%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU080+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 : Sat Jun 21 05:26:52 AM UTC 2025
% Result : Theorem 3.74s 3.94s
% Output : Proof 3.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU080+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 06:00:53 EDT 2025
% 0.14/0.36 % CPUTime :
% 3.74/3.94 % SZS status Theorem
% 3.74/3.94 % SZS output start Proof
% 3.74/3.94 tff(tptp_fun_B_12_type, type, (
% 3.74/3.94 tptp_fun_B_12: $i)).
% 3.74/3.94 tff(tptp_fun_A_13_type, type, (
% 3.74/3.94 tptp_fun_A_13: $i)).
% 3.74/3.94 tff(subset_type, type, (
% 3.74/3.94 subset: ( $i * $i ) > $o)).
% 3.74/3.94 tff(relation_inverse_image_type, type, (
% 3.74/3.94 relation_inverse_image: ( $i * $i ) > $i)).
% 3.74/3.94 tff(tptp_fun_C_11_type, type, (
% 3.74/3.94 tptp_fun_C_11: $i)).
% 3.74/3.94 tff(relation_rng_type, type, (
% 3.74/3.94 relation_rng: $i > $i)).
% 3.74/3.94 tff(function_type, type, (
% 3.74/3.94 function: $i > $o)).
% 3.74/3.94 tff(relation_type, type, (
% 3.74/3.94 relation: $i > $o)).
% 3.74/3.94 tff(1,plain,
% 3.74/3.94 ((~((A!13 = B!12) | (~(relation(C!11) & function(C!11))) | (~((relation_inverse_image(C!11, A!13) = relation_inverse_image(C!11, B!12)) & subset(A!13, relation_rng(C!11)) & subset(B!12, relation_rng(C!11)))))) <=> (~((A!13 = B!12) | (~(relation(C!11) & function(C!11))) | (~((relation_inverse_image(C!11, A!13) = relation_inverse_image(C!11, B!12)) & subset(A!13, relation_rng(C!11)) & subset(B!12, relation_rng(C!11))))))),
% 3.74/3.94 inference(rewrite,[status(thm)],[])).
% 3.74/3.94 tff(2,plain,
% 3.74/3.94 ((~![A: $i, B: $i, C: $i] : ((A = B) | (~(relation(C) & function(C))) | (~((relation_inverse_image(C, A) = relation_inverse_image(C, B)) & subset(A, relation_rng(C)) & subset(B, relation_rng(C)))))) <=> (~![A: $i, B: $i, C: $i] : ((A = B) | (~(relation(C) & function(C))) | (~((relation_inverse_image(C, A) = relation_inverse_image(C, B)) & subset(A, relation_rng(C)) & subset(B, relation_rng(C))))))),
% 3.74/3.94 inference(rewrite,[status(thm)],[])).
% 3.74/3.94 tff(3,plain,
% 3.74/3.94 ((~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => ((((relation_inverse_image(C, A) = relation_inverse_image(C, B)) & subset(A, relation_rng(C))) & subset(B, relation_rng(C))) => (A = B)))) <=> (~![A: $i, B: $i, C: $i] : ((A = B) | (~(relation(C) & function(C))) | (~((relation_inverse_image(C, A) = relation_inverse_image(C, B)) & subset(A, relation_rng(C)) & subset(B, relation_rng(C))))))),
% 3.74/3.94 inference(rewrite,[status(thm)],[])).
% 3.74/3.94 tff(4,axiom,(~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => ((((relation_inverse_image(C, A) = relation_inverse_image(C, B)) & subset(A, relation_rng(C))) & subset(B, relation_rng(C))) => (A = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t161_funct_1')).
% 3.74/3.94 tff(5,plain,
% 3.74/3.94 (~![A: $i, B: $i, C: $i] : ((A = B) | (~(relation(C) & function(C))) | (~((relation_inverse_image(C, A) = relation_inverse_image(C, B)) & subset(A, relation_rng(C)) & subset(B, relation_rng(C)))))),
% 3.74/3.94 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.74/3.94 tff(6,plain,
% 3.74/3.94 (~![A: $i, B: $i, C: $i] : ((A = B) | (~(relation(C) & function(C))) | (~((relation_inverse_image(C, A) = relation_inverse_image(C, B)) & subset(A, relation_rng(C)) & subset(B, relation_rng(C)))))),
% 3.74/3.94 inference(modus_ponens,[status(thm)],[5, 2])).
% 3.74/3.94 tff(7,plain,
% 3.74/3.94 (~![A: $i, B: $i, C: $i] : ((A = B) | (~(relation(C) & function(C))) | (~((relation_inverse_image(C, A) = relation_inverse_image(C, B)) & subset(A, relation_rng(C)) & subset(B, relation_rng(C)))))),
% 3.74/3.94 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.74/3.94 tff(8,plain,
% 3.74/3.94 (~![A: $i, B: $i, C: $i] : ((A = B) | (~(relation(C) & function(C))) | (~((relation_inverse_image(C, A) = relation_inverse_image(C, B)) & subset(A, relation_rng(C)) & subset(B, relation_rng(C)))))),
% 3.74/3.94 inference(modus_ponens,[status(thm)],[7, 2])).
% 3.74/3.94 tff(9,plain,(
% 3.74/3.94 ~((A!13 = B!12) | (~(relation(C!11) & function(C!11))) | (~((relation_inverse_image(C!11, A!13) = relation_inverse_image(C!11, B!12)) & subset(A!13, relation_rng(C!11)) & subset(B!12, relation_rng(C!11)))))),
% 3.74/3.94 inference(skolemize,[status(sab)],[8])).
% 3.74/3.94 tff(10,plain,
% 3.74/3.94 (~((A!13 = B!12) | (~(relation(C!11) & function(C!11))) | (~((relation_inverse_image(C!11, A!13) = relation_inverse_image(C!11, B!12)) & subset(A!13, relation_rng(C!11)) & subset(B!12, relation_rng(C!11)))))),
% 3.74/3.94 inference(modus_ponens,[status(thm)],[9, 1])).
% 3.74/3.94 tff(11,plain,
% 3.74/3.94 ((relation_inverse_image(C!11, A!13) = relation_inverse_image(C!11, B!12)) & subset(A!13, relation_rng(C!11)) & subset(B!12, relation_rng(C!11))),
% 3.74/3.94 inference(or_elim,[status(thm)],[10])).
% 3.74/3.94 tff(12,plain,
% 3.74/3.94 (relation_inverse_image(C!11, A!13) = relation_inverse_image(C!11, B!12)),
% 3.74/3.95 inference(and_elim,[status(thm)],[11])).
% 3.74/3.95 tff(13,plain,
% 3.74/3.95 (relation_inverse_image(C!11, B!12) = relation_inverse_image(C!11, A!13)),
% 3.74/3.95 inference(symmetry,[status(thm)],[12])).
% 3.74/3.95 tff(14,plain,
% 3.74/3.95 (subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13)) <=> subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, A!13))),
% 3.74/3.95 inference(monotonicity,[status(thm)],[13])).
% 3.74/3.95 tff(15,plain,
% 3.74/3.95 (subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, A!13)) <=> subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13))),
% 3.74/3.95 inference(symmetry,[status(thm)],[14])).
% 3.74/3.95 tff(16,plain,
% 3.74/3.95 (subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, B!12)) <=> subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, A!13))),
% 3.74/3.95 inference(monotonicity,[status(thm)],[13, 13])).
% 3.74/3.95 tff(17,plain,
% 3.74/3.95 (subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, B!12)) <=> subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13))),
% 3.74/3.95 inference(transitivity,[status(thm)],[16, 15])).
% 3.74/3.95 tff(18,assumption,(~subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, B!12))), introduced(assumption)).
% 3.74/3.95 tff(19,plain,
% 3.74/3.95 (^[A: $i] : refl(subset(A, A) <=> subset(A, A))),
% 3.74/3.95 inference(bind,[status(th)],[])).
% 3.74/3.95 tff(20,plain,
% 3.74/3.95 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 3.74/3.95 inference(quant_intro,[status(thm)],[19])).
% 3.74/3.95 tff(21,plain,
% 3.74/3.95 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(22,plain,
% 3.74/3.95 (![A: $i, B: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 3.74/3.95 inference(elim_unused_vars,[status(thm)],[])).
% 3.74/3.95 tff(23,axiom,(![A: $i, B: $i] : subset(A, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 3.74/3.95 tff(24,plain,
% 3.74/3.95 (![A: $i] : subset(A, A)),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[23, 22])).
% 3.74/3.95 tff(25,plain,
% 3.74/3.95 (![A: $i] : subset(A, A)),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[24, 21])).
% 3.74/3.95 tff(26,plain,(
% 3.74/3.95 ![A: $i] : subset(A, A)),
% 3.74/3.95 inference(skolemize,[status(sab)],[25])).
% 3.74/3.95 tff(27,plain,
% 3.74/3.95 (![A: $i] : subset(A, A)),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[26, 20])).
% 3.74/3.95 tff(28,plain,
% 3.74/3.95 ((~![A: $i] : subset(A, A)) | subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, B!12))),
% 3.74/3.95 inference(quant_inst,[status(thm)],[])).
% 3.74/3.95 tff(29,plain,
% 3.74/3.95 ($false),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[28, 27, 18])).
% 3.74/3.95 tff(30,plain,(subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, B!12))), inference(lemma,lemma(discharge,[]))).
% 3.74/3.95 tff(31,plain,
% 3.74/3.95 (subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13))),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[30, 17])).
% 3.74/3.95 tff(32,plain,
% 3.74/3.95 (subset(B!12, relation_rng(C!11))),
% 3.74/3.95 inference(and_elim,[status(thm)],[11])).
% 3.74/3.95 tff(33,plain,
% 3.74/3.95 (relation(C!11) & function(C!11)),
% 3.74/3.95 inference(or_elim,[status(thm)],[10])).
% 3.74/3.95 tff(34,plain,
% 3.74/3.95 (function(C!11)),
% 3.74/3.95 inference(and_elim,[status(thm)],[33])).
% 3.74/3.95 tff(35,plain,
% 3.74/3.95 (relation(C!11)),
% 3.74/3.95 inference(and_elim,[status(thm)],[33])).
% 3.74/3.95 tff(36,plain,
% 3.74/3.95 (^[A: $i, B: $i, C: $i] : refl((subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C)))) <=> (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C)))))),
% 3.74/3.95 inference(bind,[status(th)],[])).
% 3.74/3.95 tff(37,plain,
% 3.74/3.95 (![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C)))) <=> ![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))),
% 3.74/3.95 inference(quant_intro,[status(thm)],[36])).
% 3.74/3.95 tff(38,plain,
% 3.74/3.95 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C))) <=> (~((~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C)))))), ((~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) <=> (~(~((~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C)))))))), rewrite((~(~((~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C)))))) <=> ((~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))), ((~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) <=> ((~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C)))))), trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), ((subset(A, B) | (~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) | (~(relation(C) & function(C)))) <=> (subset(A, B) | ((~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C)))) | ((~relation(C)) | (~function(C)))))), rewrite((subset(A, B) | ((~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C)))) | ((~relation(C)) | (~function(C)))) <=> (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))), ((subset(A, B) | (~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) | (~(relation(C) & function(C)))) <=> (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))))),
% 3.74/3.95 inference(bind,[status(th)],[])).
% 3.74/3.95 tff(39,plain,
% 3.74/3.95 (![A: $i, B: $i, C: $i] : (subset(A, B) | (~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) | (~(relation(C) & function(C)))) <=> ![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))),
% 3.74/3.95 inference(quant_intro,[status(thm)],[38])).
% 3.74/3.95 tff(40,plain,
% 3.74/3.95 (![A: $i, B: $i, C: $i] : (subset(A, B) | (~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) | (~(relation(C) & function(C)))) <=> ![A: $i, B: $i, C: $i] : (subset(A, B) | (~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) | (~(relation(C) & function(C))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(41,plain,
% 3.74/3.95 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C))) => subset(A, B)) <=> ((~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) | subset(A, B))), (((relation(C) & function(C)) => ((subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C))) => subset(A, B))) <=> ((relation(C) & function(C)) => ((~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) | subset(A, B))))), rewrite(((relation(C) & function(C)) => ((~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) | subset(A, B))) <=> (subset(A, B) | (~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) | (~(relation(C) & function(C))))), (((relation(C) & function(C)) => ((subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C))) => subset(A, B))) <=> (subset(A, B) | (~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) | (~(relation(C) & function(C))))))),
% 3.74/3.95 inference(bind,[status(th)],[])).
% 3.74/3.95 tff(42,plain,
% 3.74/3.95 (![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => ((subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C))) => subset(A, B))) <=> ![A: $i, B: $i, C: $i] : (subset(A, B) | (~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) | (~(relation(C) & function(C))))),
% 3.74/3.95 inference(quant_intro,[status(thm)],[41])).
% 3.74/3.95 tff(43,axiom,(![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => ((subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C))) => subset(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t158_funct_1')).
% 3.74/3.95 tff(44,plain,
% 3.74/3.95 (![A: $i, B: $i, C: $i] : (subset(A, B) | (~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) | (~(relation(C) & function(C))))),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[43, 42])).
% 3.74/3.95 tff(45,plain,
% 3.74/3.95 (![A: $i, B: $i, C: $i] : (subset(A, B) | (~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) | (~(relation(C) & function(C))))),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[44, 40])).
% 3.74/3.95 tff(46,plain,(
% 3.74/3.95 ![A: $i, B: $i, C: $i] : (subset(A, B) | (~(subset(relation_inverse_image(C, A), relation_inverse_image(C, B)) & subset(A, relation_rng(C)))) | (~(relation(C) & function(C))))),
% 3.74/3.95 inference(skolemize,[status(sab)],[45])).
% 3.74/3.95 tff(47,plain,
% 3.74/3.95 (![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[46, 39])).
% 3.74/3.95 tff(48,plain,
% 3.74/3.95 (![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[47, 37])).
% 3.74/3.95 tff(49,plain,
% 3.74/3.95 (((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | ((~relation(C!11)) | (~function(C!11)) | (~subset(B!12, relation_rng(C!11))) | subset(B!12, A!13) | (~subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | (~relation(C!11)) | (~function(C!11)) | (~subset(B!12, relation_rng(C!11))) | subset(B!12, A!13) | (~subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(50,plain,
% 3.74/3.95 ((subset(B!12, A!13) | (~relation(C!11)) | (~function(C!11)) | (~subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13))) | (~subset(B!12, relation_rng(C!11)))) <=> ((~relation(C!11)) | (~function(C!11)) | (~subset(B!12, relation_rng(C!11))) | subset(B!12, A!13) | (~subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(51,plain,
% 3.74/3.95 (((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | (subset(B!12, A!13) | (~relation(C!11)) | (~function(C!11)) | (~subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13))) | (~subset(B!12, relation_rng(C!11))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | ((~relation(C!11)) | (~function(C!11)) | (~subset(B!12, relation_rng(C!11))) | subset(B!12, A!13) | (~subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13)))))),
% 3.74/3.95 inference(monotonicity,[status(thm)],[50])).
% 3.74/3.95 tff(52,plain,
% 3.74/3.95 (((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | (subset(B!12, A!13) | (~relation(C!11)) | (~function(C!11)) | (~subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13))) | (~subset(B!12, relation_rng(C!11))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | (~relation(C!11)) | (~function(C!11)) | (~subset(B!12, relation_rng(C!11))) | subset(B!12, A!13) | (~subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13))))),
% 3.74/3.95 inference(transitivity,[status(thm)],[51, 49])).
% 3.74/3.95 tff(53,plain,
% 3.74/3.95 ((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | (subset(B!12, A!13) | (~relation(C!11)) | (~function(C!11)) | (~subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13))) | (~subset(B!12, relation_rng(C!11))))),
% 3.74/3.95 inference(quant_inst,[status(thm)],[])).
% 3.74/3.95 tff(54,plain,
% 3.74/3.95 ((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | (~relation(C!11)) | (~function(C!11)) | (~subset(B!12, relation_rng(C!11))) | subset(B!12, A!13) | (~subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13)))),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[53, 52])).
% 3.74/3.95 tff(55,plain,
% 3.74/3.95 (subset(B!12, A!13) | (~subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, A!13)))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[54, 48, 35, 34, 32])).
% 3.74/3.95 tff(56,plain,
% 3.74/3.95 (subset(B!12, A!13)),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[55, 31])).
% 3.74/3.95 tff(57,plain,
% 3.74/3.95 (subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12)) <=> subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, A!13))),
% 3.74/3.95 inference(monotonicity,[status(thm)],[13])).
% 3.74/3.95 tff(58,plain,
% 3.74/3.95 (subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, A!13)) <=> subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12))),
% 3.74/3.95 inference(symmetry,[status(thm)],[57])).
% 3.74/3.95 tff(59,plain,
% 3.74/3.95 (subset(relation_inverse_image(C!11, B!12), relation_inverse_image(C!11, B!12)) <=> subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12))),
% 3.74/3.95 inference(transitivity,[status(thm)],[16, 58])).
% 3.74/3.95 tff(60,plain,
% 3.74/3.95 (subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12))),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[30, 59])).
% 3.74/3.95 tff(61,plain,
% 3.74/3.95 (subset(A!13, relation_rng(C!11))),
% 3.74/3.95 inference(and_elim,[status(thm)],[11])).
% 3.74/3.95 tff(62,plain,
% 3.74/3.95 (((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | ((~relation(C!11)) | (~function(C!11)) | (~subset(A!13, relation_rng(C!11))) | subset(A!13, B!12) | (~subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | (~relation(C!11)) | (~function(C!11)) | (~subset(A!13, relation_rng(C!11))) | subset(A!13, B!12) | (~subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(63,plain,
% 3.74/3.95 ((subset(A!13, B!12) | (~relation(C!11)) | (~function(C!11)) | (~subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12))) | (~subset(A!13, relation_rng(C!11)))) <=> ((~relation(C!11)) | (~function(C!11)) | (~subset(A!13, relation_rng(C!11))) | subset(A!13, B!12) | (~subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12))))),
% 3.74/3.95 inference(rewrite,[status(thm)],[])).
% 3.74/3.95 tff(64,plain,
% 3.74/3.95 (((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | (subset(A!13, B!12) | (~relation(C!11)) | (~function(C!11)) | (~subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12))) | (~subset(A!13, relation_rng(C!11))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | ((~relation(C!11)) | (~function(C!11)) | (~subset(A!13, relation_rng(C!11))) | subset(A!13, B!12) | (~subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12)))))),
% 3.74/3.95 inference(monotonicity,[status(thm)],[63])).
% 3.74/3.95 tff(65,plain,
% 3.74/3.95 (((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | (subset(A!13, B!12) | (~relation(C!11)) | (~function(C!11)) | (~subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12))) | (~subset(A!13, relation_rng(C!11))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | (~relation(C!11)) | (~function(C!11)) | (~subset(A!13, relation_rng(C!11))) | subset(A!13, B!12) | (~subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12))))),
% 3.74/3.95 inference(transitivity,[status(thm)],[64, 62])).
% 3.74/3.95 tff(66,plain,
% 3.74/3.95 ((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | (subset(A!13, B!12) | (~relation(C!11)) | (~function(C!11)) | (~subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12))) | (~subset(A!13, relation_rng(C!11))))),
% 3.74/3.95 inference(quant_inst,[status(thm)],[])).
% 3.74/3.95 tff(67,plain,
% 3.74/3.95 ((~![A: $i, B: $i, C: $i] : (subset(A, B) | (~relation(C)) | (~function(C)) | (~subset(relation_inverse_image(C, A), relation_inverse_image(C, B))) | (~subset(A, relation_rng(C))))) | (~relation(C!11)) | (~function(C!11)) | (~subset(A!13, relation_rng(C!11))) | subset(A!13, B!12) | (~subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12)))),
% 3.74/3.95 inference(modus_ponens,[status(thm)],[66, 65])).
% 3.74/3.95 tff(68,plain,
% 3.74/3.95 (subset(A!13, B!12) | (~subset(relation_inverse_image(C!11, A!13), relation_inverse_image(C!11, B!12)))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[67, 48, 35, 34, 61])).
% 3.74/3.95 tff(69,plain,
% 3.74/3.95 (subset(A!13, B!12)),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[68, 60])).
% 3.74/3.95 tff(70,plain,
% 3.74/3.95 ((~((~subset(A!13, B!12)) | (~subset(B!12, A!13)))) | (~subset(A!13, B!12)) | (~subset(B!12, A!13))),
% 3.74/3.95 inference(tautology,[status(thm)],[])).
% 3.74/3.95 tff(71,plain,
% 3.74/3.95 (~((~subset(A!13, B!12)) | (~subset(B!12, A!13)))),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[70, 69, 56])).
% 3.74/3.95 tff(72,plain,
% 3.74/3.95 (~(A!13 = B!12)),
% 3.74/3.95 inference(or_elim,[status(thm)],[10])).
% 3.74/3.95 tff(73,plain,
% 3.74/3.95 ((((~subset(A!13, B!12)) | (~subset(B!12, A!13))) <=> (A!13 = B!12)) | ((~subset(A!13, B!12)) | (~subset(B!12, A!13))) | (A!13 = B!12)),
% 3.74/3.95 inference(tautology,[status(thm)],[])).
% 3.74/3.95 tff(74,plain,
% 3.74/3.95 (((~subset(A!13, B!12)) | (~subset(B!12, A!13))) <=> (A!13 = B!12)),
% 3.74/3.95 inference(unit_resolution,[status(thm)],[73, 72, 71])).
% 3.74/3.95 tff(75,plain,
% 3.74/3.95 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))),
% 3.74/3.95 inference(bind,[status(th)],[])).
% 3.74/3.95 tff(76,plain,
% 3.74/3.95 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 3.74/3.95 inference(quant_intro,[status(thm)],[75])).
% 3.74/3.95 tff(77,plain,
% 3.74/3.95 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))))),
% 3.74/3.96 inference(bind,[status(th)],[])).
% 3.74/3.96 tff(78,plain,
% 3.74/3.96 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 3.74/3.96 inference(quant_intro,[status(thm)],[77])).
% 3.74/3.96 tff(79,plain,
% 3.74/3.96 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 3.74/3.96 inference(rewrite,[status(thm)],[])).
% 3.74/3.96 tff(80,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_xboole_0')).
% 3.74/3.96 tff(81,plain,
% 3.74/3.96 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[80, 79])).
% 3.74/3.96 tff(82,plain,(
% 3.74/3.96 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 3.74/3.96 inference(skolemize,[status(sab)],[81])).
% 3.74/3.96 tff(83,plain,
% 3.74/3.96 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[82, 78])).
% 3.74/3.96 tff(84,plain,
% 3.74/3.96 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 3.74/3.96 inference(modus_ponens,[status(thm)],[83, 76])).
% 3.74/3.96 tff(85,plain,
% 3.74/3.96 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(A!13, B!12)) | (~subset(B!12, A!13))) <=> (A!13 = B!12)))),
% 3.74/3.96 inference(quant_inst,[status(thm)],[])).
% 3.74/3.96 tff(86,plain,
% 3.74/3.96 ($false),
% 3.74/3.96 inference(unit_resolution,[status(thm)],[85, 84, 74])).
% 3.74/3.96 % SZS output end Proof
% 3.74/3.96 % E exiting
%------------------------------------------------------------------------------