TSTP Solution File: SET020+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET020+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 05:04:52 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET020+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 01:07:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(tptp_fun_U_9_type, type, (
% 0.19/0.40 tptp_fun_U_9: $i)).
% 0.19/0.40 tff(first_type, type, (
% 0.19/0.40 first: $i > $i)).
% 0.19/0.40 tff(tptp_fun_X_7_type, type, (
% 0.19/0.40 tptp_fun_X_7: $i)).
% 0.19/0.40 tff(ordered_pair_type, type, (
% 0.19/0.40 ordered_pair: ( $i * $i ) > $i)).
% 0.19/0.40 tff(tptp_fun_V_8_type, type, (
% 0.19/0.40 tptp_fun_V_8: $i)).
% 0.19/0.40 tff(second_type, type, (
% 0.19/0.40 second: $i > $i)).
% 0.19/0.40 tff(member_type, type, (
% 0.19/0.40 member: ( $i * $i ) > $o)).
% 0.19/0.40 tff(universal_class_type, type, (
% 0.19/0.40 universal_class: $i)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 ((~![U: $i, V: $i, X: $i] : ((~(member(U, universal_class) & member(V, universal_class) & (X = ordered_pair(U, V)))) | ((first(X) = U) & (second(X) = V)))) <=> (~![U: $i, V: $i, X: $i] : ((~(member(U, universal_class) & member(V, universal_class) & (X = ordered_pair(U, V)))) | ((first(X) = U) & (second(X) = V))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((~![U: $i, V: $i, X: $i] : (((member(U, universal_class) & member(V, universal_class)) & (X = ordered_pair(U, V))) => ((first(X) = U) & (second(X) = V)))) <=> (~![U: $i, V: $i, X: $i] : ((~(member(U, universal_class) & member(V, universal_class) & (X = ordered_pair(U, V)))) | ((first(X) = U) & (second(X) = V))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(3,axiom,(~![U: $i, V: $i, X: $i] : (((member(U, universal_class) & member(V, universal_class)) & (X = ordered_pair(U, V))) => ((first(X) = U) & (second(X) = V)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','unique_1st_and_2nd_in_pair_of_sets1')).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (~![U: $i, V: $i, X: $i] : ((~(member(U, universal_class) & member(V, universal_class) & (X = ordered_pair(U, V)))) | ((first(X) = U) & (second(X) = V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (~![U: $i, V: $i, X: $i] : ((~(member(U, universal_class) & member(V, universal_class) & (X = ordered_pair(U, V)))) | ((first(X) = U) & (second(X) = V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (~![U: $i, V: $i, X: $i] : ((~(member(U, universal_class) & member(V, universal_class) & (X = ordered_pair(U, V)))) | ((first(X) = U) & (second(X) = V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (~![U: $i, V: $i, X: $i] : ((~(member(U, universal_class) & member(V, universal_class) & (X = ordered_pair(U, V)))) | ((first(X) = U) & (second(X) = V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (~![U: $i, V: $i, X: $i] : ((~(member(U, universal_class) & member(V, universal_class) & (X = ordered_pair(U, V)))) | ((first(X) = U) & (second(X) = V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (~![U: $i, V: $i, X: $i] : ((~(member(U, universal_class) & member(V, universal_class) & (X = ordered_pair(U, V)))) | ((first(X) = U) & (second(X) = V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (~![U: $i, V: $i, X: $i] : ((~(member(U, universal_class) & member(V, universal_class) & (X = ordered_pair(U, V)))) | ((first(X) = U) & (second(X) = V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.19/0.40 tff(11,plain,(
% 0.19/0.40 ~((~(member(U!9, universal_class) & member(V!8, universal_class) & (X!7 = ordered_pair(U!9, V!8)))) | ((first(X!7) = U!9) & (second(X!7) = V!8)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[10])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (member(U!9, universal_class) & member(V!8, universal_class) & (X!7 = ordered_pair(U!9, V!8))),
% 0.19/0.40 inference(or_elim,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (member(V!8, universal_class)),
% 0.19/0.40 inference(and_elim,[status(thm)],[12])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (member(U!9, universal_class)),
% 0.19/0.40 inference(and_elim,[status(thm)],[12])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (^[X: $i, Y: $i] : refl(((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y))))) <=> ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y))))) <=> ![X: $i, Y: $i] : ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((member(X, universal_class) & member(Y, universal_class)) <=> (~((~member(Y, universal_class)) | (~member(X, universal_class))))), ((~(member(X, universal_class) & member(Y, universal_class))) <=> (~(~((~member(Y, universal_class)) | (~member(X, universal_class))))))), rewrite((~(~((~member(Y, universal_class)) | (~member(X, universal_class))))) <=> ((~member(Y, universal_class)) | (~member(X, universal_class)))), ((~(member(X, universal_class) & member(Y, universal_class))) <=> ((~member(Y, universal_class)) | (~member(X, universal_class))))), rewrite(((first(ordered_pair(X, Y)) = X) & (second(ordered_pair(X, Y)) = Y)) <=> (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y))))), (((~(member(X, universal_class) & member(Y, universal_class))) | ((first(ordered_pair(X, Y)) = X) & (second(ordered_pair(X, Y)) = Y))) <=> (((~member(Y, universal_class)) | (~member(X, universal_class))) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y))))))), rewrite((((~member(Y, universal_class)) | (~member(X, universal_class))) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y))))) <=> ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y)))))), (((~(member(X, universal_class) & member(Y, universal_class))) | ((first(ordered_pair(X, Y)) = X) & (second(ordered_pair(X, Y)) = Y))) <=> ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~(member(X, universal_class) & member(Y, universal_class))) | ((first(ordered_pair(X, Y)) = X) & (second(ordered_pair(X, Y)) = Y))) <=> ![X: $i, Y: $i] : ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~(member(X, universal_class) & member(Y, universal_class))) | ((first(ordered_pair(X, Y)) = X) & (second(ordered_pair(X, Y)) = Y))) <=> ![X: $i, Y: $i] : ((~(member(X, universal_class) & member(Y, universal_class))) | ((first(ordered_pair(X, Y)) = X) & (second(ordered_pair(X, Y)) = Y)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (^[X: $i, Y: $i] : rewrite(((member(X, universal_class) & member(Y, universal_class)) => ((first(ordered_pair(X, Y)) = X) & (second(ordered_pair(X, Y)) = Y))) <=> ((~(member(X, universal_class) & member(Y, universal_class))) | ((first(ordered_pair(X, Y)) = X) & (second(ordered_pair(X, Y)) = Y))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((member(X, universal_class) & member(Y, universal_class)) => ((first(ordered_pair(X, Y)) = X) & (second(ordered_pair(X, Y)) = Y))) <=> ![X: $i, Y: $i] : ((~(member(X, universal_class) & member(Y, universal_class))) | ((first(ordered_pair(X, Y)) = X) & (second(ordered_pair(X, Y)) = Y)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.40 tff(22,axiom,(![X: $i, Y: $i] : ((member(X, universal_class) & member(Y, universal_class)) => ((first(ordered_pair(X, Y)) = X) & (second(ordered_pair(X, Y)) = Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax','first_second')).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~(member(X, universal_class) & member(Y, universal_class))) | ((first(ordered_pair(X, Y)) = X) & (second(ordered_pair(X, Y)) = Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (![X: $i, Y: $i] : ((~(member(X, universal_class) & member(Y, universal_class))) | ((first(ordered_pair(X, Y)) = X) & (second(ordered_pair(X, Y)) = Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.41 tff(25,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : ((~(member(X, universal_class) & member(Y, universal_class))) | ((first(ordered_pair(X, Y)) = X) & (second(ordered_pair(X, Y)) = Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[24])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (![X: $i, Y: $i] : ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y)))))) | ((~member(U!9, universal_class)) | (~member(V!8, universal_class)) | (~((~(first(ordered_pair(U!9, V!8)) = U!9)) | (~(second(ordered_pair(U!9, V!8)) = V!8)))))) <=> ((~![X: $i, Y: $i] : ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y)))))) | (~member(U!9, universal_class)) | (~member(V!8, universal_class)) | (~((~(first(ordered_pair(U!9, V!8)) = U!9)) | (~(second(ordered_pair(U!9, V!8)) = V!8)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (((~member(V!8, universal_class)) | (~member(U!9, universal_class)) | (~((~(first(ordered_pair(U!9, V!8)) = U!9)) | (~(second(ordered_pair(U!9, V!8)) = V!8))))) <=> ((~member(U!9, universal_class)) | (~member(V!8, universal_class)) | (~((~(first(ordered_pair(U!9, V!8)) = U!9)) | (~(second(ordered_pair(U!9, V!8)) = V!8)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y)))))) | ((~member(V!8, universal_class)) | (~member(U!9, universal_class)) | (~((~(first(ordered_pair(U!9, V!8)) = U!9)) | (~(second(ordered_pair(U!9, V!8)) = V!8)))))) <=> ((~![X: $i, Y: $i] : ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y)))))) | ((~member(U!9, universal_class)) | (~member(V!8, universal_class)) | (~((~(first(ordered_pair(U!9, V!8)) = U!9)) | (~(second(ordered_pair(U!9, V!8)) = V!8))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[29])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y)))))) | ((~member(V!8, universal_class)) | (~member(U!9, universal_class)) | (~((~(first(ordered_pair(U!9, V!8)) = U!9)) | (~(second(ordered_pair(U!9, V!8)) = V!8)))))) <=> ((~![X: $i, Y: $i] : ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y)))))) | (~member(U!9, universal_class)) | (~member(V!8, universal_class)) | (~((~(first(ordered_pair(U!9, V!8)) = U!9)) | (~(second(ordered_pair(U!9, V!8)) = V!8)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[30, 28])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y)))))) | ((~member(V!8, universal_class)) | (~member(U!9, universal_class)) | (~((~(first(ordered_pair(U!9, V!8)) = U!9)) | (~(second(ordered_pair(U!9, V!8)) = V!8)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : ((~member(Y, universal_class)) | (~member(X, universal_class)) | (~((~(first(ordered_pair(X, Y)) = X)) | (~(second(ordered_pair(X, Y)) = Y)))))) | (~member(U!9, universal_class)) | (~member(V!8, universal_class)) | (~((~(first(ordered_pair(U!9, V!8)) = U!9)) | (~(second(ordered_pair(U!9, V!8)) = V!8))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (~((~(first(ordered_pair(U!9, V!8)) = U!9)) | (~(second(ordered_pair(U!9, V!8)) = V!8)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[33, 27, 14, 13])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (((~(first(ordered_pair(U!9, V!8)) = U!9)) | (~(second(ordered_pair(U!9, V!8)) = V!8))) | (first(ordered_pair(U!9, V!8)) = U!9)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (first(ordered_pair(U!9, V!8)) = U!9),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (X!7 = ordered_pair(U!9, V!8)),
% 0.19/0.41 inference(and_elim,[status(thm)],[12])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (first(X!7) = first(ordered_pair(U!9, V!8))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (first(X!7) = U!9),
% 0.19/0.41 inference(transitivity,[status(thm)],[38, 36])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (((~(first(ordered_pair(U!9, V!8)) = U!9)) | (~(second(ordered_pair(U!9, V!8)) = V!8))) | (second(ordered_pair(U!9, V!8)) = V!8)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (second(ordered_pair(U!9, V!8)) = V!8),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[40, 34])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (second(X!7) = second(ordered_pair(U!9, V!8))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (second(X!7) = V!8),
% 0.19/0.41 inference(transitivity,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ((~(~((~(first(X!7) = U!9)) | (~(second(X!7) = V!8))))) <=> ((~(first(X!7) = U!9)) | (~(second(X!7) = V!8)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (((first(X!7) = U!9) & (second(X!7) = V!8)) <=> (~((~(first(X!7) = U!9)) | (~(second(X!7) = V!8))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 ((~((first(X!7) = U!9) & (second(X!7) = V!8))) <=> (~(~((~(first(X!7) = U!9)) | (~(second(X!7) = V!8)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 ((~((first(X!7) = U!9) & (second(X!7) = V!8))) <=> ((~(first(X!7) = U!9)) | (~(second(X!7) = V!8)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[46, 44])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (~((first(X!7) = U!9) & (second(X!7) = V!8))),
% 0.19/0.41 inference(or_elim,[status(thm)],[11])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 ((~(first(X!7) = U!9)) | (~(second(X!7) = V!8))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[49, 43, 39])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------