~(A1 = A2))) & (~(A1 = A3))) & (~(A2 = A3))) => ?[Z: $i] : (icext(uri_owl_AllDifferent, Z) & iext(uri_owl_members, Z, S1))) <=> ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3)))) | ?[Z: $i] : (icext(uri_owl_AllDifferent, Z) & iext(uri_owl_members, Z, S1)))))),
% 0.69/0.74 inference(bind,[status(th)],[])).
% 0.69/0.74 tff(54,plain,
% 0.69/0.74 (![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : (((((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) & (~(A1 = A2))) & (~(A1 = A3))) & (~(A2 = A3))) => ?[Z: $i] : (icext(uri_owl_AllDifferent, Z) & iext(uri_owl_members, Z, S1))) <=> ![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3)))) | ?[Z: $i] : (icext(uri_owl_AllDifferent, Z) & iext(uri_owl_members, Z, S1)))),
% 0.69/0.74 inference(quant_intro,[status(thm)],[53])).
% 0.69/0.74 tff(55,axiom,(![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : (((((((((iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, A2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, A3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) & (~(A1 = A2))) & (~(A1 = A3))) & (~(A2 = A3))) => ?[Z: $i] : (icext(uri_owl_AllDifferent, Z) & iext(uri_owl_members, Z, S1)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_ndis_alldifferent_members_fi_003')).
% 0.69/0.74 tff(56,plain,
% 0.69/0.74 (![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3)))) | ?[Z: $i] : (icext(uri_owl_AllDifferent, Z) & iext(uri_owl_members, Z, S1)))),
% 0.69/0.74 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.69/0.74 tff(57,plain,
% 0.69/0.74 (![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3)))) | ?[Z: $i] : (icext(uri_owl_AllDifferent, Z) & iext(uri_owl_members, Z, S1)))),
% 0.69/0.74 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.69/0.74 tff(58,plain,(
% 0.69/0.74 ![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((~(iext(uri_rdf_first, S1, A1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, A2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, A3) & iext(uri_rdf_rest, S3, uri_rdf_nil) & (~(A1 = A2)) & (~(A1 = A3)) & (~(A2 = A3)))) | (icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1)) & iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))),
% 0.69/0.74 inference(skolemize,[status(sab)],[57])).
% 0.69/0.74 tff(59,plain,
% 0.69/0.74 (![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))))),
% 0.69/0.74 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.69/0.74 tff(60,plain,
% 0.69/0.74 (![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))))),
% 0.69/0.74 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.69/0.74 tff(61,plain,
% 0.69/0.74 (((~![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))))) | ((uri_ex_w1 = uri_ex_w2) | (uri_ex_w1 = uri_ex_w3) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (uri_ex_w2 = uri_ex_w3) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)))))) <=> ((~![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))))) | (uri_ex_w1 = uri_ex_w2) | (uri_ex_w1 = uri_ex_w3) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (uri_ex_w2 = uri_ex_w3) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)))))),
% 0.69/0.74 inference(rewrite,[status(thm)],[])).
% 0.69/0.74 tff(62,plain,
% 0.69/0.74 (((uri_ex_w2 = uri_ex_w3) | (uri_ex_w1 = uri_ex_w3) | (uri_ex_w1 = uri_ex_w2) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141))))) <=> ((uri_ex_w1 = uri_ex_w2) | (uri_ex_w1 = uri_ex_w3) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (uri_ex_w2 = uri_ex_w3) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)))))),
% 0.69/0.74 inference(rewrite,[status(thm)],[])).
% 0.69/0.74 tff(63,plain,
% 0.69/0.74 (((~![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))))) | ((uri_ex_w2 = uri_ex_w3) | (uri_ex_w1 = uri_ex_w3) | (uri_ex_w1 = uri_ex_w2) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)))))) <=> ((~![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))))) | ((uri_ex_w1 = uri_ex_w2) | (uri_ex_w1 = uri_ex_w3) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (uri_ex_w2 = uri_ex_w3) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141))))))),
% 0.69/0.74 inference(monotonicity,[status(thm)],[62])).
% 0.69/0.74 tff(64,plain,
% 0.69/0.74 (((~![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))))) | ((uri_ex_w2 = uri_ex_w3) | (uri_ex_w1 = uri_ex_w3) | (uri_ex_w1 = uri_ex_w2) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)))))) <=> ((~![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))))) | (uri_ex_w1 = uri_ex_w2) | (uri_ex_w1 = uri_ex_w3) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (uri_ex_w2 = uri_ex_w3) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)))))),
% 0.69/0.74 inference(transitivity,[status(thm)],[63, 61])).
% 0.69/0.74 tff(65,plain,
% 0.69/0.74 ((~![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))))) | ((uri_ex_w2 = uri_ex_w3) | (uri_ex_w1 = uri_ex_w3) | (uri_ex_w1 = uri_ex_w2) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)))))),
% 0.69/0.74 inference(quant_inst,[status(thm)],[])).
% 0.69/0.74 tff(66,plain,
% 0.69/0.74 ((~![S1: $i, A1: $i, S2: $i, A2: $i, S3: $i, A3: $i] : ((A2 = A3) | (A1 = A3) | (A1 = A2) | (~iext(uri_rdf_first, S2, A2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, A3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, A1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(S1))) | (~iext(uri_owl_members, tptp_fun_Z_79(S1), S1)))))) | (uri_ex_w1 = uri_ex_w2) | (uri_ex_w1 = uri_ex_w3) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (uri_ex_w2 = uri_ex_w3) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141))))),
% 0.69/0.74 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.69/0.74 tff(67,plain,
% 0.69/0.74 ((uri_ex_w1 = uri_ex_w2) | (uri_ex_w1 = uri_ex_w3) | (uri_ex_w2 = uri_ex_w3) | (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141))))),
% 0.69/0.74 inference(unit_resolution,[status(thm)],[66, 60, 47, 46, 45, 44, 43, 42])).
% 0.69/0.74 tff(68,plain,
% 0.69/0.74 (~((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)))),
% 0.69/0.74 inference(unit_resolution,[status(thm)],[67, 41, 35, 29])).
% 0.69/0.74 tff(69,plain,
% 0.69/0.74 (((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141))) | iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)),
% 0.69/0.74 inference(tautology,[status(thm)],[])).
% 0.69/0.74 tff(70,plain,
% 0.69/0.74 (iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)),
% 0.69/0.74 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.69/0.74 tff(71,plain,
% 0.69/0.74 (^[X2: $i, X0: $i, X1: $i, X3: $i] : refl(((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil))))),
% 0.69/0.74 inference(bind,[status(th)],[])).
% 0.69/0.74 tff(72,plain,
% 0.69/0.74 (![X2: $i, X0: $i, X1: $i, X3: $i] : ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil))) <=> ![X2: $i, X0: $i, X1: $i, X3: $i] : ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil)))),
% 0.69/0.74 inference(quant_intro,[status(thm)],[71])).
% 0.69/0.74 tff(73,plain,
% 0.69/0.74 (^[X2: $i, X0: $i, X1: $i, X3: $i] : trans(monotonicity(rewrite((iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil)))))),
% 0.69/0.74 inference(bind,[status(th)],[])).
% 0.69/0.74 tff(74,plain,
% 0.69/0.74 (![X2: $i, X0: $i, X1: $i, X3: $i] : (~(iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil))) <=> ![X2: $i, X0: $i, X1: $i, X3: $i] : ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil)))),
% 0.69/0.74 inference(quant_intro,[status(thm)],[73])).
% 0.69/0.74 tff(75,plain,
% 0.69/0.74 ((~?[X2: $i, X0: $i, X1: $i, X3: $i] : (iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil))) <=> (~?[X2: $i, X0: $i, X1: $i, X3: $i] : (iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil)))),
% 0.69/0.74 inference(rewrite,[status(thm)],[])).
% 0.69/0.74 tff(76,plain,
% 0.69/0.74 ((~?[X2: $i, X0: $i, X1: $i, X3: $i] : (((((((iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1)) & iext(uri_rdf_first, X1, uri_ex_w2)) & iext(uri_rdf_rest, X1, X2)) & iext(uri_rdf_type, X3, uri_owl_AllDifferent)) & iext(uri_owl_members, X3, X0)) & iext(uri_rdf_first, X2, uri_ex_w3)) & iext(uri_rdf_rest, X2, uri_rdf_nil))) <=> (~?[X2: $i, X0: $i, X1: $i, X3: $i] : (iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil)))),
% 0.69/0.75 inference(rewrite,[status(thm)],[])).
% 0.69/0.75 tff(77,axiom,(~?[X2: $i, X0: $i, X1: $i, X3: $i] : (((((((iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1)) & iext(uri_rdf_first, X1, uri_ex_w2)) & iext(uri_rdf_rest, X1, X2)) & iext(uri_rdf_type, X3, uri_owl_AllDifferent)) & iext(uri_owl_members, X3, X0)) & iext(uri_rdf_first, X2, uri_ex_w3)) & iext(uri_rdf_rest, X2, uri_rdf_nil))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conclusion_rdfbased_sem_ndis_alldifferent_bw')).
% 0.69/0.75 tff(78,plain,
% 0.69/0.75 (~?[X2: $i, X0: $i, X1: $i, X3: $i] : (iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 0.69/0.75 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.69/0.75 tff(79,plain,
% 0.69/0.75 (~?[X2: $i, X0: $i, X1: $i, X3: $i] : (iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 0.69/0.75 inference(modus_ponens,[status(thm)],[78, 75])).
% 0.69/0.75 tff(80,plain,
% 0.69/0.75 (~?[X2: $i, X0: $i, X1: $i, X3: $i] : (iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 0.69/0.75 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.69/0.75 tff(81,plain,
% 0.69/0.75 (~?[X2: $i, X0: $i, X1: $i, X3: $i] : (iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 0.69/0.75 inference(modus_ponens,[status(thm)],[80, 75])).
% 0.69/0.75 tff(82,plain,
% 0.69/0.75 (~?[X2: $i, X0: $i, X1: $i, X3: $i] : (iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 0.69/0.75 inference(modus_ponens,[status(thm)],[81, 75])).
% 0.69/0.75 tff(83,plain,
% 0.69/0.75 (~?[X2: $i, X0: $i, X1: $i, X3: $i] : (iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 0.69/0.75 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.69/0.75 tff(84,plain,
% 0.69/0.75 (~?[X2: $i, X0: $i, X1: $i, X3: $i] : (iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil))),
% 0.69/0.75 inference(modus_ponens,[status(thm)],[83, 75])).
% 0.69/0.75 tff(85,plain,
% 0.69/0.75 (^[X2: $i, X0: $i, X1: $i, X3: $i] : refl($oeq((~(iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil))), (~(iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil)))))),
% 0.69/0.75 inference(bind,[status(th)],[])).
% 0.69/0.75 tff(86,plain,(
% 0.69/0.75 ![X2: $i, X0: $i, X1: $i, X3: $i] : (~(iext(uri_rdf_first, X0, uri_ex_w1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_w2) & iext(uri_rdf_rest, X1, X2) & iext(uri_rdf_type, X3, uri_owl_AllDifferent) & iext(uri_owl_members, X3, X0) & iext(uri_rdf_first, X2, uri_ex_w3) & iext(uri_rdf_rest, X2, uri_rdf_nil)))),
% 0.69/0.75 inference(nnf-neg,[status(sab)],[84, 85])).
% 0.69/0.75 tff(87,plain,
% 0.69/0.75 (![X2: $i, X0: $i, X1: $i, X3: $i] : ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil)))),
% 0.69/0.75 inference(modus_ponens,[status(thm)],[86, 74])).
% 0.69/0.75 tff(88,plain,
% 0.69/0.75 (![X2: $i, X0: $i, X1: $i, X3: $i] : ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil)))),
% 0.69/0.75 inference(modus_ponens,[status(thm)],[87, 72])).
% 0.69/0.75 tff(89,plain,
% 0.69/0.75 (((~![X2: $i, X0: $i, X1: $i, X3: $i] : ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil)))) | ((~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)) | (~iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent)))) <=> ((~![X2: $i, X0: $i, X1: $i, X3: $i] : ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil)))) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)) | (~iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent)))),
% 0.69/0.75 inference(rewrite,[status(thm)],[])).
% 0.69/0.75 tff(90,plain,
% 0.69/0.75 (((~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent)) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)) | (~iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent)))),
% 0.69/0.75 inference(rewrite,[status(thm)],[])).
% 0.69/0.75 tff(91,plain,
% 0.69/0.75 (((~![X2: $i, X0: $i, X1: $i, X3: $i] : ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil)))) | ((~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent)) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)))) <=> ((~![X2: $i, X0: $i, X1: $i, X3: $i] : ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil)))) | ((~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)) | (~iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent))))),
% 0.69/0.75 inference(monotonicity,[status(thm)],[90])).
% 0.69/0.75 tff(92,plain,
% 0.69/0.75 (((~![X2: $i, X0: $i, X1: $i, X3: $i] : ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil)))) | ((~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent)) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)))) <=> ((~![X2: $i, X0: $i, X1: $i, X3: $i] : ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil)))) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)) | (~iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent)))),
% 0.69/0.75 inference(transitivity,[status(thm)],[91, 89])).
% 0.69/0.75 tff(93,plain,
% 0.69/0.75 ((~![X2: $i, X0: $i, X1: $i, X3: $i] : ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil)))) | ((~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent)) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)))),
% 0.69/0.75 inference(quant_inst,[status(thm)],[])).
% 0.69/0.75 tff(94,plain,
% 0.69/0.75 ((~![X2: $i, X0: $i, X1: $i, X3: $i] : ((~iext(uri_rdf_first, X0, uri_ex_w1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_w2)) | (~iext(uri_rdf_rest, X1, X2)) | (~iext(uri_rdf_type, X3, uri_owl_AllDifferent)) | (~iext(uri_owl_members, X3, X0)) | (~iext(uri_rdf_first, X2, uri_ex_w3)) | (~iext(uri_rdf_rest, X2, uri_rdf_nil)))) | (~iext(uri_rdf_first, X0!142, uri_ex_w3)) | (~iext(uri_rdf_rest, X0!142, uri_rdf_nil)) | (~iext(uri_rdf_first, X1!140, uri_ex_w2)) | (~iext(uri_rdf_rest, X1!140, X0!142)) | (~iext(uri_rdf_first, X2!141, uri_ex_w1)) | (~iext(uri_rdf_rest, X2!141, X1!140)) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141)) | (~iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent))),
% 0.77/0.77 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.77/0.77 tff(95,plain,
% 0.77/0.77 (~iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent)),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[94, 88, 47, 46, 45, 44, 43, 42, 70])).
% 0.77/0.77 tff(96,plain,
% 0.77/0.77 (((~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))) | (~iext(uri_owl_members, tptp_fun_Z_79(X2!141), X2!141))) | icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))),
% 0.77/0.77 inference(tautology,[status(thm)],[])).
% 0.77/0.77 tff(97,plain,
% 0.77/0.77 (icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141))),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[96, 68])).
% 0.77/0.77 tff(98,plain,
% 0.77/0.77 ((~(iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent) <=> icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141)))) | iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent) | (~icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141)))),
% 0.77/0.77 inference(tautology,[status(thm)],[])).
% 0.77/0.77 tff(99,plain,
% 0.77/0.77 ((~(iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent) <=> icext(uri_owl_AllDifferent, tptp_fun_Z_79(X2!141)))) | iext(uri_rdf_type, tptp_fun_Z_79(X2!141), uri_owl_AllDifferent)),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.77/0.77 tff(100,plain,
% 0.77/0.77 ($false),
% 0.77/0.77 inference(unit_resolution,[status(thm)],[99, 95, 9])).
% 0.77/0.77 % SZS output end Proof
%------------------------------------------------------------------------------