TSTP Solution File: SEU362+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU362+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 07:29:08 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU362+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 12:30:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(in_type, type, (
% 0.19/0.41 in: ( $i * $i ) > $o)).
% 0.19/0.41 tff(the_InternalRel_type, type, (
% 0.19/0.41 the_InternalRel: $i > $i)).
% 0.19/0.41 tff(tptp_fun_B_11_type, type, (
% 0.19/0.41 tptp_fun_B_11: $i)).
% 0.19/0.41 tff(ordered_pair_type, type, (
% 0.19/0.41 ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.41 tff(tptp_fun_D_13_type, type, (
% 0.19/0.41 tptp_fun_D_13: $i)).
% 0.19/0.41 tff(tptp_fun_C_12_type, type, (
% 0.19/0.41 tptp_fun_C_12: $i)).
% 0.19/0.41 tff(related_type, type, (
% 0.19/0.41 related: ( $i * $i * $i ) > $o)).
% 0.19/0.41 tff(element_type, type, (
% 0.19/0.41 element: ( $i * $i ) > $o)).
% 0.19/0.41 tff(the_carrier_type, type, (
% 0.19/0.41 the_carrier: $i > $i)).
% 0.19/0.41 tff(rel_str_type, type, (
% 0.19/0.41 rel_str: $i > $o)).
% 0.19/0.41 tff(subrelstr_type, type, (
% 0.19/0.41 subrelstr: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_A_10_type, type, (
% 0.19/0.41 tptp_fun_A_10: $i)).
% 0.19/0.41 tff(tptp_fun_F_15_type, type, (
% 0.19/0.41 tptp_fun_F_15: $i)).
% 0.19/0.41 tff(tptp_fun_E_14_type, type, (
% 0.19/0.41 tptp_fun_E_14: $i)).
% 0.19/0.41 tff(empty_type, type, (
% 0.19/0.41 empty: $i > $o)).
% 0.19/0.41 tff(powerset_type, type, (
% 0.19/0.41 powerset: $i > $i)).
% 0.19/0.41 tff(subset_type, type, (
% 0.19/0.41 subset: ( $i * $i ) > $o)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 ((rel_str(A!10) & (subrelstr(B!11, A!10) & element(C!12, the_carrier(A!10)) & element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))) <=> (rel_str(A!10) & subrelstr(B!11, A!10) & element(C!12, the_carrier(A!10)) & element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 ((subrelstr(B!11, A!10) & (element(C!12, the_carrier(A!10)) & element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))) <=> (subrelstr(B!11, A!10) & element(C!12, the_carrier(A!10)) & element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 ((element(C!12, the_carrier(A!10)) & (element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))) <=> (element(C!12, the_carrier(A!10)) & element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 ((element(D!13, the_carrier(A!10)) & (element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))) <=> (element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (((~(~element(E!14, the_carrier(B!11)))) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11)))))) <=> (element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 ((~(~element(D!13, the_carrier(A!10)))) <=> element(D!13, the_carrier(A!10))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (((~(~element(D!13, the_carrier(A!10)))) & ((~(~element(E!14, the_carrier(B!11)))) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))) <=> (element(D!13, the_carrier(A!10)) & (element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11)))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[6, 5])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (((~(~element(D!13, the_carrier(A!10)))) & ((~(~element(E!14, the_carrier(B!11)))) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))) <=> (element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[7, 4])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 ((~(~element(C!12, the_carrier(A!10)))) <=> element(C!12, the_carrier(A!10))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (((~(~element(C!12, the_carrier(A!10)))) & ((~(~element(D!13, the_carrier(A!10)))) & ((~(~element(E!14, the_carrier(B!11)))) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11)))))))) <=> (element(C!12, the_carrier(A!10)) & (element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11)))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[9, 8])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (((~(~element(C!12, the_carrier(A!10)))) & ((~(~element(D!13, the_carrier(A!10)))) & ((~(~element(E!14, the_carrier(B!11)))) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11)))))))) <=> (element(C!12, the_carrier(A!10)) & element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[10, 3])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 ((~(~subrelstr(B!11, A!10))) <=> subrelstr(B!11, A!10)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (((~(~subrelstr(B!11, A!10))) & ((~(~element(C!12, the_carrier(A!10)))) & ((~(~element(D!13, the_carrier(A!10)))) & ((~(~element(E!14, the_carrier(B!11)))) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))))) <=> (subrelstr(B!11, A!10) & (element(C!12, the_carrier(A!10)) & element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11)))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[12, 11])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (((~(~subrelstr(B!11, A!10))) & ((~(~element(C!12, the_carrier(A!10)))) & ((~(~element(D!13, the_carrier(A!10)))) & ((~(~element(E!14, the_carrier(B!11)))) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))))) <=> (subrelstr(B!11, A!10) & element(C!12, the_carrier(A!10)) & element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[13, 2])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 ((~(~rel_str(A!10))) <=> rel_str(A!10)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (((~(~rel_str(A!10))) & ((~(~subrelstr(B!11, A!10))) & ((~(~element(C!12, the_carrier(A!10)))) & ((~(~element(D!13, the_carrier(A!10)))) & ((~(~element(E!14, the_carrier(B!11)))) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11)))))))))) <=> (rel_str(A!10) & (subrelstr(B!11, A!10) & element(C!12, the_carrier(A!10)) & element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11)))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[15, 14])).
% 0.19/0.42 tff(17,plain,
% 0.19/0.42 (((~(~rel_str(A!10))) & ((~(~subrelstr(B!11, A!10))) & ((~(~element(C!12, the_carrier(A!10)))) & ((~(~element(D!13, the_carrier(A!10)))) & ((~(~element(E!14, the_carrier(B!11)))) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11)))))))))) <=> (rel_str(A!10) & subrelstr(B!11, A!10) & element(C!12, the_carrier(A!10)) & element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[16, 1])).
% 0.19/0.42 tff(18,plain,
% 0.19/0.42 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(A, C, D) | (~((E = C) & (F = D) & related(B, E, F))) | (~element(F, the_carrier(B)))))))))) <=> (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(A, C, D) | (~((E = C) & (F = D) & related(B, E, F))) | (~element(F, the_carrier(B))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(19,plain,
% 0.19/0.42 ((~![A: $i] : (rel_str(A) => ![B: $i] : (subrelstr(B, A) => ![C: $i] : (element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((E = C) & (F = D)) & related(B, E, F)) => related(A, C, D))))))))) <=> (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(A, C, D) | (~((E = C) & (F = D) & related(B, E, F))) | (~element(F, the_carrier(B))))))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(20,axiom,(~![A: $i] : (rel_str(A) => ![B: $i] : (subrelstr(B, A) => ![C: $i] : (element(C, the_carrier(A)) => ![D: $i] : (element(D, the_carrier(A)) => ![E: $i] : (element(E, the_carrier(B)) => ![F: $i] : (element(F, the_carrier(B)) => ((((E = C) & (F = D)) & related(B, E, F)) => related(A, C, D))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t60_yellow_0')).
% 0.19/0.42 tff(21,plain,
% 0.19/0.42 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(A, C, D) | (~((E = C) & (F = D) & related(B, E, F))) | (~element(F, the_carrier(B)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(A, C, D) | (~((E = C) & (F = D) & related(B, E, F))) | (~element(F, the_carrier(B)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(A, C, D) | (~((E = C) & (F = D) & related(B, E, F))) | (~element(F, the_carrier(B)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(A, C, D) | (~((E = C) & (F = D) & related(B, E, F))) | (~element(F, the_carrier(B)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(A, C, D) | (~((E = C) & (F = D) & related(B, E, F))) | (~element(F, the_carrier(B)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(A, C, D) | (~((E = C) & (F = D) & related(B, E, F))) | (~element(F, the_carrier(B)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | ![C: $i] : ((~element(C, the_carrier(A))) | ![D: $i] : ((~element(D, the_carrier(A))) | ![E: $i] : ((~element(E, the_carrier(B))) | ![F: $i] : (related(A, C, D) | (~((E = C) & (F = D) & related(B, E, F))) | (~element(F, the_carrier(B)))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[26, 18])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 (rel_str(A!10) & subrelstr(B!11, A!10) & element(C!12, the_carrier(A!10)) & element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (rel_str(A!10)),
% 0.19/0.42 inference(and_elim,[status(thm)],[28])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))) <=> ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))) <=> ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[33, 31])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((subrelstr(B, A) => rel_str(B)) <=> (rel_str(B) | (~subrelstr(B, A))))), (![B: $i] : (subrelstr(B, A) => rel_str(B)) <=> ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))), ((rel_str(A) => ![B: $i] : (subrelstr(B, A) => rel_str(B))) <=> (rel_str(A) => ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))))), rewrite((rel_str(A) => ![B: $i] : (rel_str(B) | (~subrelstr(B, A)))) <=> ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))), ((rel_str(A) => ![B: $i] : (subrelstr(B, A) => rel_str(B))) <=> ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 (![A: $i] : (rel_str(A) => ![B: $i] : (subrelstr(B, A) => rel_str(B))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.19/0.42 tff(38,axiom,(![A: $i] : (rel_str(A) => ![B: $i] : (subrelstr(B, A) => rel_str(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_yellow_0')).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.19/0.42 tff(41,plain,(
% 0.19/0.42 ![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[40])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))) | ((~rel_str(A!10)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A!10))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))) | (~rel_str(A!10)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A!10))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))) | ((~rel_str(A!10)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A!10))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))) | (~rel_str(A!10)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[45, 42, 29])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (subrelstr(B!11, A!10)),
% 0.19/0.42 inference(and_elim,[status(thm)],[28])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (((~![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))) | (rel_str(B!11) | (~subrelstr(B!11, A!10)))) <=> ((~![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))) | rel_str(B!11) | (~subrelstr(B!11, A!10)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 ((~![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))) | (rel_str(B!11) | (~subrelstr(B!11, A!10)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 ((~![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))) | rel_str(B!11) | (~subrelstr(B!11, A!10))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (rel_str(B!11)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[50, 47, 46])).
% 0.19/0.42 tff(52,plain,
% 0.19/0.42 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(55,plain,
% 0.19/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[55, 53])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))) <=> ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))), (![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> (element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), ((rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> (rel_str(A) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))))), rewrite((rel_str(A) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), ((rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 (![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.42 tff(60,axiom,(![A: $i] : (rel_str(A) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_orders_2')).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.43 tff(63,plain,(
% 0.19/0.43 ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[62])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.19/0.43 tff(65,plain,
% 0.19/0.43 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | ((~rel_str(B!11)) | ![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | (~rel_str(B!11)) | ![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | ((~rel_str(B!11)) | ![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | (~rel_str(B!11)) | ![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.43 tff(68,plain,
% 0.19/0.43 ((~rel_str(B!11)) | ![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[67, 64])).
% 0.19/0.43 tff(69,plain,
% 0.19/0.43 (![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[68, 51])).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (~(related(A!10, C!12, D!13) | (~((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15))) | (~element(F!15, the_carrier(B!11))))),
% 0.19/0.43 inference(and_elim,[status(thm)],[28])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 ((E!14 = C!12) & (F!15 = D!13) & related(B!11, E!14, F!15)),
% 0.19/0.43 inference(or_elim,[status(thm)],[70])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 (E!14 = C!12),
% 0.19/0.43 inference(and_elim,[status(thm)],[71])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 (C!12 = E!14),
% 0.19/0.43 inference(symmetry,[status(thm)],[72])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 (element(C!12, the_carrier(B!11)) <=> element(E!14, the_carrier(B!11))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[73])).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 (element(E!14, the_carrier(B!11)) <=> element(C!12, the_carrier(B!11))),
% 0.19/0.43 inference(symmetry,[status(thm)],[74])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 (element(E!14, the_carrier(B!11))),
% 0.19/0.43 inference(and_elim,[status(thm)],[28])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 (element(C!12, the_carrier(B!11))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.43 tff(78,plain,
% 0.19/0.43 (((~![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11)))))) | ((~element(C!12, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11)))))) | (~element(C!12, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(79,plain,
% 0.19/0.43 ((~![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11)))))) | ((~element(C!12, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 ((~![B: $i] : ((~element(B, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, B, C) <=> in(ordered_pair(B, C), the_InternalRel(B!11)))))) | (~element(C!12, the_carrier(B!11))) | ![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 (![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[80, 77, 69])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 (F!15 = D!13),
% 0.19/0.43 inference(and_elim,[status(thm)],[71])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (D!13 = F!15),
% 0.19/0.43 inference(symmetry,[status(thm)],[82])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.43 (element(D!13, the_carrier(B!11)) <=> element(F!15, the_carrier(B!11))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[83])).
% 0.19/0.43 tff(85,plain,
% 0.19/0.43 (element(F!15, the_carrier(B!11)) <=> element(D!13, the_carrier(B!11))),
% 0.19/0.43 inference(symmetry,[status(thm)],[84])).
% 0.19/0.43 tff(86,plain,
% 0.19/0.43 (element(F!15, the_carrier(B!11))),
% 0.19/0.43 inference(or_elim,[status(thm)],[70])).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 (element(D!13, the_carrier(B!11))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.43 tff(88,plain,
% 0.19/0.43 (((~![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11))))) | ((~element(D!13, the_carrier(B!11))) | (related(B!11, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11))))) <=> ((~![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11))))) | (~element(D!13, the_carrier(B!11))) | (related(B!11, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(89,plain,
% 0.19/0.43 ((~![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11))))) | ((~element(D!13, the_carrier(B!11))) | (related(B!11, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 ((~![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11))))) | (~element(D!13, the_carrier(B!11))) | (related(B!11, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 (related(B!11, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[90, 87, 81])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 (related(B!11, C!12, D!13) <=> related(B!11, E!14, F!15)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[73, 83])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 (related(B!11, E!14, F!15) <=> related(B!11, C!12, D!13)),
% 0.19/0.43 inference(symmetry,[status(thm)],[92])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 (related(B!11, E!14, F!15)),
% 0.19/0.43 inference(and_elim,[status(thm)],[71])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 (related(B!11, C!12, D!13)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 ((~(related(B!11, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11)))) | (~related(B!11, C!12, D!13)) | in(ordered_pair(C!12, D!13), the_InternalRel(B!11))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 (in(ordered_pair(C!12, D!13), the_InternalRel(B!11))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[96, 95, 91])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(101,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.43 tff(103,plain,(
% 0.19/0.43 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.43 inference(skolemize,[status(sab)],[102])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(the_InternalRel(B!11), powerset(the_InternalRel(A!10))) <=> subset(the_InternalRel(B!11), the_InternalRel(A!10)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (element(the_InternalRel(B!11), powerset(the_InternalRel(A!10))) <=> subset(the_InternalRel(B!11), the_InternalRel(A!10))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A)))))))) <=> ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A)))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[107])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A)))))))) <=> ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A)))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A)))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[110, 108])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A)))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((rel_str(B) => (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A))))) <=> ((~rel_str(B)) | (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A))))))), (![B: $i] : (rel_str(B) => (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A))))) <=> ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A))))))), ((rel_str(A) => ![B: $i] : (rel_str(B) => (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A)))))) <=> (rel_str(A) => ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A)))))))), rewrite((rel_str(A) => ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A))))))), ((rel_str(A) => ![B: $i] : (rel_str(B) => (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(116,plain,
% 0.19/0.43 (![A: $i] : (rel_str(A) => ![B: $i] : (rel_str(B) => (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.43 tff(117,axiom,(![A: $i] : (rel_str(A) => ![B: $i] : (rel_str(B) => (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d13_yellow_0')).
% 0.19/0.43 tff(118,plain,
% 0.19/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.43 tff(119,plain,
% 0.19/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.19/0.43 tff(120,plain,(
% 0.19/0.43 ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (subset(the_carrier(B), the_carrier(A)) & subset(the_InternalRel(B), the_InternalRel(A))))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[119])).
% 0.19/0.43 tff(121,plain,
% 0.19/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A))))))))) | ((~rel_str(A!10)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A!10) <=> (~((~subset(the_carrier(B), the_carrier(A!10))) | (~subset(the_InternalRel(B), the_InternalRel(A!10))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A))))))))) | (~rel_str(A!10)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A!10) <=> (~((~subset(the_carrier(B), the_carrier(A!10))) | (~subset(the_InternalRel(B), the_InternalRel(A!10))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A))))))))) | ((~rel_str(A!10)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A!10) <=> (~((~subset(the_carrier(B), the_carrier(A!10))) | (~subset(the_InternalRel(B), the_InternalRel(A!10))))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A) <=> (~((~subset(the_carrier(B), the_carrier(A))) | (~subset(the_InternalRel(B), the_InternalRel(A))))))))) | (~rel_str(A!10)) | ![B: $i] : ((~rel_str(B)) | (subrelstr(B, A!10) <=> (~((~subset(the_carrier(B), the_carrier(A!10))) | (~subset(the_InternalRel(B), the_InternalRel(A!10)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 (![B: $i] : ((~rel_str(B)) | (subrelstr(B, A!10) <=> (~((~subset(the_carrier(B), the_carrier(A!10))) | (~subset(the_InternalRel(B), the_InternalRel(A!10)))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[125, 122, 29])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 (((~![B: $i] : ((~rel_str(B)) | (subrelstr(B, A!10) <=> (~((~subset(the_carrier(B), the_carrier(A!10))) | (~subset(the_InternalRel(B), the_InternalRel(A!10)))))))) | ((~rel_str(B!11)) | (subrelstr(B!11, A!10) <=> (~((~subset(the_carrier(B!11), the_carrier(A!10))) | (~subset(the_InternalRel(B!11), the_InternalRel(A!10)))))))) <=> ((~![B: $i] : ((~rel_str(B)) | (subrelstr(B, A!10) <=> (~((~subset(the_carrier(B), the_carrier(A!10))) | (~subset(the_InternalRel(B), the_InternalRel(A!10)))))))) | (~rel_str(B!11)) | (subrelstr(B!11, A!10) <=> (~((~subset(the_carrier(B!11), the_carrier(A!10))) | (~subset(the_InternalRel(B!11), the_InternalRel(A!10)))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 ((~![B: $i] : ((~rel_str(B)) | (subrelstr(B, A!10) <=> (~((~subset(the_carrier(B), the_carrier(A!10))) | (~subset(the_InternalRel(B), the_InternalRel(A!10)))))))) | ((~rel_str(B!11)) | (subrelstr(B!11, A!10) <=> (~((~subset(the_carrier(B!11), the_carrier(A!10))) | (~subset(the_InternalRel(B!11), the_InternalRel(A!10)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(129,plain,
% 0.19/0.44 ((~![B: $i] : ((~rel_str(B)) | (subrelstr(B, A!10) <=> (~((~subset(the_carrier(B), the_carrier(A!10))) | (~subset(the_InternalRel(B), the_InternalRel(A!10)))))))) | (~rel_str(B!11)) | (subrelstr(B!11, A!10) <=> (~((~subset(the_carrier(B!11), the_carrier(A!10))) | (~subset(the_InternalRel(B!11), the_InternalRel(A!10))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.44 tff(130,plain,
% 0.19/0.44 (subrelstr(B!11, A!10) <=> (~((~subset(the_carrier(B!11), the_carrier(A!10))) | (~subset(the_InternalRel(B!11), the_InternalRel(A!10)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[129, 126, 51])).
% 0.19/0.44 tff(131,plain,
% 0.19/0.44 ((~(subrelstr(B!11, A!10) <=> (~((~subset(the_carrier(B!11), the_carrier(A!10))) | (~subset(the_InternalRel(B!11), the_InternalRel(A!10))))))) | (~subrelstr(B!11, A!10)) | (~((~subset(the_carrier(B!11), the_carrier(A!10))) | (~subset(the_InternalRel(B!11), the_InternalRel(A!10)))))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(132,plain,
% 0.19/0.44 ((~(subrelstr(B!11, A!10) <=> (~((~subset(the_carrier(B!11), the_carrier(A!10))) | (~subset(the_InternalRel(B!11), the_InternalRel(A!10))))))) | (~((~subset(the_carrier(B!11), the_carrier(A!10))) | (~subset(the_InternalRel(B!11), the_InternalRel(A!10)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[131, 47])).
% 0.19/0.44 tff(133,plain,
% 0.19/0.44 (~((~subset(the_carrier(B!11), the_carrier(A!10))) | (~subset(the_InternalRel(B!11), the_InternalRel(A!10))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[132, 130])).
% 0.19/0.44 tff(134,plain,
% 0.19/0.44 (((~subset(the_carrier(B!11), the_carrier(A!10))) | (~subset(the_InternalRel(B!11), the_InternalRel(A!10)))) | subset(the_InternalRel(B!11), the_InternalRel(A!10))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(135,plain,
% 0.19/0.44 (subset(the_InternalRel(B!11), the_InternalRel(A!10))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.44 tff(136,plain,
% 0.19/0.44 ((~(element(the_InternalRel(B!11), powerset(the_InternalRel(A!10))) <=> subset(the_InternalRel(B!11), the_InternalRel(A!10)))) | element(the_InternalRel(B!11), powerset(the_InternalRel(A!10))) | (~subset(the_InternalRel(B!11), the_InternalRel(A!10)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(137,plain,
% 0.19/0.44 ((~(element(the_InternalRel(B!11), powerset(the_InternalRel(A!10))) <=> subset(the_InternalRel(B!11), the_InternalRel(A!10)))) | element(the_InternalRel(B!11), powerset(the_InternalRel(A!10)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.19/0.44 tff(138,plain,
% 0.19/0.44 (element(the_InternalRel(B!11), powerset(the_InternalRel(A!10)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[137, 106])).
% 0.19/0.44 tff(139,plain,
% 0.19/0.44 (^[A: $i, B: $i, C: $i] : refl(((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(140,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[139])).
% 0.19/0.44 tff(141,plain,
% 0.19/0.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C)) & empty(C)) <=> (~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> (~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(142,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[141])).
% 0.19/0.44 tff(143,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(144,plain,
% 0.19/0.44 (^[A: $i, B: $i, C: $i] : rewrite((~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> (~(in(A, B) & element(B, powerset(C)) & empty(C))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(145,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[144])).
% 0.19/0.44 tff(146,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_subset')).
% 0.19/0.44 tff(147,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.44 tff(148,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.19/0.44 tff(149,plain,(
% 0.19/0.44 ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[148])).
% 0.19/0.44 tff(150,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.19/0.44 tff(151,plain,
% 0.19/0.44 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[150, 140])).
% 0.19/0.44 tff(152,plain,
% 0.19/0.44 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))) | (~element(the_InternalRel(B!11), powerset(the_InternalRel(A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))) | (~element(the_InternalRel(B!11), powerset(the_InternalRel(A!10)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(153,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))) | (~element(the_InternalRel(B!11), powerset(the_InternalRel(A!10)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(154,plain,
% 0.19/0.44 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))) | (~element(the_InternalRel(B!11), powerset(the_InternalRel(A!10))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.44 tff(155,plain,
% 0.19/0.44 ((~empty(the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[154, 151, 138])).
% 0.19/0.44 tff(156,plain,
% 0.19/0.44 (~empty(the_InternalRel(A!10))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[155, 97])).
% 0.19/0.44 tff(157,plain,
% 0.19/0.44 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | ((~rel_str(A!10)) | ![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | (~rel_str(A!10)) | ![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(158,plain,
% 0.19/0.44 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | ((~rel_str(A!10)) | ![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(159,plain,
% 0.19/0.44 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (related(A, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A))))))) | (~rel_str(A!10)) | ![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.44 tff(160,plain,
% 0.19/0.44 (![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[159, 64, 29])).
% 0.19/0.44 tff(161,plain,
% 0.19/0.44 (element(C!12, the_carrier(A!10))),
% 0.19/0.44 inference(and_elim,[status(thm)],[28])).
% 0.19/0.44 tff(162,plain,
% 0.19/0.44 (((~![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10)))))) | ((~element(C!12, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10)))))) | (~element(C!12, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(163,plain,
% 0.19/0.44 ((~![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10)))))) | ((~element(C!12, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(164,plain,
% 0.19/0.44 ((~![B: $i] : ((~element(B, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, B, C) <=> in(ordered_pair(B, C), the_InternalRel(A!10)))))) | (~element(C!12, the_carrier(A!10))) | ![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.44 tff(165,plain,
% 0.19/0.44 (![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[164, 161, 160])).
% 0.19/0.44 tff(166,plain,
% 0.19/0.44 (element(D!13, the_carrier(A!10))),
% 0.19/0.44 inference(and_elim,[status(thm)],[28])).
% 0.19/0.44 tff(167,plain,
% 0.19/0.44 (((~![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10))))) | ((~element(D!13, the_carrier(A!10))) | (related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10))))) | (~element(D!13, the_carrier(A!10))) | (related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(168,plain,
% 0.19/0.44 ((~![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10))))) | ((~element(D!13, the_carrier(A!10))) | (related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(169,plain,
% 0.19/0.44 ((~![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10))))) | (~element(D!13, the_carrier(A!10))) | (related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.19/0.44 tff(170,plain,
% 0.19/0.44 (related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[169, 166, 165])).
% 0.19/0.44 tff(171,plain,
% 0.19/0.45 (~related(A!10, C!12, D!13)),
% 0.19/0.45 inference(or_elim,[status(thm)],[70])).
% 0.19/0.45 tff(172,plain,
% 0.19/0.45 ((~(related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10)))) | related(A!10, C!12, D!13) | (~in(ordered_pair(C!12, D!13), the_InternalRel(A!10)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(173,plain,
% 0.19/0.45 ((~(related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10)))) | (~in(ordered_pair(C!12, D!13), the_InternalRel(A!10)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.19/0.45 tff(174,plain,
% 0.19/0.45 (~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[173, 170])).
% 0.19/0.45 tff(175,plain,
% 0.19/0.45 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(176,plain,
% 0.19/0.45 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[175])).
% 0.19/0.45 tff(177,plain,
% 0.19/0.45 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(178,plain,
% 0.19/0.45 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(179,plain,
% 0.19/0.45 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[178])).
% 0.19/0.45 tff(180,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 0.19/0.45 tff(181,plain,
% 0.19/0.45 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.45 tff(182,plain,
% 0.19/0.45 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.19/0.45 tff(183,plain,(
% 0.19/0.45 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[182])).
% 0.19/0.45 tff(184,plain,
% 0.19/0.45 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[183, 176])).
% 0.19/0.45 tff(185,plain,
% 0.19/0.45 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (in(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | empty(the_InternalRel(A!10)) | (~element(ordered_pair(C!12, D!13), the_InternalRel(A!10))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | empty(the_InternalRel(A!10)) | (~element(ordered_pair(C!12, D!13), the_InternalRel(A!10))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(186,plain,
% 0.19/0.45 ((empty(the_InternalRel(A!10)) | in(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | (~element(ordered_pair(C!12, D!13), the_InternalRel(A!10)))) <=> (in(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | empty(the_InternalRel(A!10)) | (~element(ordered_pair(C!12, D!13), the_InternalRel(A!10))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(187,plain,
% 0.19/0.45 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_InternalRel(A!10)) | in(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | (~element(ordered_pair(C!12, D!13), the_InternalRel(A!10))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (in(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | empty(the_InternalRel(A!10)) | (~element(ordered_pair(C!12, D!13), the_InternalRel(A!10)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[186])).
% 0.19/0.45 tff(188,plain,
% 0.19/0.45 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_InternalRel(A!10)) | in(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | (~element(ordered_pair(C!12, D!13), the_InternalRel(A!10))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | empty(the_InternalRel(A!10)) | (~element(ordered_pair(C!12, D!13), the_InternalRel(A!10))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[187, 185])).
% 0.19/0.45 tff(189,plain,
% 0.19/0.45 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_InternalRel(A!10)) | in(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | (~element(ordered_pair(C!12, D!13), the_InternalRel(A!10))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(190,plain,
% 0.19/0.45 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | empty(the_InternalRel(A!10)) | (~element(ordered_pair(C!12, D!13), the_InternalRel(A!10)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.19/0.45 tff(191,plain,
% 0.19/0.45 (empty(the_InternalRel(A!10)) | (~element(ordered_pair(C!12, D!13), the_InternalRel(A!10)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[190, 184, 174])).
% 0.19/0.45 tff(192,plain,
% 0.19/0.45 (~element(ordered_pair(C!12, D!13), the_InternalRel(A!10))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[191, 156])).
% 0.19/0.45 tff(193,plain,
% 0.19/0.45 (^[A: $i, B: $i, C: $i] : refl((element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(194,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[193])).
% 0.19/0.45 tff(195,plain,
% 0.19/0.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C))) <=> (~((~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)))) <=> (~(~((~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)))) <=> ((~in(A, B)) | (~element(B, powerset(C)))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)))), rewrite((((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(196,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[195])).
% 0.19/0.45 tff(197,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(198,plain,
% 0.19/0.45 (^[A: $i, B: $i, C: $i] : rewrite(((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(199,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[198])).
% 0.19/0.45 tff(200,axiom,(![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_subset')).
% 0.19/0.45 tff(201,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.19/0.45 tff(202,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[201, 197])).
% 0.19/0.45 tff(203,plain,(
% 0.19/0.45 ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 0.19/0.45 inference(skolemize,[status(sab)],[202])).
% 0.19/0.45 tff(204,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[203, 196])).
% 0.19/0.45 tff(205,plain,
% 0.19/0.45 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[204, 194])).
% 0.19/0.45 tff(206,plain,
% 0.19/0.45 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(the_InternalRel(B!11), powerset(the_InternalRel(A!10)))) | element(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(B!11), powerset(the_InternalRel(A!10)))) | element(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(207,plain,
% 0.19/0.45 ((element(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))) | (~element(the_InternalRel(B!11), powerset(the_InternalRel(A!10))))) <=> ((~element(the_InternalRel(B!11), powerset(the_InternalRel(A!10)))) | element(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(208,plain,
% 0.19/0.45 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))) | (~element(the_InternalRel(B!11), powerset(the_InternalRel(A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(the_InternalRel(B!11), powerset(the_InternalRel(A!10)))) | element(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[207])).
% 0.19/0.45 tff(209,plain,
% 0.19/0.45 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))) | (~element(the_InternalRel(B!11), powerset(the_InternalRel(A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(B!11), powerset(the_InternalRel(A!10)))) | element(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[208, 206])).
% 0.19/0.45 tff(210,plain,
% 0.19/0.45 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))) | (~element(the_InternalRel(B!11), powerset(the_InternalRel(A!10)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(211,plain,
% 0.19/0.45 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(the_InternalRel(B!11), powerset(the_InternalRel(A!10)))) | element(ordered_pair(C!12, D!13), the_InternalRel(A!10)) | (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.19/0.45 tff(212,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[211, 205, 138, 192, 97])).
% 0.19/0.45 % SZS output end Proof
%------------------------------------------------------------------------------