%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU056+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:26:51 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU056+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.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 : Fri Jun 20 05:59:42 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(empty_set_type, type, (
% 0.12/0.38 empty_set: $i)).
% 0.12/0.38 tff(set_intersection2_type, type, (
% 0.12/0.38 set_intersection2: ( $i * $i ) > $i)).
% 0.12/0.38 tff(relation_image_type, type, (
% 0.12/0.38 relation_image: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_B_12_type, type, (
% 0.12/0.38 tptp_fun_B_12: $i)).
% 0.12/0.38 tff(tptp_fun_C_11_type, type, (
% 0.12/0.38 tptp_fun_C_11: $i)).
% 0.12/0.38 tff(tptp_fun_A_13_type, type, (
% 0.12/0.38 tptp_fun_A_13: $i)).
% 0.12/0.38 tff(relation_type, type, (
% 0.12/0.38 relation: $i > $o)).
% 0.12/0.38 tff(function_type, type, (
% 0.12/0.38 function: $i > $o)).
% 0.12/0.38 tff(one_to_one_type, type, (
% 0.12/0.38 one_to_one: $i > $o)).
% 0.12/0.38 tff(disjoint_type, type, (
% 0.12/0.38 disjoint: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[A: $i] : refl(((~relation(A)) | (relation_image(A, empty_set) = empty_set)) <=> ((~relation(A)) | (relation_image(A, empty_set) = empty_set)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set)) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set)) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (^[A: $i] : rewrite((relation(A) => (relation_image(A, empty_set) = empty_set)) <=> ((~relation(A)) | (relation_image(A, empty_set) = empty_set)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![A: $i] : (relation(A) => (relation_image(A, empty_set) = empty_set)) <=> ![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.38 tff(6,axiom,(![A: $i] : (relation(A) => (relation_image(A, empty_set) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t149_relat_1')).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.38 tff(9,plain,(
% 0.12/0.38 ![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 0.12/0.38 inference(skolemize,[status(sab)],[8])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 ((~(disjoint(relation_image(C!11, A!13), relation_image(C!11, B!12)) | (~(relation(C!11) & function(C!11))) | (~(disjoint(A!13, B!12) & one_to_one(C!11))))) <=> (~(disjoint(relation_image(C!11, A!13), relation_image(C!11, B!12)) | (~(relation(C!11) & function(C!11))) | (~(disjoint(A!13, B!12) & one_to_one(C!11)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 ((~![A: $i, B: $i, C: $i] : (disjoint(relation_image(C, A), relation_image(C, B)) | (~(relation(C) & function(C))) | (~(disjoint(A, B) & one_to_one(C))))) <=> (~![A: $i, B: $i, C: $i] : (disjoint(relation_image(C, A), relation_image(C, B)) | (~(relation(C) & function(C))) | (~(disjoint(A, B) & one_to_one(C)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 ((~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => ((disjoint(A, B) & one_to_one(C)) => disjoint(relation_image(C, A), relation_image(C, B))))) <=> (~![A: $i, B: $i, C: $i] : (disjoint(relation_image(C, A), relation_image(C, B)) | (~(relation(C) & function(C))) | (~(disjoint(A, B) & one_to_one(C)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(14,axiom,(~![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => ((disjoint(A, B) & one_to_one(C)) => disjoint(relation_image(C, A), relation_image(C, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t125_funct_1')).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (~![A: $i, B: $i, C: $i] : (disjoint(relation_image(C, A), relation_image(C, B)) | (~(relation(C) & function(C))) | (~(disjoint(A, B) & one_to_one(C))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (~![A: $i, B: $i, C: $i] : (disjoint(relation_image(C, A), relation_image(C, B)) | (~(relation(C) & function(C))) | (~(disjoint(A, B) & one_to_one(C))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (~![A: $i, B: $i, C: $i] : (disjoint(relation_image(C, A), relation_image(C, B)) | (~(relation(C) & function(C))) | (~(disjoint(A, B) & one_to_one(C))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (~![A: $i, B: $i, C: $i] : (disjoint(relation_image(C, A), relation_image(C, B)) | (~(relation(C) & function(C))) | (~(disjoint(A, B) & one_to_one(C))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.12/0.38 tff(19,plain,(
% 0.12/0.38 ~(disjoint(relation_image(C!11, A!13), relation_image(C!11, B!12)) | (~(relation(C!11) & function(C!11))) | (~(disjoint(A!13, B!12) & one_to_one(C!11))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[18])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (~(disjoint(relation_image(C!11, A!13), relation_image(C!11, B!12)) | (~(relation(C!11) & function(C!11))) | (~(disjoint(A!13, B!12) & one_to_one(C!11))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (relation(C!11) & function(C!11)),
% 0.12/0.38 inference(or_elim,[status(thm)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (relation(C!11)),
% 0.12/0.38 inference(and_elim,[status(thm)],[21])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (((~![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))) | ((~relation(C!11)) | (relation_image(C!11, empty_set) = empty_set))) <=> ((~![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))) | (~relation(C!11)) | (relation_image(C!11, empty_set) = empty_set))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((~![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))) | ((~relation(C!11)) | (relation_image(C!11, empty_set) = empty_set))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ((~![A: $i] : ((~relation(A)) | (relation_image(A, empty_set) = empty_set))) | (~relation(C!11)) | (relation_image(C!11, empty_set) = empty_set)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (relation_image(C!11, empty_set) = empty_set),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[25, 22, 10])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(30,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_xboole_0')).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.38 tff(32,plain,(
% 0.12/0.38 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.12/0.38 inference(skolemize,[status(sab)],[31])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(A!13, B!12) <=> (set_intersection2(A!13, B!12) = empty_set))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (disjoint(A!13, B!12) <=> (set_intersection2(A!13, B!12) = empty_set)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (disjoint(A!13, B!12) & one_to_one(C!11)),
% 0.12/0.38 inference(or_elim,[status(thm)],[20])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (disjoint(A!13, B!12)),
% 0.12/0.38 inference(and_elim,[status(thm)],[36])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 ((~(disjoint(A!13, B!12) <=> (set_intersection2(A!13, B!12) = empty_set))) | (~disjoint(A!13, B!12)) | (set_intersection2(A!13, B!12) = empty_set)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 ((~(disjoint(A!13, B!12) <=> (set_intersection2(A!13, B!12) = empty_set))) | (set_intersection2(A!13, B!12) = empty_set)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (set_intersection2(A!13, B!12) = empty_set),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[39, 35])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (relation_image(C!11, set_intersection2(A!13, B!12)) = relation_image(C!11, empty_set)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[40])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (one_to_one(C!11)),
% 0.12/0.38 inference(and_elim,[status(thm)],[36])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (function(C!11)),
% 0.12/0.38 inference(and_elim,[status(thm)],[21])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (^[A: $i, B: $i, C: $i] : refl(((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C))) <=> ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C))) <=> ![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(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))))), (((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~(relation(C) & function(C)))) <=> ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | ((~relation(C)) | (~function(C)))))), rewrite(((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | ((~relation(C)) | (~function(C)))) <=> ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C)))), (((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~(relation(C) & function(C)))) <=> ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~(relation(C) & function(C)))) <=> ![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~(relation(C) & function(C)))) <=> ![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~(relation(C) & function(C))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((one_to_one(C) => (relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B)))) <=> ((~one_to_one(C)) | (relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))))), (((relation(C) & function(C)) => (one_to_one(C) => (relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))))) <=> ((relation(C) & function(C)) => ((~one_to_one(C)) | (relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))))))), rewrite(((relation(C) & function(C)) => ((~one_to_one(C)) | (relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))))) <=> ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~(relation(C) & function(C))))), (((relation(C) & function(C)) => (one_to_one(C) => (relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))))) <=> ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~(relation(C) & function(C))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (one_to_one(C) => (relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))))) <=> ![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~(relation(C) & function(C))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.38 tff(51,axiom,(![A: $i, B: $i, C: $i] : ((relation(C) & function(C)) => (one_to_one(C) => (relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t121_funct_1')).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~(relation(C) & function(C))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~(relation(C) & function(C))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.12/0.38 tff(54,plain,(
% 0.12/0.38 ![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~(relation(C) & function(C))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[53])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (((~![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C)))) | ((~relation(C!11)) | (relation_image(C!11, set_intersection2(A!13, B!12)) = set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12))) | (~one_to_one(C!11)) | (~function(C!11)))) <=> ((~![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C)))) | (~relation(C!11)) | (relation_image(C!11, set_intersection2(A!13, B!12)) = set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12))) | (~one_to_one(C!11)) | (~function(C!11)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.39 (((relation_image(C!11, set_intersection2(A!13, B!12)) = set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12))) | (~one_to_one(C!11)) | (~relation(C!11)) | (~function(C!11))) <=> ((~relation(C!11)) | (relation_image(C!11, set_intersection2(A!13, B!12)) = set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12))) | (~one_to_one(C!11)) | (~function(C!11)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (((~![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C)))) | ((relation_image(C!11, set_intersection2(A!13, B!12)) = set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12))) | (~one_to_one(C!11)) | (~relation(C!11)) | (~function(C!11)))) <=> ((~![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C)))) | ((~relation(C!11)) | (relation_image(C!11, set_intersection2(A!13, B!12)) = set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12))) | (~one_to_one(C!11)) | (~function(C!11))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[58])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (((~![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C)))) | ((relation_image(C!11, set_intersection2(A!13, B!12)) = set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12))) | (~one_to_one(C!11)) | (~relation(C!11)) | (~function(C!11)))) <=> ((~![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C)))) | (~relation(C!11)) | (relation_image(C!11, set_intersection2(A!13, B!12)) = set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12))) | (~one_to_one(C!11)) | (~function(C!11)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[59, 57])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C)))) | ((relation_image(C!11, set_intersection2(A!13, B!12)) = set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12))) | (~one_to_one(C!11)) | (~relation(C!11)) | (~function(C!11)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 ((~![A: $i, B: $i, C: $i] : ((relation_image(C, set_intersection2(A, B)) = set_intersection2(relation_image(C, A), relation_image(C, B))) | (~one_to_one(C)) | (~relation(C)) | (~function(C)))) | (~relation(C!11)) | (relation_image(C!11, set_intersection2(A!13, B!12)) = set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12))) | (~one_to_one(C!11)) | (~function(C!11))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 (relation_image(C!11, set_intersection2(A!13, B!12)) = set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[62, 56, 22, 43, 42])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12)) = relation_image(C!11, set_intersection2(A!13, B!12))),
% 0.12/0.39 inference(symmetry,[status(thm)],[63])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12)) = empty_set),
% 0.12/0.39 inference(transitivity,[status(thm)],[64, 41, 26])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(relation_image(C!11, A!13), relation_image(C!11, B!12)) <=> (set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12)) = empty_set))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (disjoint(relation_image(C!11, A!13), relation_image(C!11, B!12)) <=> (set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12)) = empty_set)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[66, 33])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (~disjoint(relation_image(C!11, A!13), relation_image(C!11, B!12))),
% 0.12/0.39 inference(or_elim,[status(thm)],[20])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 ((~(disjoint(relation_image(C!11, A!13), relation_image(C!11, B!12)) <=> (set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12)) = empty_set))) | disjoint(relation_image(C!11, A!13), relation_image(C!11, B!12)) | (~(set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12)) = empty_set))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 ((~(disjoint(relation_image(C!11, A!13), relation_image(C!11, B!12)) <=> (set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12)) = empty_set))) | (~(set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12)) = empty_set))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (~(set_intersection2(relation_image(C!11, A!13), relation_image(C!11, B!12)) = empty_set)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[70, 67])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[71, 65])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------