TSTP Solution File: SET979+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 05:08:48 EDT 2022
% Result : Theorem 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n029.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Sep 3 08:59:30 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.34 Usage: tptp [options] [-file:]file
% 0.11/0.34 -h, -? prints this message.
% 0.11/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.34 -m, -model generate model.
% 0.11/0.34 -p, -proof generate proof.
% 0.11/0.34 -c, -core generate unsat core of named formulas.
% 0.11/0.34 -st, -statistics display statistics.
% 0.11/0.34 -t:timeout set timeout (in second).
% 0.11/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.34 -<param>:<value> configuration parameter and value.
% 0.11/0.34 -o:<output-file> file to place output in.
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(set_union2_type, type, (
% 0.11/0.38 set_union2: ( $i * $i ) > $i)).
% 0.11/0.38 tff(cartesian_product2_type, type, (
% 0.11/0.38 cartesian_product2: ( $i * $i ) > $i)).
% 0.11/0.38 tff(tptp_fun_C_2_type, type, (
% 0.11/0.38 tptp_fun_C_2: $i)).
% 0.11/0.38 tff(singleton_type, type, (
% 0.11/0.38 singleton: $i > $i)).
% 0.11/0.38 tff(tptp_fun_B_3_type, type, (
% 0.11/0.38 tptp_fun_B_3: $i)).
% 0.11/0.38 tff(tptp_fun_A_4_type, type, (
% 0.11/0.38 tptp_fun_A_4: $i)).
% 0.11/0.38 tff(unordered_pair_type, type, (
% 0.11/0.38 unordered_pair: ( $i * $i ) > $i)).
% 0.11/0.38 tff(1,plain,
% 0.11/0.38 (^[A: $i, B: $i, C: $i] : refl((~((~(cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C)))) | (~(cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B)))))) <=> (~((~(cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C)))) | (~(cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : (~((~(cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C)))) | (~(cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~(cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C)))) | (~(cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (^[A: $i, B: $i, C: $i] : rewrite(((cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C))) & (cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B)))) <=> (~((~(cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C)))) | (~(cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B)))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : ((cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C))) & (cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B)))) <=> ![A: $i, B: $i, C: $i] : (~((~(cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C)))) | (~(cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : ((cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C))) & (cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B)))) <=> ![A: $i, B: $i, C: $i] : ((cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C))) & (cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(6,axiom,(![A: $i, B: $i, C: $i] : ((cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C))) & (cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t120_zfmisc_1')).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : ((cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C))) & (cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.11/0.38 tff(8,plain,(
% 0.11/0.38 ![A: $i, B: $i, C: $i] : ((cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C))) & (cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[7])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : (~((~(cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C)))) | (~(cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : (~((~(cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C)))) | (~(cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 ((~![A: $i, B: $i, C: $i] : (~((~(cartesian_product2(set_union2(A, B), C) = set_union2(cartesian_product2(A, C), cartesian_product2(B, C)))) | (~(cartesian_product2(C, set_union2(A, B)) = set_union2(cartesian_product2(C, A), cartesian_product2(C, B))))))) | (~((~(cartesian_product2(set_union2(singleton(A!4), singleton(B!3)), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2)))) | (~(cartesian_product2(C!2, set_union2(singleton(A!4), singleton(B!3))) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3)))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (~((~(cartesian_product2(set_union2(singleton(A!4), singleton(B!3)), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2)))) | (~(cartesian_product2(C!2, set_union2(singleton(A!4), singleton(B!3))) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (((~(cartesian_product2(set_union2(singleton(A!4), singleton(B!3)), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2)))) | (~(cartesian_product2(C!2, set_union2(singleton(A!4), singleton(B!3))) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3)))))) | (cartesian_product2(set_union2(singleton(A!4), singleton(B!3)), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (cartesian_product2(set_union2(singleton(A!4), singleton(B!3)), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = set_union2(singleton(A), singleton(B))) <=> (unordered_pair(A, B) = set_union2(singleton(A), singleton(B))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B))) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B))) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(18,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t41_enumset1')).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.38 tff(20,plain,(
% 0.11/0.38 ![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[19])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : (unordered_pair(A, B) = set_union2(singleton(A), singleton(B)))) | (unordered_pair(A!4, B!3) = set_union2(singleton(A!4), singleton(B!3)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (unordered_pair(A!4, B!3) = set_union2(singleton(A!4), singleton(B!3))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (cartesian_product2(unordered_pair(A!4, B!3), C!2) = cartesian_product2(set_union2(singleton(A!4), singleton(B!3)), C!2)),
% 0.11/0.38 inference(monotonicity,[status(thm)],[23])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (cartesian_product2(unordered_pair(A!4, B!3), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2))),
% 0.11/0.38 inference(transitivity,[status(thm)],[24, 14])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 (((~(cartesian_product2(set_union2(singleton(A!4), singleton(B!3)), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2)))) | (~(cartesian_product2(C!2, set_union2(singleton(A!4), singleton(B!3))) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3)))))) | (cartesian_product2(C!2, set_union2(singleton(A!4), singleton(B!3))) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3))))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 (cartesian_product2(C!2, set_union2(singleton(A!4), singleton(B!3))) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[26, 12])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (cartesian_product2(C!2, unordered_pair(A!4, B!3)) = cartesian_product2(C!2, set_union2(singleton(A!4), singleton(B!3)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[23])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (cartesian_product2(C!2, unordered_pair(A!4, B!3)) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3)))),
% 0.11/0.38 inference(transitivity,[status(thm)],[28, 27])).
% 0.11/0.38 tff(30,assumption,(~(cartesian_product2(C!2, unordered_pair(A!4, B!3)) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3))))), introduced(assumption)).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.11/0.38 tff(32,plain,(cartesian_product2(C!2, unordered_pair(A!4, B!3)) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3)))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 ((~(~((~(cartesian_product2(unordered_pair(A!4, B!3), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2)))) | (~(cartesian_product2(C!2, unordered_pair(A!4, B!3)) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3)))))))) <=> ((~(cartesian_product2(unordered_pair(A!4, B!3), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2)))) | (~(cartesian_product2(C!2, unordered_pair(A!4, B!3)) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 (((cartesian_product2(unordered_pair(A!4, B!3), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2))) & (cartesian_product2(C!2, unordered_pair(A!4, B!3)) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3))))) <=> (~((~(cartesian_product2(unordered_pair(A!4, B!3), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2)))) | (~(cartesian_product2(C!2, unordered_pair(A!4, B!3)) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3)))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 ((~((cartesian_product2(unordered_pair(A!4, B!3), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2))) & (cartesian_product2(C!2, unordered_pair(A!4, B!3)) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3)))))) <=> (~(~((~(cartesian_product2(unordered_pair(A!4, B!3), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2)))) | (~(cartesian_product2(C!2, unordered_pair(A!4, B!3)) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3))))))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[34])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 ((~((cartesian_product2(unordered_pair(A!4, B!3), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2))) & (cartesian_product2(C!2, unordered_pair(A!4, B!3)) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3)))))) <=> ((~(cartesian_product2(unordered_pair(A!4, B!3), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2)))) | (~(cartesian_product2(C!2, unordered_pair(A!4, B!3)) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[35, 33])).
% 0.11/0.38 tff(37,plain,
% 0.11/0.38 ((~![A: $i, B: $i, C: $i] : ((cartesian_product2(unordered_pair(A, B), C) = set_union2(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), C))) & (cartesian_product2(C, unordered_pair(A, B)) = set_union2(cartesian_product2(C, singleton(A)), cartesian_product2(C, singleton(B)))))) <=> (~![A: $i, B: $i, C: $i] : ((cartesian_product2(unordered_pair(A, B), C) = set_union2(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), C))) & (cartesian_product2(C, unordered_pair(A, B)) = set_union2(cartesian_product2(C, singleton(A)), cartesian_product2(C, singleton(B))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(38,axiom,(~![A: $i, B: $i, C: $i] : ((cartesian_product2(unordered_pair(A, B), C) = set_union2(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), C))) & (cartesian_product2(C, unordered_pair(A, B)) = set_union2(cartesian_product2(C, singleton(A)), cartesian_product2(C, singleton(B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t132_zfmisc_1')).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (~![A: $i, B: $i, C: $i] : ((cartesian_product2(unordered_pair(A, B), C) = set_union2(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), C))) & (cartesian_product2(C, unordered_pair(A, B)) = set_union2(cartesian_product2(C, singleton(A)), cartesian_product2(C, singleton(B)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (~![A: $i, B: $i, C: $i] : ((cartesian_product2(unordered_pair(A, B), C) = set_union2(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), C))) & (cartesian_product2(C, unordered_pair(A, B)) = set_union2(cartesian_product2(C, singleton(A)), cartesian_product2(C, singleton(B)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[39, 37])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (~![A: $i, B: $i, C: $i] : ((cartesian_product2(unordered_pair(A, B), C) = set_union2(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), C))) & (cartesian_product2(C, unordered_pair(A, B)) = set_union2(cartesian_product2(C, singleton(A)), cartesian_product2(C, singleton(B)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (~![A: $i, B: $i, C: $i] : ((cartesian_product2(unordered_pair(A, B), C) = set_union2(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), C))) & (cartesian_product2(C, unordered_pair(A, B)) = set_union2(cartesian_product2(C, singleton(A)), cartesian_product2(C, singleton(B)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (~![A: $i, B: $i, C: $i] : ((cartesian_product2(unordered_pair(A, B), C) = set_union2(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), C))) & (cartesian_product2(C, unordered_pair(A, B)) = set_union2(cartesian_product2(C, singleton(A)), cartesian_product2(C, singleton(B)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[42, 37])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (~![A: $i, B: $i, C: $i] : ((cartesian_product2(unordered_pair(A, B), C) = set_union2(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), C))) & (cartesian_product2(C, unordered_pair(A, B)) = set_union2(cartesian_product2(C, singleton(A)), cartesian_product2(C, singleton(B)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[43, 37])).
% 0.11/0.39 tff(45,plain,
% 0.11/0.39 (~![A: $i, B: $i, C: $i] : ((cartesian_product2(unordered_pair(A, B), C) = set_union2(cartesian_product2(singleton(A), C), cartesian_product2(singleton(B), C))) & (cartesian_product2(C, unordered_pair(A, B)) = set_union2(cartesian_product2(C, singleton(A)), cartesian_product2(C, singleton(B)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.11/0.39 tff(46,plain,(
% 0.11/0.39 ~((cartesian_product2(unordered_pair(A!4, B!3), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2))) & (cartesian_product2(C!2, unordered_pair(A!4, B!3)) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3)))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[45])).
% 0.11/0.39 tff(47,plain,
% 0.11/0.39 ((~(cartesian_product2(unordered_pair(A!4, B!3), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2)))) | (~(cartesian_product2(C!2, unordered_pair(A!4, B!3)) = set_union2(cartesian_product2(C!2, singleton(A!4)), cartesian_product2(C!2, singleton(B!3)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.11/0.39 tff(48,plain,
% 0.11/0.39 (~(cartesian_product2(unordered_pair(A!4, B!3), C!2) = set_union2(cartesian_product2(singleton(A!4), C!2), cartesian_product2(singleton(B!3), C!2)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[47, 32])).
% 0.11/0.39 tff(49,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[48, 25])).
% 0.11/0.39 % SZS output end Proof
%------------------------------------------------------------------------------