TSTP Solution File: SEU250+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU250+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 07:28:30 EDT 2022
% Result : Theorem 0.16s 0.38s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU250+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Sep 3 11:18:54 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.16/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.32 Usage: tptp [options] [-file:]file
% 0.16/0.32 -h, -? prints this message.
% 0.16/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.32 -m, -model generate model.
% 0.16/0.32 -p, -proof generate proof.
% 0.16/0.32 -c, -core generate unsat core of named formulas.
% 0.16/0.32 -st, -statistics display statistics.
% 0.16/0.32 -t:timeout set timeout (in second).
% 0.16/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.32 -<param>:<value> configuration parameter and value.
% 0.16/0.32 -o:<output-file> file to place output in.
% 0.16/0.38 % SZS status Theorem
% 0.16/0.38 % SZS output start Proof
% 0.16/0.38 tff(in_type, type, (
% 0.16/0.38 in: ( $i * $i ) > $o)).
% 0.16/0.38 tff(tptp_fun_A_8_type, type, (
% 0.16/0.38 tptp_fun_A_8: $i)).
% 0.16/0.38 tff(tptp_fun_C_0_type, type, (
% 0.16/0.38 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.16/0.38 tff(relation_field_type, type, (
% 0.16/0.38 relation_field: $i > $i)).
% 0.16/0.38 tff(relation_restriction_type, type, (
% 0.16/0.38 relation_restriction: ( $i * $i ) > $i)).
% 0.16/0.38 tff(tptp_fun_B_7_type, type, (
% 0.16/0.38 tptp_fun_B_7: $i)).
% 0.16/0.38 tff(subset_type, type, (
% 0.16/0.38 subset: ( $i * $i ) > $o)).
% 0.16/0.38 tff(relation_type, type, (
% 0.16/0.38 relation: $i > $o)).
% 0.16/0.38 tff(set_union2_type, type, (
% 0.16/0.38 set_union2: ( $i * $i ) > $i)).
% 0.16/0.38 tff(relation_rng_type, type, (
% 0.16/0.38 relation_rng: $i > $i)).
% 0.16/0.38 tff(relation_dom_type, type, (
% 0.16/0.38 relation_dom: $i > $i)).
% 0.16/0.38 tff(1,assumption,(~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8))), introduced(assumption)).
% 0.16/0.38 tff(2,plain,
% 0.16/0.38 (((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(3,plain,
% 0.16/0.38 (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.16/0.38 tff(4,plain,
% 0.16/0.38 (((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(5,plain,
% 0.16/0.38 ((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7)))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[4, 3])).
% 0.16/0.38 tff(6,plain,
% 0.16/0.38 (((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(7,plain,
% 0.16/0.38 (in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.16/0.38 tff(8,plain,
% 0.16/0.38 ((~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(9,plain,
% 0.16/0.38 ((~![A: $i, B: $i] : (relation(B) => (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))) <=> (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(10,axiom,(~![A: $i, B: $i] : (relation(B) => (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t20_wellord1')).
% 0.16/0.38 tff(11,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.16/0.38 tff(12,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[11, 8])).
% 0.16/0.38 tff(13,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.16/0.38 tff(14,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[13, 8])).
% 0.16/0.38 tff(15,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[14, 8])).
% 0.16/0.38 tff(16,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.16/0.38 tff(17,plain,
% 0.16/0.38 (~![A: $i, B: $i] : ((~relation(B)) | (subset(relation_field(relation_restriction(B, A)), relation_field(B)) & subset(relation_field(relation_restriction(B, A)), A)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[16, 8])).
% 0.16/0.38 tff(18,plain,(
% 0.16/0.38 ~((~relation(B!7)) | (subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7)) & subset(relation_field(relation_restriction(B!7, A!8)), A!8)))),
% 0.16/0.38 inference(skolemize,[status(sab)],[17])).
% 0.16/0.38 tff(19,plain,
% 0.16/0.38 (relation(B!7)),
% 0.16/0.38 inference(or_elim,[status(thm)],[18])).
% 0.16/0.38 tff(20,plain,
% 0.16/0.38 (^[A: $i, B: $i, C: $i] : refl(((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B))))) <=> ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(21,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.16/0.38 tff(22,plain,
% 0.16/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_field(C)) & in(A, B)) <=> (~((~in(A, relation_field(C))) | (~in(A, B))))), (((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ((~((~in(A, relation_field(C))) | (~in(A, B)))) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))))), rewrite(((~((~in(A, relation_field(C))) | (~in(A, B)))) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))), (((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(23,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.16/0.38 tff(24,plain,
% 0.16/0.38 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(25,plain,
% 0.16/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B))) <=> ((~in(A, relation_field(relation_restriction(C, B)))) | (in(A, relation_field(C)) & in(A, B)))), ((relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B)))) <=> (relation(C) => ((~in(A, relation_field(relation_restriction(C, B)))) | (in(A, relation_field(C)) & in(A, B)))))), rewrite((relation(C) => ((~in(A, relation_field(relation_restriction(C, B)))) | (in(A, relation_field(C)) & in(A, B)))) <=> ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))), ((relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B)))) <=> ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(26,plain,
% 0.16/0.39 (![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.16/0.39 tff(27,axiom,(![A: $i, B: $i, C: $i] : (relation(C) => (in(A, relation_field(relation_restriction(C, B))) => (in(A, relation_field(C)) & in(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t19_wellord1')).
% 0.16/0.39 tff(28,plain,
% 0.16/0.39 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.16/0.39 tff(29,plain,
% 0.16/0.39 (![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.16/0.39 tff(30,plain,(
% 0.16/0.39 ![A: $i, B: $i, C: $i] : ((in(A, relation_field(C)) & in(A, B)) | (~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))))),
% 0.16/0.39 inference(skolemize,[status(sab)],[29])).
% 0.16/0.39 tff(31,plain,
% 0.16/0.39 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.16/0.39 tff(32,plain,
% 0.16/0.39 (![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.16/0.39 tff(33,plain,
% 0.16/0.39 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(34,plain,
% 0.16/0.39 (((~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8))))) <=> ((~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(35,plain,
% 0.16/0.39 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7)))))))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[34])).
% 0.16/0.39 tff(36,plain,
% 0.16/0.39 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))))))),
% 0.16/0.39 inference(transitivity,[status(thm)],[35, 33])).
% 0.16/0.39 tff(37,plain,
% 0.16/0.39 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)))))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(38,plain,
% 0.16/0.39 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!7)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)) | (~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(B!7)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.16/0.39 tff(39,plain,
% 0.16/0.39 ($false),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[38, 32, 19, 7, 5])).
% 0.16/0.39 tff(40,plain,((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.39 tff(41,plain,
% 0.16/0.39 (^[A: $i] : refl(((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(42,plain,
% 0.16/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.16/0.39 tff(43,plain,
% 0.16/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(44,plain,
% 0.16/0.39 (^[A: $i] : rewrite((relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(45,plain,
% 0.16/0.39 (![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A)))) <=> ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[44])).
% 0.16/0.39 tff(46,axiom,(![A: $i] : (relation(A) => (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_relat_1')).
% 0.16/0.39 tff(47,plain,
% 0.16/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.16/0.39 tff(48,plain,
% 0.16/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.16/0.39 tff(49,plain,(
% 0.16/0.39 ![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.16/0.39 inference(skolemize,[status(sab)],[48])).
% 0.16/0.39 tff(50,plain,
% 0.16/0.39 (![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.16/0.39 tff(51,plain,
% 0.16/0.39 (((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(B!7)) | (relation_field(B!7) = set_union2(relation_dom(B!7), relation_rng(B!7))))) <=> ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(B!7)) | (relation_field(B!7) = set_union2(relation_dom(B!7), relation_rng(B!7))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(52,plain,
% 0.16/0.39 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | ((~relation(B!7)) | (relation_field(B!7) = set_union2(relation_dom(B!7), relation_rng(B!7))))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(53,plain,
% 0.16/0.39 ((~![A: $i] : ((~relation(A)) | (relation_field(A) = set_union2(relation_dom(A), relation_rng(A))))) | (~relation(B!7)) | (relation_field(B!7) = set_union2(relation_dom(B!7), relation_rng(B!7)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.16/0.39 tff(54,plain,
% 0.16/0.39 (relation_field(B!7) = set_union2(relation_dom(B!7), relation_rng(B!7))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[53, 50, 19])).
% 0.16/0.39 tff(55,plain,
% 0.16/0.39 (set_union2(relation_dom(B!7), relation_rng(B!7)) = relation_field(B!7)),
% 0.16/0.39 inference(symmetry,[status(thm)],[54])).
% 0.16/0.39 tff(56,plain,
% 0.16/0.39 (subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) <=> subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[55])).
% 0.16/0.39 tff(57,plain,
% 0.16/0.39 (subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7)) <=> subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7)))),
% 0.16/0.39 inference(symmetry,[status(thm)],[56])).
% 0.16/0.39 tff(58,plain,
% 0.16/0.39 ((~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))) <=> (~subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))))),
% 0.16/0.39 inference(monotonicity,[status(thm)],[57])).
% 0.16/0.39 tff(59,assumption,(~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))), introduced(assumption)).
% 0.16/0.39 tff(60,plain,
% 0.16/0.39 (~subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.16/0.39 tff(61,plain,
% 0.16/0.39 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(62,plain,
% 0.16/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.16/0.39 tff(63,plain,
% 0.16/0.39 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(64,plain,
% 0.16/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.16/0.39 tff(65,plain,
% 0.16/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.16/0.39 inference(transitivity,[status(thm)],[64, 62])).
% 0.16/0.39 tff(66,plain,
% 0.16/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(67,plain,
% 0.16/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[66])).
% 0.16/0.39 tff(68,plain,
% 0.16/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(69,plain,
% 0.16/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(70,plain,
% 0.16/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[69])).
% 0.16/0.39 tff(71,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.16/0.39 tff(72,plain,
% 0.16/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.16/0.39 tff(73,plain,
% 0.16/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.16/0.39 tff(74,plain,(
% 0.16/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.16/0.39 inference(skolemize,[status(sab)],[73])).
% 0.16/0.39 tff(75,plain,
% 0.16/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.16/0.39 tff(76,plain,
% 0.16/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.16/0.39 tff(77,plain,
% 0.16/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7)))) | ![C: $i] : ((~in(C, relation_field(relation_restriction(B!7, A!8)))) | in(C, set_union2(relation_dom(B!7), relation_rng(B!7)))))) | (~(subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))))))))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(78,plain,
% 0.16/0.39 (~((~((~subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7)))) | ![C: $i] : ((~in(C, relation_field(relation_restriction(B!7, A!8)))) | in(C, set_union2(relation_dom(B!7), relation_rng(B!7)))))) | (~(subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7))))))))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.16/0.39 tff(79,plain,
% 0.16/0.39 (((~((~subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7)))) | ![C: $i] : ((~in(C, relation_field(relation_restriction(B!7, A!8)))) | in(C, set_union2(relation_dom(B!7), relation_rng(B!7)))))) | (~(subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))))))) | (subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7))))))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(80,plain,
% 0.16/0.40 (subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.16/0.40 tff(81,plain,
% 0.16/0.40 (in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7)) <=> in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))),
% 0.16/0.40 inference(monotonicity,[status(thm)],[54])).
% 0.16/0.40 tff(82,plain,
% 0.16/0.40 (in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7))) <=> in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))),
% 0.16/0.40 inference(symmetry,[status(thm)],[81])).
% 0.16/0.40 tff(83,plain,
% 0.16/0.40 ((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))) <=> (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7)))),
% 0.16/0.40 inference(monotonicity,[status(thm)],[82])).
% 0.16/0.40 tff(84,assumption,(~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7))))), introduced(assumption)).
% 0.16/0.40 tff(85,plain,
% 0.16/0.40 (((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7))))),
% 0.16/0.40 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(86,plain,
% 0.16/0.40 (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.16/0.40 tff(87,plain,
% 0.16/0.40 (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[86, 83])).
% 0.16/0.40 tff(88,plain,
% 0.16/0.40 (((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))),
% 0.16/0.40 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(89,plain,
% 0.16/0.40 (in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[88, 84])).
% 0.16/0.40 tff(90,plain,
% 0.16/0.40 (((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), A!8)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!7)) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), A!8)))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(91,plain,
% 0.16/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | ((~relation(B!7)) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), A!8)))))),
% 0.16/0.40 inference(quant_inst,[status(thm)],[])).
% 0.16/0.40 tff(92,plain,
% 0.16/0.40 ((~![A: $i, B: $i, C: $i] : ((~relation(C)) | (~in(A, relation_field(relation_restriction(C, B)))) | (~((~in(A, relation_field(C))) | (~in(A, B)))))) | (~relation(B!7)) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), A!8))))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.16/0.40 tff(93,plain,
% 0.16/0.40 (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), A!8)))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[92, 32, 19, 89])).
% 0.16/0.40 tff(94,plain,
% 0.16/0.40 (((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))) | (~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), A!8))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))),
% 0.16/0.40 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(95,plain,
% 0.16/0.40 (in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(B!7))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.16/0.40 tff(96,plain,
% 0.16/0.40 ($false),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[95, 87])).
% 0.16/0.40 tff(97,plain,((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.40 tff(98,plain,
% 0.16/0.40 ((~(subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7))))))) | subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7)))))),
% 0.16/0.40 inference(tautology,[status(thm)],[])).
% 0.16/0.40 tff(99,plain,
% 0.16/0.40 ((~(subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7))) | (~((~in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(set_union2(relation_dom(B!7), relation_rng(B!7)), relation_field(relation_restriction(B!7, A!8))), set_union2(relation_dom(B!7), relation_rng(B!7))))))) | subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7)))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.16/0.40 tff(100,plain,
% 0.16/0.40 (subset(relation_field(relation_restriction(B!7, A!8)), set_union2(relation_dom(B!7), relation_rng(B!7)))),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[99, 80])).
% 0.16/0.40 tff(101,plain,
% 0.16/0.40 ($false),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[100, 60])).
% 0.16/0.40 tff(102,plain,(subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))), inference(lemma,lemma(discharge,[]))).
% 0.16/0.40 tff(103,plain,
% 0.16/0.40 ((~(~((~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~subset(relation_field(relation_restriction(B!7, A!8)), A!8))))) <=> ((~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~subset(relation_field(relation_restriction(B!7, A!8)), A!8)))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(104,plain,
% 0.16/0.40 ((subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7)) & subset(relation_field(relation_restriction(B!7, A!8)), A!8)) <=> (~((~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~subset(relation_field(relation_restriction(B!7, A!8)), A!8))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(105,plain,
% 0.16/0.40 ((~(subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7)) & subset(relation_field(relation_restriction(B!7, A!8)), A!8))) <=> (~(~((~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~subset(relation_field(relation_restriction(B!7, A!8)), A!8)))))),
% 0.16/0.40 inference(monotonicity,[status(thm)],[104])).
% 0.16/0.40 tff(106,plain,
% 0.16/0.40 ((~(subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7)) & subset(relation_field(relation_restriction(B!7, A!8)), A!8))) <=> ((~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~subset(relation_field(relation_restriction(B!7, A!8)), A!8)))),
% 0.16/0.40 inference(transitivity,[status(thm)],[105, 103])).
% 0.16/0.40 tff(107,plain,
% 0.16/0.40 (~(subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7)) & subset(relation_field(relation_restriction(B!7, A!8)), A!8))),
% 0.16/0.40 inference(or_elim,[status(thm)],[18])).
% 0.16/0.40 tff(108,plain,
% 0.16/0.40 ((~subset(relation_field(relation_restriction(B!7, A!8)), relation_field(B!7))) | (~subset(relation_field(relation_restriction(B!7, A!8)), A!8))),
% 0.16/0.40 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.16/0.40 tff(109,plain,
% 0.16/0.40 (~subset(relation_field(relation_restriction(B!7, A!8)), A!8)),
% 0.16/0.40 inference(unit_resolution,[status(thm)],[108, 102])).
% 0.16/0.40 tff(110,plain,
% 0.16/0.40 ((~(subset(relation_field(relation_restriction(B!7, A!8)), A!8) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8))))) | subset(relation_field(relation_restriction(B!7, A!8)), A!8) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(111,plain,
% 0.16/0.41 (~(subset(relation_field(relation_restriction(B!7, A!8)), A!8) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8))))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[110, 109, 40])).
% 0.16/0.41 tff(112,plain,
% 0.16/0.41 (((~((~subset(relation_field(relation_restriction(B!7, A!8)), A!8)) | ![C: $i] : ((~in(C, relation_field(relation_restriction(B!7, A!8)))) | in(C, A!8)))) | (~(subset(relation_field(relation_restriction(B!7, A!8)), A!8) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)))))) | (subset(relation_field(relation_restriction(B!7, A!8)), A!8) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8))))),
% 0.16/0.41 inference(tautology,[status(thm)],[])).
% 0.16/0.41 tff(113,plain,
% 0.16/0.41 ((~((~subset(relation_field(relation_restriction(B!7, A!8)), A!8)) | ![C: $i] : ((~in(C, relation_field(relation_restriction(B!7, A!8)))) | in(C, A!8)))) | (~(subset(relation_field(relation_restriction(B!7, A!8)), A!8) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)))))),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.16/0.41 tff(114,plain,
% 0.16/0.41 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(relation_field(relation_restriction(B!7, A!8)), A!8)) | ![C: $i] : ((~in(C, relation_field(relation_restriction(B!7, A!8)))) | in(C, A!8)))) | (~(subset(relation_field(relation_restriction(B!7, A!8)), A!8) | (~((~in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), relation_field(relation_restriction(B!7, A!8)))) | in(tptp_fun_C_0(A!8, relation_field(relation_restriction(B!7, A!8))), A!8)))))))),
% 0.16/0.41 inference(quant_inst,[status(thm)],[])).
% 0.16/0.41 tff(115,plain,
% 0.16/0.41 ($false),
% 0.16/0.41 inference(unit_resolution,[status(thm)],[114, 76, 113])).
% 0.16/0.41 % SZS output end Proof
%------------------------------------------------------------------------------