TSTP Solution File: SEU133+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU133+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 07:27:39 EDT 2022
% Result : Theorem 0.17s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU133+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 : n024.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
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Sep 3 09:38:03 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.17/0.37 % SZS status Theorem
% 0.17/0.37 % SZS output start Proof
% 0.17/0.37 tff(in_type, type, (
% 0.17/0.37 in: ( $i * $i ) > $o)).
% 0.17/0.37 tff(tptp_fun_B_4_type, type, (
% 0.17/0.37 tptp_fun_B_4: $i)).
% 0.17/0.37 tff(tptp_fun_C_0_type, type, (
% 0.17/0.37 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.17/0.37 tff(set_difference_type, type, (
% 0.17/0.37 set_difference: ( $i * $i ) > $i)).
% 0.17/0.37 tff(tptp_fun_A_5_type, type, (
% 0.17/0.37 tptp_fun_A_5: $i)).
% 0.17/0.37 tff(subset_type, type, (
% 0.17/0.37 subset: ( $i * $i ) > $o)).
% 0.17/0.37 tff(tptp_fun_D_1_type, type, (
% 0.17/0.37 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.17/0.37 tff(1,plain,
% 0.17/0.37 (^[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))))))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(2,plain,
% 0.17/0.37 (![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)))))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.17/0.37 tff(3,plain,
% 0.17/0.37 (^[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))))))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(4,plain,
% 0.17/0.37 (![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)))))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.17/0.37 tff(5,plain,
% 0.17/0.37 (![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)))))))),
% 0.17/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.17/0.37 tff(6,plain,
% 0.17/0.37 (^[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)))))))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(7,plain,
% 0.17/0.37 (![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)))))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.17/0.38 tff(8,plain,
% 0.17/0.38 (![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)))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(9,plain,
% 0.17/0.38 (^[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))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(10,plain,
% 0.17/0.38 (![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)))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.17/0.38 tff(11,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')).
% 0.17/0.38 tff(12,plain,
% 0.17/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.17/0.38 tff(13,plain,
% 0.17/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.17/0.38 tff(14,plain,(
% 0.17/0.38 ![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)))))),
% 0.17/0.38 inference(skolemize,[status(sab)],[13])).
% 0.17/0.38 tff(15,plain,
% 0.17/0.38 (![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)))))))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.17/0.38 tff(16,plain,
% 0.17/0.38 (![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)))))))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.17/0.38 tff(17,plain,
% 0.17/0.38 ((~![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(set_difference(A!5, B!4), A!5)) | ![C: $i] : ((~in(C, set_difference(A!5, B!4))) | in(C, A!5)))) | (~(subset(set_difference(A!5, B!4), A!5) | (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)))))))),
% 0.17/0.38 inference(quant_inst,[status(thm)],[])).
% 0.17/0.38 tff(18,plain,
% 0.17/0.38 (~((~((~subset(set_difference(A!5, B!4), A!5)) | ![C: $i] : ((~in(C, set_difference(A!5, B!4))) | in(C, A!5)))) | (~(subset(set_difference(A!5, B!4), A!5) | (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5))))))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.17/0.38 tff(19,plain,
% 0.17/0.38 (((~((~subset(set_difference(A!5, B!4), A!5)) | ![C: $i] : ((~in(C, set_difference(A!5, B!4))) | in(C, A!5)))) | (~(subset(set_difference(A!5, B!4), A!5) | (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)))))) | (subset(set_difference(A!5, B!4), A!5) | (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5))))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(20,plain,
% 0.17/0.38 (subset(set_difference(A!5, B!4), A!5) | (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.17/0.38 tff(21,plain,
% 0.17/0.38 ((~![A: $i, B: $i] : subset(set_difference(A, B), A)) <=> (~![A: $i, B: $i] : subset(set_difference(A, B), A))),
% 0.17/0.38 inference(rewrite,[status(thm)],[])).
% 0.17/0.38 tff(22,axiom,(~![A: $i, B: $i] : subset(set_difference(A, B), A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t36_xboole_1')).
% 0.17/0.38 tff(23,plain,
% 0.17/0.38 (~![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.17/0.38 tff(24,plain,
% 0.17/0.38 (~![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[23, 21])).
% 0.17/0.38 tff(25,plain,
% 0.17/0.38 (~![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.17/0.38 tff(26,plain,
% 0.17/0.38 (~![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.17/0.38 tff(27,plain,
% 0.17/0.38 (~![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.17/0.38 tff(28,plain,
% 0.17/0.38 (~![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.17/0.38 tff(29,plain,
% 0.17/0.38 (~![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.17/0.38 tff(30,plain,(
% 0.17/0.38 ~subset(set_difference(A!5, B!4), A!5)),
% 0.17/0.38 inference(skolemize,[status(sab)],[29])).
% 0.17/0.38 tff(31,plain,
% 0.17/0.38 ((~(subset(set_difference(A!5, B!4), A!5) | (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5))))) | subset(set_difference(A!5, B!4), A!5) | (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(32,plain,
% 0.17/0.38 ((~(subset(set_difference(A!5, B!4), A!5) | (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5))))) | (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.17/0.38 tff(33,plain,
% 0.17/0.38 (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[32, 20])).
% 0.17/0.38 tff(34,plain,
% 0.17/0.38 (((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | (~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(35,plain,
% 0.17/0.38 (~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.17/0.38 tff(36,plain,
% 0.17/0.38 (((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(37,plain,
% 0.17/0.38 ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.17/0.38 tff(38,plain,
% 0.17/0.38 (((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(39,plain,
% 0.17/0.38 (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[38, 33])).
% 0.17/0.38 tff(40,plain,
% 0.17/0.38 ((~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))) | (~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) | (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))),
% 0.17/0.38 inference(tautology,[status(thm)],[])).
% 0.17/0.38 tff(41,plain,
% 0.17/0.38 (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[40, 39, 37])).
% 0.17/0.38 tff(42,plain,
% 0.17/0.38 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(43,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[42])).
% 0.17/0.38 tff(44,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.17/0.38 inference(pull_quant,[status(thm)],[])).
% 0.17/0.38 tff(45,plain,
% 0.17/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B))))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(46,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[45])).
% 0.17/0.38 tff(47,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.17/0.38 inference(transitivity,[status(thm)],[46, 44])).
% 0.17/0.38 tff(48,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.17/0.38 inference(transitivity,[status(thm)],[47, 43])).
% 0.17/0.38 tff(49,plain,
% 0.17/0.38 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(50,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.17/0.38 tff(51,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.17/0.38 inference(transitivity,[status(thm)],[50, 48])).
% 0.17/0.38 tff(52,plain,
% 0.17/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))), rewrite(((C = set_difference(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))) <=> ((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B)))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) & ((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B))))) & ((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(53,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[52])).
% 0.17/0.38 tff(54,plain,
% 0.17/0.38 (^[A: $i, B: $i, C: $i] : rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.17/0.38 inference(bind,[status(th)],[])).
% 0.17/0.38 tff(55,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))))),
% 0.17/0.38 inference(quant_intro,[status(thm)],[54])).
% 0.17/0.38 tff(56,plain,
% 0.17/0.38 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(57,axiom,(![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_xboole_0')).
% 0.17/0.39 tff(58,plain,
% 0.17/0.39 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.17/0.39 tff(59,plain,(
% 0.17/0.39 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.17/0.39 inference(skolemize,[status(sab)],[58])).
% 0.17/0.39 tff(60,plain,
% 0.17/0.39 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | ((~in(tptp_fun_D_1(C, B, A), C)) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.17/0.39 tff(61,plain,
% 0.17/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.17/0.39 tff(62,plain,
% 0.17/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.17/0.39 tff(63,plain,
% 0.17/0.39 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4))))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(64,plain,
% 0.17/0.39 ((~(in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(65,plain,
% 0.17/0.39 (((in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4))) | $false) <=> (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(66,plain,
% 0.17/0.39 ((~$true) <=> $false),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(67,plain,
% 0.17/0.39 (($true | (in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), A!5)) | in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), B!4)))) <=> $true),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(68,plain,
% 0.17/0.39 ((set_difference(A!5, B!4) = set_difference(A!5, B!4)) <=> $true),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(69,plain,
% 0.17/0.39 (((set_difference(A!5, B!4) = set_difference(A!5, B!4)) | (in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), A!5)) | in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), B!4)))) <=> ($true | (in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), A!5)) | in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), B!4))))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[68])).
% 0.17/0.39 tff(70,plain,
% 0.17/0.39 (((set_difference(A!5, B!4) = set_difference(A!5, B!4)) | (in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), A!5)) | in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), B!4)))) <=> $true),
% 0.17/0.39 inference(transitivity,[status(thm)],[69, 67])).
% 0.17/0.39 tff(71,plain,
% 0.17/0.39 ((~((set_difference(A!5, B!4) = set_difference(A!5, B!4)) | (in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), A!5)) | in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), B!4))))) <=> (~$true)),
% 0.17/0.39 inference(monotonicity,[status(thm)],[70])).
% 0.17/0.39 tff(72,plain,
% 0.17/0.39 ((~((set_difference(A!5, B!4) = set_difference(A!5, B!4)) | (in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), A!5)) | in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), B!4))))) <=> $false),
% 0.17/0.39 inference(transitivity,[status(thm)],[71, 66])).
% 0.17/0.39 tff(73,plain,
% 0.17/0.39 ((~(in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4))))) <=> (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(74,plain,
% 0.17/0.39 (($false | (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4))))) <=> (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4))))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(75,plain,
% 0.17/0.39 ((~(set_difference(A!5, B!4) = set_difference(A!5, B!4))) <=> (~$true)),
% 0.17/0.39 inference(monotonicity,[status(thm)],[68])).
% 0.17/0.39 tff(76,plain,
% 0.17/0.39 ((~(set_difference(A!5, B!4) = set_difference(A!5, B!4))) <=> $false),
% 0.17/0.39 inference(transitivity,[status(thm)],[75, 66])).
% 0.17/0.39 tff(77,plain,
% 0.17/0.39 (((~(set_difference(A!5, B!4) = set_difference(A!5, B!4))) | (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4))))) <=> ($false | (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[76])).
% 0.17/0.39 tff(78,plain,
% 0.17/0.39 (((~(set_difference(A!5, B!4) = set_difference(A!5, B!4))) | (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4))))) <=> (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4))))),
% 0.17/0.39 inference(transitivity,[status(thm)],[77, 74])).
% 0.17/0.39 tff(79,plain,
% 0.17/0.39 ((~((~(set_difference(A!5, B!4) = set_difference(A!5, B!4))) | (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))))) <=> (~(in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[78])).
% 0.17/0.39 tff(80,plain,
% 0.17/0.39 ((~((~(set_difference(A!5, B!4) = set_difference(A!5, B!4))) | (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))))) <=> (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))),
% 0.17/0.39 inference(transitivity,[status(thm)],[79, 73])).
% 0.17/0.39 tff(81,plain,
% 0.17/0.39 (((~((~(set_difference(A!5, B!4) = set_difference(A!5, B!4))) | (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))))) | (~((set_difference(A!5, B!4) = set_difference(A!5, B!4)) | (in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), A!5)) | in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), B!4)))))) <=> ((in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4))) | $false)),
% 0.17/0.39 inference(monotonicity,[status(thm)],[80, 72])).
% 0.17/0.39 tff(82,plain,
% 0.17/0.39 (((~((~(set_difference(A!5, B!4) = set_difference(A!5, B!4))) | (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))))) | (~((set_difference(A!5, B!4) = set_difference(A!5, B!4)) | (in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), A!5)) | in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), B!4)))))) <=> (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))),
% 0.17/0.39 inference(transitivity,[status(thm)],[81, 65])).
% 0.17/0.39 tff(83,plain,
% 0.17/0.39 ((~((~((~(set_difference(A!5, B!4) = set_difference(A!5, B!4))) | (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))))) | (~((set_difference(A!5, B!4) = set_difference(A!5, B!4)) | (in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), A!5)) | in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), B!4))))))) <=> (~(in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4))))),
% 0.17/0.39 inference(monotonicity,[status(thm)],[82])).
% 0.17/0.39 tff(84,plain,
% 0.17/0.39 ((~((~((~(set_difference(A!5, B!4) = set_difference(A!5, B!4))) | (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))))) | (~((set_difference(A!5, B!4) = set_difference(A!5, B!4)) | (in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), A!5)) | in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), B!4))))))) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))),
% 0.17/0.40 inference(transitivity,[status(thm)],[83, 64])).
% 0.17/0.40 tff(85,plain,
% 0.17/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_difference(A!5, B!4) = set_difference(A!5, B!4))) | (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))))) | (~((set_difference(A!5, B!4) = set_difference(A!5, B!4)) | (in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), A!5)) | in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), B!4)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4))))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[84])).
% 0.17/0.40 tff(86,plain,
% 0.17/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_difference(A!5, B!4) = set_difference(A!5, B!4))) | (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))))) | (~((set_difference(A!5, B!4) = set_difference(A!5, B!4)) | (in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), A!5)) | in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), B!4)))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4))))),
% 0.17/0.40 inference(transitivity,[status(thm)],[85, 63])).
% 0.17/0.40 tff(87,plain,
% 0.17/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | (~((~((~(set_difference(A!5, B!4) = set_difference(A!5, B!4))) | (in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4)) <=> (~((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))))) | (~((set_difference(A!5, B!4) = set_difference(A!5, B!4)) | (in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), set_difference(A!5, B!4)) <=> ((~in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), A!5)) | in(tptp_fun_D_1(set_difference(A!5, B!4), B!4, A!5), B!4)))))))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(88,plain,
% 0.17/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (in(D, C) <=> (~((~in(D, A)) | in(D, B)))))) | (~((C = set_difference(A, B)) | (in(tptp_fun_D_1(C, B, A), C) <=> ((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)))))))) | ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), set_difference(A!5, B!4))) <=> ((~in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), A!5)) | in(tptp_fun_C_0(A!5, set_difference(A!5, B!4)), B!4)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.17/0.40 tff(89,plain,
% 0.17/0.40 ($false),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[88, 62, 41])).
% 0.17/0.40 % SZS output end Proof
%------------------------------------------------------------------------------