TSTP Solution File: SEU363+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU363+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:29:08 EDT 2022
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU363+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 12:52:24 EDT 2022
% 0.13/0.35 % 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.
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 tff(in_type, type, (
% 0.20/0.44 in: ( $i * $i ) > $o)).
% 0.20/0.44 tff(the_carrier_type, type, (
% 0.20/0.44 the_carrier: $i > $i)).
% 0.20/0.44 tff(tptp_fun_B_11_type, type, (
% 0.20/0.44 tptp_fun_B_11: $i)).
% 0.20/0.44 tff(tptp_fun_D_13_type, type, (
% 0.20/0.44 tptp_fun_D_13: $i)).
% 0.20/0.44 tff(tptp_fun_C_12_type, type, (
% 0.20/0.44 tptp_fun_C_12: $i)).
% 0.20/0.44 tff(cartesian_product2_type, type, (
% 0.20/0.44 cartesian_product2: ( $i * $i ) > $i)).
% 0.20/0.44 tff(ordered_pair_type, type, (
% 0.20/0.44 ordered_pair: ( $i * $i ) > $i)).
% 0.20/0.44 tff(tptp_fun_F_15_type, type, (
% 0.20/0.44 tptp_fun_F_15: $i)).
% 0.20/0.44 tff(tptp_fun_E_14_type, type, (
% 0.20/0.44 tptp_fun_E_14: $i)).
% 0.20/0.44 tff(related_type, type, (
% 0.20/0.44 related: ( $i * $i * $i ) > $o)).
% 0.20/0.44 tff(tptp_fun_A_10_type, type, (
% 0.20/0.44 tptp_fun_A_10: $i)).
% 0.20/0.44 tff(element_type, type, (
% 0.20/0.44 element: ( $i * $i ) > $o)).
% 0.20/0.44 tff(subrelstr_type, type, (
% 0.20/0.44 subrelstr: ( $i * $i ) > $o)).
% 0.20/0.44 tff(full_subrelstr_type, type, (
% 0.20/0.44 full_subrelstr: ( $i * $i ) > $o)).
% 0.20/0.44 tff(rel_str_type, type, (
% 0.20/0.44 rel_str: $i > $o)).
% 0.20/0.44 tff(the_InternalRel_type, type, (
% 0.20/0.44 the_InternalRel: $i > $i)).
% 0.20/0.44 tff(relation_restriction_type, type, (
% 0.20/0.44 relation_restriction: ( $i * $i ) > $i)).
% 0.20/0.44 tff(relation_type, type, (
% 0.20/0.44 relation: $i > $o)).
% 0.20/0.44 tff(powerset_type, type, (
% 0.20/0.44 powerset: $i > $i)).
% 0.20/0.44 tff(relation_of2_as_subset_type, type, (
% 0.20/0.44 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 0.20/0.44 tff(relation_restriction_as_relation_of_type, type, (
% 0.20/0.44 relation_restriction_as_relation_of: ( $i * $i ) > $i)).
% 0.20/0.44 tff(1,plain,
% 0.20/0.44 ((rel_str(A!10) & (full_subrelstr(B!11, 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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))) <=> (rel_str(A!10) & full_subrelstr(B!11, 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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(2,plain,
% 0.20/0.44 (((full_subrelstr(B!11, 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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))) <=> (full_subrelstr(B!11, 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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(3,plain,
% 0.20/0.44 ((element(C!12, the_carrier(A!10)) & (element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(4,plain,
% 0.20/0.44 ((element(D!13, the_carrier(A!10)) & (element(E!14, the_carrier(B!11)) & (~(related(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))) <=> (element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(5,plain,
% 0.20/0.44 (((~(~element(E!14, the_carrier(B!11)))) & (~(related(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11)))))) <=> (element(E!14, the_carrier(B!11)) & (~(related(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(6,plain,
% 0.20/0.44 ((~(~element(D!13, the_carrier(A!10)))) <=> element(D!13, the_carrier(A!10))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(7,plain,
% 0.20/0.44 (((~(~element(D!13, the_carrier(A!10)))) & ((~(~element(E!14, the_carrier(B!11)))) & (~(related(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))) <=> (element(D!13, the_carrier(A!10)) & (element(E!14, the_carrier(B!11)) & (~(related(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11)))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[6, 5])).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 (((~(~element(D!13, the_carrier(A!10)))) & ((~(~element(E!14, the_carrier(B!11)))) & (~(related(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))) <=> (element(D!13, the_carrier(A!10)) & element(E!14, the_carrier(B!11)) & (~(related(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[7, 4])).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 ((~(~element(C!12, the_carrier(A!10)))) <=> element(C!12, the_carrier(A!10))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 (((~(~element(C!12, the_carrier(A!10)))) & ((~(~element(D!13, the_carrier(A!10)))) & ((~(~element(E!14, the_carrier(B!11)))) & (~(related(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11)))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[9, 8])).
% 0.20/0.44 tff(11,plain,
% 0.20/0.44 (((~(~element(C!12, the_carrier(A!10)))) & ((~(~element(D!13, the_carrier(A!10)))) & ((~(~element(E!14, the_carrier(B!11)))) & (~(related(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[10, 3])).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 ((~(~(full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10)))) <=> (full_subrelstr(B!11, A!10) & subrelstr(B!11, A!10))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 (((~(~(full_subrelstr(B!11, 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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))))) <=> ((full_subrelstr(B!11, 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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11)))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[12, 11])).
% 0.20/0.45 tff(14,plain,
% 0.20/0.45 (((~(~(full_subrelstr(B!11, 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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))))) <=> (full_subrelstr(B!11, 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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[13, 2])).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 ((~(~rel_str(A!10))) <=> rel_str(A!10)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(16,plain,
% 0.20/0.45 (((~(~rel_str(A!10))) & ((~(~(full_subrelstr(B!11, 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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11)))))))))) <=> (rel_str(A!10) & (full_subrelstr(B!11, 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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11)))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[15, 14])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 (((~(~rel_str(A!10))) & ((~(~(full_subrelstr(B!11, 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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11)))))))))) <=> (rel_str(A!10) & full_subrelstr(B!11, 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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[16, 1])).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & 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(B, E, F) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))) | (~element(F, the_carrier(B)))))))))) <=> (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & 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(B, E, F) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))) | (~element(F, the_carrier(B))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 ((~![A: $i] : (rel_str(A) => ![B: $i] : ((full_subrelstr(B, A) & 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(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F))))))))) <=> (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & 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(B, E, F) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))) | (~element(F, the_carrier(B))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(20,axiom,(~![A: $i] : (rel_str(A) => ![B: $i] : ((full_subrelstr(B, A) & 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(A, C, D)) & in(E, the_carrier(B))) & in(F, the_carrier(B))) => related(B, E, F))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t61_yellow_0')).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & 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(B, E, F) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))) | (~element(F, the_carrier(B)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & 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(B, E, F) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))) | (~element(F, the_carrier(B)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.20/0.45 tff(23,plain,
% 0.20/0.45 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & 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(B, E, F) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))) | (~element(F, the_carrier(B)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & 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(B, E, F) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))) | (~element(F, the_carrier(B)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & 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(B, E, F) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))) | (~element(F, the_carrier(B)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[24, 18])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & 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(B, E, F) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))) | (~element(F, the_carrier(B)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~(full_subrelstr(B, A) & 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(B, E, F) | (~((E = C) & (F = D) & related(A, C, D) & in(E, the_carrier(B)) & in(F, the_carrier(B)))) | (~element(F, the_carrier(B)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[26, 18])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 (rel_str(A!10) & full_subrelstr(B!11, 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(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[27, 17])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 (~(related(B!11, E!14, F!15) | (~((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11)))) | (~element(F!15, the_carrier(B!11))))),
% 0.20/0.45 inference(and_elim,[status(thm)],[28])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 ((E!14 = C!12) & (F!15 = D!13) & related(A!10, C!12, D!13) & in(E!14, the_carrier(B!11)) & in(F!15, the_carrier(B!11))),
% 0.20/0.45 inference(or_elim,[status(thm)],[29])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (F!15 = D!13),
% 0.20/0.45 inference(and_elim,[status(thm)],[30])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 (D!13 = F!15),
% 0.20/0.45 inference(symmetry,[status(thm)],[31])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 (in(D!13, the_carrier(B!11)) <=> in(F!15, the_carrier(B!11))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[32])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 (in(F!15, the_carrier(B!11)) <=> in(D!13, the_carrier(B!11))),
% 0.20/0.45 inference(symmetry,[status(thm)],[33])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 (in(F!15, the_carrier(B!11))),
% 0.20/0.45 inference(and_elim,[status(thm)],[30])).
% 0.20/0.45 tff(36,plain,
% 0.20/0.45 (in(D!13, the_carrier(B!11))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.45 tff(37,plain,
% 0.20/0.45 (E!14 = C!12),
% 0.20/0.45 inference(and_elim,[status(thm)],[30])).
% 0.20/0.45 tff(38,plain,
% 0.20/0.45 (C!12 = E!14),
% 0.20/0.45 inference(symmetry,[status(thm)],[37])).
% 0.20/0.45 tff(39,plain,
% 0.20/0.45 (in(C!12, the_carrier(B!11)) <=> in(E!14, the_carrier(B!11))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.45 tff(40,plain,
% 0.20/0.45 (in(E!14, the_carrier(B!11)) <=> in(C!12, the_carrier(B!11))),
% 0.20/0.45 inference(symmetry,[status(thm)],[39])).
% 0.20/0.45 tff(41,plain,
% 0.20/0.45 (in(E!14, the_carrier(B!11))),
% 0.20/0.45 inference(and_elim,[status(thm)],[30])).
% 0.20/0.45 tff(42,plain,
% 0.20/0.45 (in(C!12, the_carrier(B!11))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.45 tff(43,plain,
% 0.20/0.45 ((~((~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11))))) | (~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(44,plain,
% 0.20/0.45 (~((~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[43, 42, 36])).
% 0.20/0.45 tff(45,plain,
% 0.20/0.45 (rel_str(A!10)),
% 0.20/0.45 inference(and_elim,[status(thm)],[28])).
% 0.20/0.45 tff(46,plain,
% 0.20/0.45 (^[A: $i] : refl(((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(47,plain,
% 0.20/0.45 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.45 tff(48,plain,
% 0.20/0.45 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(49,plain,
% 0.20/0.45 (^[A: $i] : rewrite((rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(50,plain,
% 0.20/0.45 (![A: $i] : (rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.45 tff(51,axiom,(![A: $i] : (rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u1_orders_2')).
% 0.20/0.45 tff(52,plain,
% 0.20/0.45 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.45 tff(53,plain,
% 0.20/0.45 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.20/0.45 tff(54,plain,(
% 0.20/0.45 ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[53])).
% 0.20/0.45 tff(55,plain,
% 0.20/0.45 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.20/0.45 tff(56,plain,
% 0.20/0.45 (((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | ((~rel_str(A!10)) | relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10)))) <=> ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | (~rel_str(A!10)) | relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(57,plain,
% 0.20/0.45 ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | ((~rel_str(A!10)) | relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(58,plain,
% 0.20/0.45 ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | (~rel_str(A!10)) | relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.45 tff(59,plain,
% 0.20/0.45 (relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[58, 55, 45])).
% 0.20/0.45 tff(60,plain,
% 0.20/0.45 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(61,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.45 tff(62,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(63,plain,
% 0.20/0.45 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.45 tff(65,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.20/0.46 tff(68,plain,(
% 0.20/0.46 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[67])).
% 0.20/0.46 tff(69,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.20/0.46 tff(70,plain,
% 0.20/0.46 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10))) | element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10))) | element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(71,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10))) | element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(72,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(the_InternalRel(A!10), the_carrier(A!10), the_carrier(A!10))) | element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.46 tff(73,plain,
% 0.20/0.46 (element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[72, 69, 59])).
% 0.20/0.46 tff(74,plain,
% 0.20/0.46 (^[A: $i, B: $i, C: $i] : refl((relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(75,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.46 tff(76,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(77,plain,
% 0.20/0.46 (^[A: $i, B: $i, C: $i] : rewrite((element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(78,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.46 tff(79,axiom,(![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_relset_1')).
% 0.20/0.46 tff(80,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.46 tff(81,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.46 tff(82,plain,(
% 0.20/0.46 ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[81])).
% 0.20/0.46 tff(83,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.20/0.46 tff(84,plain,
% 0.20/0.46 (((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(the_InternalRel(A!10)) | (~element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10))))))) <=> ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(the_InternalRel(A!10)) | (~element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(85,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(the_InternalRel(A!10)) | (~element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(86,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(the_InternalRel(A!10)) | (~element(the_InternalRel(A!10), powerset(cartesian_product2(the_carrier(A!10), the_carrier(A!10)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (relation(the_InternalRel(A!10))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[86, 83, 73])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B))))))) <=> ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.46 tff(90,plain,
% 0.20/0.46 (^[A: $i, B: $i, C: $i] : rewrite(((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (^[A: $i, B: $i, C: $i] : rewrite((relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.46 tff(95,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t16_wellord1')).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.20/0.46 tff(98,plain,(
% 0.20/0.46 ![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (in(A, C) & in(A, cartesian_product2(B, B)))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[97])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.20/0.46 tff(100,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))) | ((~relation(the_InternalRel(A!10))) | (in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))) <=> (~((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))) | (~relation(the_InternalRel(A!10))) | (in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))) <=> (~((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))) | ((~relation(the_InternalRel(A!10))) | (in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))) <=> (~((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (in(A, relation_restriction(C, B)) <=> (~((~in(A, C)) | (~in(A, cartesian_product2(B, B)))))))) | (~relation(the_InternalRel(A!10))) | (in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))) <=> (~((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 (in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))) <=> (~((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[103, 100, 87])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(106,plain,
% 0.20/0.46 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.46 tff(107,plain,
% 0.20/0.46 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[108, 106])).
% 0.20/0.46 tff(110,plain,
% 0.20/0.46 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(111,plain,
% 0.20/0.46 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((subrelstr(B, A) => (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))) <=> ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))), (![B: $i] : (subrelstr(B, A) => (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))) <=> ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))), ((rel_str(A) => ![B: $i] : (subrelstr(B, A) => (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> (rel_str(A) => ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))))), rewrite((rel_str(A) => ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))), ((rel_str(A) => ![B: $i] : (subrelstr(B, A) => (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(112,plain,
% 0.20/0.46 (![A: $i] : (rel_str(A) => ![B: $i] : (subrelstr(B, A) => (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.46 tff(113,axiom,(![A: $i] : (rel_str(A) => ![B: $i] : (subrelstr(B, A) => (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d14_yellow_0')).
% 0.20/0.46 tff(114,plain,
% 0.20/0.46 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.20/0.46 tff(116,plain,(
% 0.20/0.46 ![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[115])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 (![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))) | ((~rel_str(A!10)) | ![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))) | (~rel_str(A!10)) | ![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))) | ((~rel_str(A!10)) | ![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : ((~subrelstr(B, A)) | (full_subrelstr(B, A) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A), the_carrier(B))))))) | (~rel_str(A!10)) | ![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[120, 117, 45])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 (subrelstr(B!11, A!10)),
% 0.20/0.46 inference(and_elim,[status(thm)],[28])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 (((~![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B)))))) | ((~subrelstr(B!11, A!10)) | (full_subrelstr(B!11, A!10) <=> (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)))))) <=> ((~![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B)))))) | (~subrelstr(B!11, A!10)) | (full_subrelstr(B!11, A!10) <=> (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 ((~![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B)))))) | ((~subrelstr(B!11, A!10)) | (full_subrelstr(B!11, A!10) <=> (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 ((~![B: $i] : ((~subrelstr(B, A!10)) | (full_subrelstr(B, A!10) <=> (the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B)))))) | (~subrelstr(B!11, A!10)) | (full_subrelstr(B!11, A!10) <=> (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 (full_subrelstr(B!11, A!10) <=> (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[125, 122, 121])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 (full_subrelstr(B!11, A!10)),
% 0.20/0.46 inference(and_elim,[status(thm)],[28])).
% 0.20/0.46 tff(128,plain,
% 0.20/0.46 ((~(full_subrelstr(B!11, A!10) <=> (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11))))) | (~full_subrelstr(B!11, A!10)) | (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 ((~(full_subrelstr(B!11, A!10) <=> (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11))))) | (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 (the_InternalRel(B!11) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[129, 126])).
% 0.20/0.46 tff(131,plain,
% 0.20/0.46 (relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)) = the_InternalRel(B!11)),
% 0.20/0.46 inference(symmetry,[status(thm)],[130])).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 (^[A: $i, B: $i] : refl(((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B))) <=> ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[132])).
% 0.20/0.46 tff(134,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 (^[A: $i, B: $i] : rewrite((relation(A) => (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B))) <=> ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 (![A: $i, B: $i] : (relation(A) => (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B))) <=> ![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.46 tff(137,axiom,(![A: $i, B: $i] : (relation(A) => (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k1_toler_1')).
% 0.20/0.46 tff(138,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.20/0.46 tff(140,plain,(
% 0.20/0.46 ![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[139])).
% 0.20/0.46 tff(141,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 (((~![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))) | ((~relation(the_InternalRel(A!10))) | (relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)) = relation_restriction(the_InternalRel(A!10), the_carrier(B!11))))) <=> ((~![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))) | (~relation(the_InternalRel(A!10))) | (relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)) = relation_restriction(the_InternalRel(A!10), the_carrier(B!11))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))) | ((~relation(the_InternalRel(A!10))) | (relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)) = relation_restriction(the_InternalRel(A!10), the_carrier(B!11))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : ((~relation(A)) | (relation_restriction_as_relation_of(A, B) = relation_restriction(A, B)))) | (~relation(the_InternalRel(A!10))) | (relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)) = relation_restriction(the_InternalRel(A!10), the_carrier(B!11)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11)) = relation_restriction(the_InternalRel(A!10), the_carrier(B!11))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[144, 141, 87])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (relation_restriction(the_InternalRel(A!10), the_carrier(B!11)) = relation_restriction_as_relation_of(the_InternalRel(A!10), the_carrier(B!11))),
% 0.20/0.47 inference(symmetry,[status(thm)],[145])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 (relation_restriction(the_InternalRel(A!10), the_carrier(B!11)) = the_InternalRel(B!11)),
% 0.20/0.47 inference(transitivity,[status(thm)],[146, 131])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 (in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[147])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 (in(ordered_pair(C!12, D!13), the_InternalRel(B!11)) <=> in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11)))),
% 0.20/0.47 inference(symmetry,[status(thm)],[148])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 ((~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))) <=> (~in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[149])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (element(D!13, the_carrier(B!11)) <=> element(F!15, the_carrier(B!11))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[32])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 (element(F!15, the_carrier(B!11)) <=> element(D!13, the_carrier(B!11))),
% 0.20/0.47 inference(symmetry,[status(thm)],[151])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 (element(F!15, the_carrier(B!11))),
% 0.20/0.47 inference(or_elim,[status(thm)],[29])).
% 0.20/0.47 tff(154,plain,
% 0.20/0.47 (element(D!13, the_carrier(B!11))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 (element(C!12, the_carrier(B!11)) <=> element(E!14, the_carrier(B!11))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.47 tff(156,plain,
% 0.20/0.47 (element(E!14, the_carrier(B!11)) <=> element(C!12, the_carrier(B!11))),
% 0.20/0.47 inference(symmetry,[status(thm)],[155])).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 (element(E!14, the_carrier(B!11))),
% 0.20/0.47 inference(and_elim,[status(thm)],[28])).
% 0.20/0.47 tff(158,plain,
% 0.20/0.47 (element(C!12, the_carrier(B!11))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.47 tff(159,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[159])).
% 0.20/0.47 tff(161,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[161])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[162, 160])).
% 0.20/0.47 tff(164,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(165,plain,
% 0.20/0.47 (^[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))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(166,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[165])).
% 0.20/0.47 tff(167,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')).
% 0.20/0.47 tff(168,plain,
% 0.20/0.47 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.47 tff(169,plain,
% 0.20/0.47 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.20/0.47 tff(170,plain,(
% 0.20/0.47 ![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[169])).
% 0.20/0.47 tff(171,plain,
% 0.20/0.47 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (rel_str(B) | (~subrelstr(B, A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.20/0.47 tff(172,plain,
% 0.20/0.47 (((~![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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(173,plain,
% 0.20/0.47 ((~![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))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(174,plain,
% 0.20/0.47 ((~![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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.47 tff(175,plain,
% 0.20/0.47 (![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[174, 171, 45])).
% 0.20/0.47 tff(176,plain,
% 0.20/0.47 (((~![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(177,plain,
% 0.20/0.47 ((~![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))) | (rel_str(B!11) | (~subrelstr(B!11, A!10)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(178,plain,
% 0.20/0.47 ((~![B: $i] : (rel_str(B) | (~subrelstr(B, A!10)))) | rel_str(B!11) | (~subrelstr(B!11, A!10))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.47 tff(179,plain,
% 0.20/0.47 (rel_str(B!11)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[178, 122, 175])).
% 0.20/0.47 tff(180,plain,
% 0.20/0.47 (^[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)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(181,plain,
% 0.20/0.47 (![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))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[180])).
% 0.20/0.47 tff(182,plain,
% 0.20/0.47 (^[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)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(183,plain,
% 0.20/0.47 (![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))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[182])).
% 0.20/0.47 tff(184,plain,
% 0.20/0.47 (![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))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[183, 181])).
% 0.20/0.47 tff(185,plain,
% 0.20/0.47 (![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))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(186,plain,
% 0.20/0.47 (^[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))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(187,plain,
% 0.20/0.47 (![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))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[186])).
% 0.20/0.47 tff(188,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')).
% 0.20/0.47 tff(189,plain,
% 0.20/0.47 (![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))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.20/0.47 tff(190,plain,
% 0.20/0.47 (![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))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.20/0.47 tff(191,plain,(
% 0.20/0.47 ![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))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[190])).
% 0.20/0.47 tff(192,plain,
% 0.20/0.47 (![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))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.20/0.47 tff(193,plain,
% 0.20/0.47 (((~![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))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(194,plain,
% 0.20/0.47 ((~![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))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(195,plain,
% 0.20/0.47 ((~![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)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.20/0.47 tff(196,plain,
% 0.20/0.47 ((~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)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[195, 192])).
% 0.20/0.47 tff(197,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[196, 179])).
% 0.20/0.47 tff(198,plain,
% 0.20/0.47 (((~![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)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(199,plain,
% 0.20/0.47 ((~![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)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(200,plain,
% 0.20/0.47 ((~![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))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.20/0.47 tff(201,plain,
% 0.20/0.47 ((~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))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[200, 197])).
% 0.20/0.47 tff(202,plain,
% 0.20/0.47 (![C: $i] : ((~element(C, the_carrier(B!11))) | (related(B!11, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(B!11))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[201, 158])).
% 0.20/0.47 tff(203,plain,
% 0.20/0.47 (((~![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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(204,plain,
% 0.20/0.47 ((~![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))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(205,plain,
% 0.20/0.48 ((~![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)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.20/0.48 tff(206,plain,
% 0.20/0.48 (related(B!11, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(B!11))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[205, 202, 154])).
% 0.20/0.48 tff(207,plain,
% 0.20/0.48 (related(B!11, C!12, D!13) <=> related(B!11, E!14, F!15)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[38, 32])).
% 0.20/0.48 tff(208,plain,
% 0.20/0.48 (related(B!11, E!14, F!15) <=> related(B!11, C!12, D!13)),
% 0.20/0.48 inference(symmetry,[status(thm)],[207])).
% 0.20/0.48 tff(209,plain,
% 0.20/0.48 ((~related(B!11, E!14, F!15)) <=> (~related(B!11, C!12, D!13))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[208])).
% 0.20/0.48 tff(210,plain,
% 0.20/0.48 (~related(B!11, E!14, F!15)),
% 0.20/0.48 inference(or_elim,[status(thm)],[29])).
% 0.20/0.48 tff(211,plain,
% 0.20/0.48 (~related(B!11, C!12, D!13)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.20/0.48 tff(212,plain,
% 0.20/0.48 ((~(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)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 (~in(ordered_pair(C!12, D!13), the_InternalRel(B!11))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[212, 211, 206])).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 (~in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[213, 150])).
% 0.20/0.48 tff(215,plain,
% 0.20/0.48 ((~(in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))) <=> (~((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))))))) | in(ordered_pair(C!12, D!13), relation_restriction(the_InternalRel(A!10), the_carrier(B!11))) | ((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(216,plain,
% 0.20/0.48 ((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[215, 214, 104])).
% 0.20/0.48 tff(217,plain,
% 0.20/0.48 (((~![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))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(218,plain,
% 0.20/0.48 ((~![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))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(219,plain,
% 0.20/0.48 ((~![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)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.48 tff(220,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[219, 192, 45])).
% 0.20/0.48 tff(221,plain,
% 0.20/0.48 (element(C!12, the_carrier(A!10))),
% 0.20/0.48 inference(and_elim,[status(thm)],[28])).
% 0.20/0.48 tff(222,plain,
% 0.20/0.48 (((~![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)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(223,plain,
% 0.20/0.48 ((~![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)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(224,plain,
% 0.20/0.48 ((~![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))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.20/0.48 tff(225,plain,
% 0.20/0.48 (![C: $i] : ((~element(C, the_carrier(A!10))) | (related(A!10, C!12, C) <=> in(ordered_pair(C!12, C), the_InternalRel(A!10))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[224, 221, 220])).
% 0.20/0.48 tff(226,plain,
% 0.20/0.48 (element(D!13, the_carrier(A!10))),
% 0.20/0.48 inference(and_elim,[status(thm)],[28])).
% 0.20/0.48 tff(227,plain,
% 0.20/0.48 (((~![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))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(228,plain,
% 0.20/0.48 ((~![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))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(229,plain,
% 0.20/0.48 ((~![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)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.20/0.48 tff(230,plain,
% 0.20/0.48 (related(A!10, C!12, D!13) <=> in(ordered_pair(C!12, D!13), the_InternalRel(A!10))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[229, 226, 225])).
% 0.20/0.48 tff(231,plain,
% 0.20/0.48 (related(A!10, C!12, D!13)),
% 0.20/0.48 inference(and_elim,[status(thm)],[30])).
% 0.20/0.48 tff(232,plain,
% 0.20/0.48 ((~(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))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(233,plain,
% 0.20/0.48 ((~(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))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.20/0.48 tff(234,plain,
% 0.20/0.48 (in(ordered_pair(C!12, D!13), the_InternalRel(A!10))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[233, 230])).
% 0.20/0.48 tff(235,plain,
% 0.20/0.48 ((~((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))))) | (~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(236,plain,
% 0.20/0.48 ((~((~in(ordered_pair(C!12, D!13), the_InternalRel(A!10))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))))) | (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.20/0.48 tff(237,plain,
% 0.20/0.48 (~in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[236, 216])).
% 0.20/0.48 tff(238,plain,
% 0.20/0.48 ((~(in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))) <=> (~((~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11))))))) | in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))) | ((~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(239,plain,
% 0.20/0.48 (~(in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))) <=> (~((~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[238, 237, 44])).
% 0.20/0.48 tff(240,plain,
% 0.20/0.48 (^[A: $i, B: $i, C: $i, D: $i] : refl((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(241,plain,
% 0.20/0.48 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[240])).
% 0.20/0.48 tff(242,plain,
% 0.20/0.48 (^[A: $i, B: $i, C: $i, D: $i] : rewrite((in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(243,plain,
% 0.20/0.48 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[242])).
% 0.20/0.48 tff(244,plain,
% 0.20/0.48 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(245,axiom,(![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t106_zfmisc_1')).
% 0.20/0.48 tff(246,plain,
% 0.20/0.48 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.20/0.48 tff(247,plain,(
% 0.20/0.48 ![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (in(A, C) & in(B, D)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[246])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.20/0.48 tff(249,plain,
% 0.20/0.48 (![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[248, 241])).
% 0.20/0.48 tff(250,plain,
% 0.20/0.48 ((~![A: $i, B: $i, C: $i, D: $i] : (in(ordered_pair(A, B), cartesian_product2(C, D)) <=> (~((~in(A, C)) | (~in(B, D)))))) | (in(ordered_pair(C!12, D!13), cartesian_product2(the_carrier(B!11), the_carrier(B!11))) <=> (~((~in(C!12, the_carrier(B!11))) | (~in(D!13, the_carrier(B!11))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(251,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[250, 249, 239])).
% 0.20/0.48 % SZS output end Proof
%------------------------------------------------------------------------------