TSTP Solution File: SEU355+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU355+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 07:29:06 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU355+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 12:32:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(in_type, type, (
% 0.13/0.40 in: ( $i * $i ) > $o)).
% 0.13/0.40 tff(empty_set_type, type, (
% 0.13/0.40 empty_set: $i)).
% 0.13/0.40 tff(tptp_fun_D_1_type, type, (
% 0.13/0.40 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_A_8_type, type, (
% 0.13/0.40 tptp_fun_A_8: $i)).
% 0.13/0.40 tff(tptp_fun_B_9_type, type, (
% 0.13/0.40 tptp_fun_B_9: $i)).
% 0.13/0.40 tff(element_type, type, (
% 0.13/0.40 element: ( $i * $i ) > $o)).
% 0.13/0.40 tff(the_carrier_type, type, (
% 0.13/0.40 the_carrier: $i > $i)).
% 0.13/0.40 tff(related_type, type, (
% 0.13/0.40 related: ( $i * $i * $i ) > $o)).
% 0.13/0.40 tff(relstr_set_smaller_type, type, (
% 0.13/0.40 relstr_set_smaller: ( $i * $i * $i ) > $o)).
% 0.13/0.40 tff(rel_str_type, type, (
% 0.13/0.40 rel_str: $i > $o)).
% 0.13/0.40 tff(relstr_element_smaller_type, type, (
% 0.13/0.40 relstr_element_smaller: ( $i * $i * $i ) > $o)).
% 0.13/0.40 tff(tptp_fun_D_0_type, type, (
% 0.13/0.40 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.13/0.40 tff(empty_type, type, (
% 0.13/0.40 empty: $i > $o)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (((~(~rel_str(A!8))) & (~((~element(B!9, the_carrier(A!8))) | (relstr_set_smaller(A!8, empty_set, B!9) & relstr_element_smaller(A!8, empty_set, B!9))))) <=> (rel_str(A!8) & (~((~element(B!9, the_carrier(A!8))) | (relstr_set_smaller(A!8, empty_set, B!9) & relstr_element_smaller(A!8, empty_set, B!9)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))) <=> (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 ((~![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))) <=> (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,axiom,(~![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t6_yellow_0')).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (relstr_set_smaller(A, empty_set, B) & relstr_element_smaller(A, empty_set, B))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (rel_str(A!8) & (~((~element(B!9, the_carrier(A!8))) | (relstr_set_smaller(A!8, empty_set, B!9) & relstr_element_smaller(A!8, empty_set, B!9))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (rel_str(A!8)),
% 0.20/0.40 inference(and_elim,[status(thm)],[12])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[17, 15])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : trans(monotonicity(rewrite((relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C)))) <=> (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))), ((element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C))))) <=> (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), rewrite((element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) <=> ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))))), ((element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C))))) <=> ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))))))), (![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C))))) <=> ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C)))))) <=> (rel_str(A) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))))))), rewrite((rel_str(A) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C)))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.40 tff(24,axiom,(![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_set_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, D, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_lattice3')).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_set_smaller(A, B, C) <=> ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.40 tff(27,plain,(
% 0.20/0.40 ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[26])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8)))))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, D, C) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))))))))))) <=> ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8)))))))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, D, C) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))))))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, D, C) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8)))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[32, 30])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, D, C) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8)))))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_set_smaller(A, B, C)) | ![D: $i] : (related(A, D, C) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_set_smaller(A, B, C) | (~(related(A, tptp_fun_D_1(C, B, A), C) | (~in(tptp_fun_D_1(C, B, A), B)) | (~element(tptp_fun_D_1(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[35, 29, 13])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (~((~element(B!9, the_carrier(A!8))) | (relstr_set_smaller(A!8, empty_set, B!9) & relstr_element_smaller(A!8, empty_set, B!9)))),
% 0.20/0.41 inference(and_elim,[status(thm)],[12])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (element(B!9, the_carrier(A!8))),
% 0.20/0.41 inference(or_elim,[status(thm)],[37])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))))))))))) | ((~element(B!9, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, D, B!9)))) | (~(relstr_set_smaller(A!8, empty_set, B!9) | (~(related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))))))))))) <=> ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))))))))))) | (~element(B!9, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, D, B!9)))) | (~(relstr_set_smaller(A!8, empty_set, B!9) | (~(related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))))))))))) | ((~element(B!9, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, D, B!9)))) | (~(relstr_set_smaller(A!8, empty_set, B!9) | (~(related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, D, C)))) | (~(relstr_set_smaller(A!8, B, C) | (~(related(A!8, tptp_fun_D_1(C, B, A!8), C) | (~in(tptp_fun_D_1(C, B, A!8), B)) | (~element(tptp_fun_D_1(C, B, A!8), the_carrier(A!8))))))))))) | (~element(B!9, the_carrier(A!8))) | (~((~((~relstr_set_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, D, B!9)))) | (~(relstr_set_smaller(A!8, empty_set, B!9) | (~(related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8)))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (~((~((~relstr_set_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, D, B!9)))) | (~(relstr_set_smaller(A!8, empty_set, B!9) | (~(related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[41, 38, 36])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (((~((~relstr_set_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, D, B!9)))) | (~(relstr_set_smaller(A!8, empty_set, B!9) | (~(related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8)))))))) | (relstr_set_smaller(A!8, empty_set, B!9) | (~(related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (relstr_set_smaller(A!8, empty_set, B!9) | (~(related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.41 tff(45,assumption,((~((~relstr_element_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, B!9, D)))) | (~(relstr_element_smaller(A!8, empty_set, B!9) | (~(related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8)))))))), introduced(assumption)).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[49, 47])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i] : trans(monotonicity(rewrite((relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))) <=> (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))), ((element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))) <=> (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), rewrite((element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) <=> ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))), ((element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))) <=> ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))))), (![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))) <=> ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))))) <=> (rel_str(A) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))))), rewrite((rel_str(A) => ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))), ((rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))))) <=> ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.42 tff(56,axiom,(![A: $i] : (rel_str(A) => ![B: $i, C: $i] : (element(C, the_carrier(A)) => (relstr_element_smaller(A, B, C) <=> ![D: $i] : (element(D, the_carrier(A)) => (in(D, B) => related(A, C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_lattice3')).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (relstr_element_smaller(A, B, C) <=> ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.42 tff(59,plain,(
% 0.20/0.42 ![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A))))) & (relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[58])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8)))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, C, D) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))))))))))) <=> ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8)))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, C, D) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))))))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[63])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, C, D) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8)))))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[64, 62])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | ((~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : (related(A!8, C, D) | (~in(D, B)) | (~element(D, the_carrier(A!8)))))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8)))))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 ((~![A: $i] : ((~rel_str(A)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A))) | (~((~((~relstr_element_smaller(A, B, C)) | ![D: $i] : (related(A, C, D) | (~in(D, B)) | (~element(D, the_carrier(A)))))) | (~(relstr_element_smaller(A, B, C) | (~(related(A, C, tptp_fun_D_0(C, B, A)) | (~in(tptp_fun_D_0(C, B, A), B)) | (~element(tptp_fun_D_0(C, B, A), the_carrier(A)))))))))))) | (~rel_str(A!8)) | ![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))))))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[67, 61, 13])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))))))))))) | ((~element(B!9, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, B!9, D)))) | (~(relstr_element_smaller(A!8, empty_set, B!9) | (~(related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))))))))))) <=> ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))))))))))) | (~element(B!9, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, B!9, D)))) | (~(relstr_element_smaller(A!8, empty_set, B!9) | (~(related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))))))))))) | ((~element(B!9, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, B!9, D)))) | (~(relstr_element_smaller(A!8, empty_set, B!9) | (~(related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 ((~![B: $i, C: $i] : ((~element(C, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, B, C)) | ![D: $i] : ((~in(D, B)) | (~element(D, the_carrier(A!8))) | related(A!8, C, D)))) | (~(relstr_element_smaller(A!8, B, C) | (~(related(A!8, C, tptp_fun_D_0(C, B, A!8)) | (~in(tptp_fun_D_0(C, B, A!8), B)) | (~element(tptp_fun_D_0(C, B, A!8), the_carrier(A!8))))))))))) | (~element(B!9, the_carrier(A!8))) | (~((~((~relstr_element_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, B!9, D)))) | (~(relstr_element_smaller(A!8, empty_set, B!9) | (~(related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8)))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[71, 38, 68, 45])).
% 0.20/0.43 tff(73,plain,(~((~((~relstr_element_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, B!9, D)))) | (~(relstr_element_smaller(A!8, empty_set, B!9) | (~(related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (((~((~relstr_element_smaller(A!8, empty_set, B!9)) | ![D: $i] : ((~in(D, empty_set)) | (~element(D, the_carrier(A!8))) | related(A!8, B!9, D)))) | (~(relstr_element_smaller(A!8, empty_set, B!9) | (~(related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8)))))))) | (relstr_element_smaller(A!8, empty_set, B!9) | (~(related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (relstr_element_smaller(A!8, empty_set, B!9) | (~(related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.20/0.43 tff(76,assumption,(in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)), introduced(assumption)).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (^[A: $i, B: $i] : refl(((~empty(B)) | (~in(A, B))) <=> ((~empty(B)) | (~in(A, B))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~empty(B)) | (~in(A, B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~empty(B)) | (~in(A, B))))))), rewrite((~(~((~empty(B)) | (~in(A, B))))) <=> ((~empty(B)) | (~in(A, B)))), ((~(in(A, B) & empty(B))) <=> ((~empty(B)) | (~in(A, B)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(82,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_boole')).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.43 tff(84,plain,(
% 0.20/0.43 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[83])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (empty(empty_set) <=> empty(empty_set)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(88,axiom,(empty(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (empty(empty_set)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[92, 89, 86, 76])).
% 0.20/0.43 tff(94,plain,(~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 ((related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8)))) | in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 ((~(relstr_element_smaller(A!8, empty_set, B!9) | (~(related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))))))) | relstr_element_smaller(A!8, empty_set, B!9) | (~(related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 ((~(relstr_element_smaller(A!8, empty_set, B!9) | (~(related(A!8, B!9, tptp_fun_D_0(B!9, empty_set, A!8)) | (~in(tptp_fun_D_0(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_0(B!9, empty_set, A!8), the_carrier(A!8))))))) | relstr_element_smaller(A!8, empty_set, B!9)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 (relstr_element_smaller(A!8, empty_set, B!9)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[98, 75])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 ((~(~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9))))) <=> ((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 ((relstr_set_smaller(A!8, empty_set, B!9) & relstr_element_smaller(A!8, empty_set, B!9)) <=> (~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 ((~(relstr_set_smaller(A!8, empty_set, B!9) & relstr_element_smaller(A!8, empty_set, B!9))) <=> (~(~((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[101])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 ((~(relstr_set_smaller(A!8, empty_set, B!9) & relstr_element_smaller(A!8, empty_set, B!9))) <=> ((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[102, 100])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (~(relstr_set_smaller(A!8, empty_set, B!9) & relstr_element_smaller(A!8, empty_set, B!9))),
% 0.20/0.43 inference(or_elim,[status(thm)],[37])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 ((~relstr_set_smaller(A!8, empty_set, B!9)) | (~relstr_element_smaller(A!8, empty_set, B!9))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (~relstr_set_smaller(A!8, empty_set, B!9)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[105, 99])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 ((~(relstr_set_smaller(A!8, empty_set, B!9) | (~(related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))))))) | relstr_set_smaller(A!8, empty_set, B!9) | (~(related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 ((~(relstr_set_smaller(A!8, empty_set, B!9) | (~(related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))))))) | (~(related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 (~(related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[108, 44])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 ((related(A!8, tptp_fun_D_1(B!9, empty_set, A!8), B!9) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)) | (~element(tptp_fun_D_1(B!9, empty_set, A!8), the_carrier(A!8)))) | in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(111,plain,
% 0.20/0.43 (in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(114,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_1(B!9, empty_set, A!8), empty_set))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[114, 89, 86, 111])).
% 0.20/0.43 % SZS output end Proof
%------------------------------------------------------------------------------