%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU291+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:27:30 AM UTC 2025
% Result : Theorem 1.74s 1.91s
% Output : Proof 1.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU291+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:38:03 EDT 2025
% 0.13/0.34 % CPUTime :
% 1.74/1.91 % SZS status Theorem
% 1.74/1.91 % SZS output start Proof
% 1.74/1.91 tff(relation_dom_as_subset_type, type, (
% 1.74/1.91 relation_dom_as_subset: ( $i * $i * $i ) > $i)).
% 1.74/1.91 tff(tptp_fun_D_17_type, type, (
% 1.74/1.91 tptp_fun_D_17: $i)).
% 1.74/1.91 tff(tptp_fun_C_18_type, type, (
% 1.74/1.91 tptp_fun_C_18: $i)).
% 1.74/1.91 tff(tptp_fun_A_20_type, type, (
% 1.74/1.91 tptp_fun_A_20: $i)).
% 1.74/1.91 tff(tptp_fun_B_19_type, type, (
% 1.74/1.91 tptp_fun_B_19: $i)).
% 1.74/1.91 tff(relation_dom_type, type, (
% 1.74/1.91 relation_dom: $i > $i)).
% 1.74/1.91 tff(relation_of2_type, type, (
% 1.74/1.91 relation_of2: ( $i * $i * $i ) > $o)).
% 1.74/1.91 tff(relation_of2_as_subset_type, type, (
% 1.74/1.91 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 1.74/1.91 tff(quasi_total_type, type, (
% 1.74/1.91 quasi_total: ( $i * $i * $i ) > $o)).
% 1.74/1.91 tff(function_type, type, (
% 1.74/1.91 function: $i > $o)).
% 1.74/1.91 tff(subset_type, type, (
% 1.74/1.91 subset: ( $i * $i ) > $o)).
% 1.74/1.91 tff(empty_set_type, type, (
% 1.74/1.91 empty_set: $i)).
% 1.74/1.91 tff(1,plain,
% 1.74/1.91 (^[A: $i, B: $i, C: $i] : refl((relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)))),
% 1.74/1.91 inference(bind,[status(th)],[])).
% 1.74/1.91 tff(2,plain,
% 1.74/1.91 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 1.74/1.91 inference(quant_intro,[status(thm)],[1])).
% 1.74/1.91 tff(3,plain,
% 1.74/1.91 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(4,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 1.74/1.91 tff(5,plain,
% 1.74/1.91 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.74/1.91 tff(6,plain,(
% 1.74/1.91 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 1.74/1.91 inference(skolemize,[status(sab)],[5])).
% 1.74/1.91 tff(7,plain,
% 1.74/1.91 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.74/1.91 tff(8,plain,
% 1.74/1.91 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(D!17, A!20, B!19) <=> relation_of2(D!17, A!20, B!19))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(9,plain,
% 1.74/1.91 (relation_of2_as_subset(D!17, A!20, B!19) <=> relation_of2(D!17, A!20, B!19)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.74/1.91 tff(10,plain,
% 1.74/1.91 ((~(((B!19 = empty_set) & (~(A!20 = empty_set))) | (function(D!17) & quasi_total(D!17, A!20, C!18) & relation_of2_as_subset(D!17, A!20, C!18)) | (~subset(B!19, C!18)) | (~(function(D!17) & quasi_total(D!17, A!20, B!19) & relation_of2_as_subset(D!17, A!20, B!19))))) <=> (~(((B!19 = empty_set) & (~(A!20 = empty_set))) | (function(D!17) & quasi_total(D!17, A!20, C!18) & relation_of2_as_subset(D!17, A!20, C!18)) | (~subset(B!19, C!18)) | (~(function(D!17) & quasi_total(D!17, A!20, B!19) & relation_of2_as_subset(D!17, A!20, B!19)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(11,plain,
% 1.74/1.91 ((~![A: $i, B: $i, C: $i, D: $i] : (((B = empty_set) & (~(A = empty_set))) | (function(D) & quasi_total(D, A, C) & relation_of2_as_subset(D, A, C)) | (~subset(B, C)) | (~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (((B = empty_set) & (~(A = empty_set))) | (function(D) & quasi_total(D, A, C) & relation_of2_as_subset(D, A, C)) | (~subset(B, C)) | (~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(12,plain,
% 1.74/1.91 ((~![A: $i, B: $i, C: $i, D: $i] : (((function(D) & quasi_total(D, A, B)) & relation_of2_as_subset(D, A, B)) => (subset(B, C) => (((B = empty_set) & (~(A = empty_set))) | ((function(D) & quasi_total(D, A, C)) & relation_of2_as_subset(D, A, C)))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : (((B = empty_set) & (~(A = empty_set))) | (function(D) & quasi_total(D, A, C) & relation_of2_as_subset(D, A, C)) | (~subset(B, C)) | (~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(13,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (((function(D) & quasi_total(D, A, B)) & relation_of2_as_subset(D, A, B)) => (subset(B, C) => (((B = empty_set) & (~(A = empty_set))) | ((function(D) & quasi_total(D, A, C)) & relation_of2_as_subset(D, A, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t9_funct_2')).
% 1.74/1.91 tff(14,plain,
% 1.74/1.91 (~![A: $i, B: $i, C: $i, D: $i] : (((B = empty_set) & (~(A = empty_set))) | (function(D) & quasi_total(D, A, C) & relation_of2_as_subset(D, A, C)) | (~subset(B, C)) | (~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[13, 12])).
% 1.74/1.91 tff(15,plain,
% 1.74/1.91 (~![A: $i, B: $i, C: $i, D: $i] : (((B = empty_set) & (~(A = empty_set))) | (function(D) & quasi_total(D, A, C) & relation_of2_as_subset(D, A, C)) | (~subset(B, C)) | (~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[14, 11])).
% 1.74/1.91 tff(16,plain,
% 1.74/1.91 (~![A: $i, B: $i, C: $i, D: $i] : (((B = empty_set) & (~(A = empty_set))) | (function(D) & quasi_total(D, A, C) & relation_of2_as_subset(D, A, C)) | (~subset(B, C)) | (~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[15, 11])).
% 1.74/1.91 tff(17,plain,
% 1.74/1.91 (~![A: $i, B: $i, C: $i, D: $i] : (((B = empty_set) & (~(A = empty_set))) | (function(D) & quasi_total(D, A, C) & relation_of2_as_subset(D, A, C)) | (~subset(B, C)) | (~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[16, 11])).
% 1.74/1.91 tff(18,plain,(
% 1.74/1.91 ~(((B!19 = empty_set) & (~(A!20 = empty_set))) | (function(D!17) & quasi_total(D!17, A!20, C!18) & relation_of2_as_subset(D!17, A!20, C!18)) | (~subset(B!19, C!18)) | (~(function(D!17) & quasi_total(D!17, A!20, B!19) & relation_of2_as_subset(D!17, A!20, B!19))))),
% 1.74/1.91 inference(skolemize,[status(sab)],[17])).
% 1.74/1.91 tff(19,plain,
% 1.74/1.91 (~(((B!19 = empty_set) & (~(A!20 = empty_set))) | (function(D!17) & quasi_total(D!17, A!20, C!18) & relation_of2_as_subset(D!17, A!20, C!18)) | (~subset(B!19, C!18)) | (~(function(D!17) & quasi_total(D!17, A!20, B!19) & relation_of2_as_subset(D!17, A!20, B!19))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[18, 10])).
% 1.74/1.91 tff(20,plain,
% 1.74/1.91 (function(D!17) & quasi_total(D!17, A!20, B!19) & relation_of2_as_subset(D!17, A!20, B!19)),
% 1.74/1.91 inference(or_elim,[status(thm)],[19])).
% 1.74/1.91 tff(21,plain,
% 1.74/1.91 (relation_of2_as_subset(D!17, A!20, B!19)),
% 1.74/1.91 inference(and_elim,[status(thm)],[20])).
% 1.74/1.91 tff(22,plain,
% 1.74/1.91 ((~(relation_of2_as_subset(D!17, A!20, B!19) <=> relation_of2(D!17, A!20, B!19))) | (~relation_of2_as_subset(D!17, A!20, B!19)) | relation_of2(D!17, A!20, B!19)),
% 1.74/1.91 inference(tautology,[status(thm)],[])).
% 1.74/1.91 tff(23,plain,
% 1.74/1.91 ((~(relation_of2_as_subset(D!17, A!20, B!19) <=> relation_of2(D!17, A!20, B!19))) | relation_of2(D!17, A!20, B!19)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[22, 21])).
% 1.74/1.91 tff(24,plain,
% 1.74/1.91 (relation_of2(D!17, A!20, B!19)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[23, 9])).
% 1.74/1.91 tff(25,plain,
% 1.74/1.91 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C))) <=> ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C))))),
% 1.74/1.91 inference(bind,[status(th)],[])).
% 1.74/1.91 tff(26,plain,
% 1.74/1.91 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 1.74/1.91 inference(quant_intro,[status(thm)],[25])).
% 1.74/1.91 tff(27,plain,
% 1.74/1.91 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(28,plain,
% 1.74/1.91 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2(C, A, B) => (relation_dom_as_subset(A, B, C) = relation_dom(C))) <=> ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C))))),
% 1.74/1.91 inference(bind,[status(th)],[])).
% 1.74/1.91 tff(29,plain,
% 1.74/1.91 (![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) => (relation_dom_as_subset(A, B, C) = relation_dom(C))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 1.74/1.91 inference(quant_intro,[status(thm)],[28])).
% 1.74/1.91 tff(30,axiom,(![A: $i, B: $i, C: $i] : (relation_of2(C, A, B) => (relation_dom_as_subset(A, B, C) = relation_dom(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k4_relset_1')).
% 1.74/1.91 tff(31,plain,
% 1.74/1.91 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[30, 29])).
% 1.74/1.91 tff(32,plain,
% 1.74/1.91 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[31, 27])).
% 1.74/1.91 tff(33,plain,(
% 1.74/1.91 ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 1.74/1.91 inference(skolemize,[status(sab)],[32])).
% 1.74/1.91 tff(34,plain,
% 1.74/1.91 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[33, 26])).
% 1.74/1.91 tff(35,plain,
% 1.74/1.91 (((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | ((~relation_of2(D!17, A!20, B!19)) | (relation_dom_as_subset(A!20, B!19, D!17) = relation_dom(D!17)))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | (~relation_of2(D!17, A!20, B!19)) | (relation_dom_as_subset(A!20, B!19, D!17) = relation_dom(D!17)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(36,plain,
% 1.74/1.91 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | ((~relation_of2(D!17, A!20, B!19)) | (relation_dom_as_subset(A!20, B!19, D!17) = relation_dom(D!17)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(37,plain,
% 1.74/1.91 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | (~relation_of2(D!17, A!20, B!19)) | (relation_dom_as_subset(A!20, B!19, D!17) = relation_dom(D!17))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.74/1.91 tff(38,plain,
% 1.74/1.91 (relation_dom_as_subset(A!20, B!19, D!17) = relation_dom(D!17)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[37, 34, 24])).
% 1.74/1.91 tff(39,plain,
% 1.74/1.91 (relation_dom(D!17) = relation_dom_as_subset(A!20, B!19, D!17)),
% 1.74/1.91 inference(symmetry,[status(thm)],[38])).
% 1.74/1.91 tff(40,plain,
% 1.74/1.91 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(D!17, A!20, C!18) <=> relation_of2(D!17, A!20, C!18))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(41,plain,
% 1.74/1.91 (relation_of2_as_subset(D!17, A!20, C!18) <=> relation_of2(D!17, A!20, C!18)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[40, 7])).
% 1.74/1.91 tff(42,plain,
% 1.74/1.91 (subset(B!19, C!18)),
% 1.74/1.91 inference(or_elim,[status(thm)],[19])).
% 1.74/1.91 tff(43,assumption,(~relation_of2_as_subset(D!17, A!20, C!18)), introduced(assumption)).
% 1.74/1.91 tff(44,plain,
% 1.74/1.91 (^[A: $i, B: $i, C: $i, D: $i] : refl((relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A))) <=> (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A))))),
% 1.74/1.91 inference(bind,[status(th)],[])).
% 1.74/1.91 tff(45,plain,
% 1.74/1.91 (![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A)))),
% 1.74/1.91 inference(quant_intro,[status(thm)],[44])).
% 1.74/1.91 tff(46,plain,
% 1.74/1.91 (![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(47,plain,
% 1.74/1.92 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite((subset(A, B) => relation_of2_as_subset(D, C, B)) <=> ((~subset(A, B)) | relation_of2_as_subset(D, C, B))), ((relation_of2_as_subset(D, C, A) => (subset(A, B) => relation_of2_as_subset(D, C, B))) <=> (relation_of2_as_subset(D, C, A) => ((~subset(A, B)) | relation_of2_as_subset(D, C, B))))), rewrite((relation_of2_as_subset(D, C, A) => ((~subset(A, B)) | relation_of2_as_subset(D, C, B))) <=> (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A)))), ((relation_of2_as_subset(D, C, A) => (subset(A, B) => relation_of2_as_subset(D, C, B))) <=> (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A)))))),
% 1.74/1.92 inference(bind,[status(th)],[])).
% 1.74/1.92 tff(48,plain,
% 1.74/1.92 (![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, A) => (subset(A, B) => relation_of2_as_subset(D, C, B))) <=> ![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A)))),
% 1.74/1.92 inference(quant_intro,[status(thm)],[47])).
% 1.74/1.92 tff(49,axiom,(![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, A) => (subset(A, B) => relation_of2_as_subset(D, C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t16_relset_1')).
% 1.74/1.92 tff(50,plain,
% 1.74/1.92 (![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.74/1.92 tff(51,plain,
% 1.74/1.92 (![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.74/1.92 tff(52,plain,(
% 1.74/1.92 ![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A)))),
% 1.74/1.92 inference(skolemize,[status(sab)],[51])).
% 1.74/1.92 tff(53,plain,
% 1.74/1.92 (![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.74/1.92 tff(54,plain,
% 1.74/1.92 (((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A)))) | (relation_of2_as_subset(D!17, A!20, C!18) | (~subset(B!19, C!18)) | (~relation_of2_as_subset(D!17, A!20, B!19)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A)))) | relation_of2_as_subset(D!17, A!20, C!18) | (~subset(B!19, C!18)) | (~relation_of2_as_subset(D!17, A!20, B!19)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(55,plain,
% 1.74/1.92 ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A)))) | (relation_of2_as_subset(D!17, A!20, C!18) | (~subset(B!19, C!18)) | (~relation_of2_as_subset(D!17, A!20, B!19)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(56,plain,
% 1.74/1.92 ((~![A: $i, B: $i, C: $i, D: $i] : (relation_of2_as_subset(D, C, B) | (~subset(A, B)) | (~relation_of2_as_subset(D, C, A)))) | relation_of2_as_subset(D!17, A!20, C!18) | (~subset(B!19, C!18)) | (~relation_of2_as_subset(D!17, A!20, B!19))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.74/1.92 tff(57,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[56, 53, 43, 42, 21])).
% 1.74/1.92 tff(58,plain,(relation_of2_as_subset(D!17, A!20, C!18)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(59,plain,
% 1.74/1.92 ((~(relation_of2_as_subset(D!17, A!20, C!18) <=> relation_of2(D!17, A!20, C!18))) | (~relation_of2_as_subset(D!17, A!20, C!18)) | relation_of2(D!17, A!20, C!18)),
% 1.74/1.92 inference(tautology,[status(thm)],[])).
% 1.74/1.92 tff(60,plain,
% 1.74/1.92 ((~(relation_of2_as_subset(D!17, A!20, C!18) <=> relation_of2(D!17, A!20, C!18))) | relation_of2(D!17, A!20, C!18)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[59, 58])).
% 1.74/1.92 tff(61,plain,
% 1.74/1.92 (relation_of2(D!17, A!20, C!18)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[60, 41])).
% 1.74/1.92 tff(62,plain,
% 1.74/1.92 (((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | ((~relation_of2(D!17, A!20, C!18)) | (relation_dom_as_subset(A!20, C!18, D!17) = relation_dom(D!17)))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | (~relation_of2(D!17, A!20, C!18)) | (relation_dom_as_subset(A!20, C!18, D!17) = relation_dom(D!17)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(63,plain,
% 1.74/1.92 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | ((~relation_of2(D!17, A!20, C!18)) | (relation_dom_as_subset(A!20, C!18, D!17) = relation_dom(D!17)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(64,plain,
% 1.74/1.92 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | (~relation_of2(D!17, A!20, C!18)) | (relation_dom_as_subset(A!20, C!18, D!17) = relation_dom(D!17))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.74/1.92 tff(65,plain,
% 1.74/1.92 (relation_dom_as_subset(A!20, C!18, D!17) = relation_dom(D!17)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[64, 34, 61])).
% 1.74/1.92 tff(66,plain,
% 1.74/1.92 (relation_dom_as_subset(A!20, C!18, D!17) = relation_dom_as_subset(A!20, B!19, D!17)),
% 1.74/1.92 inference(transitivity,[status(thm)],[65, 39])).
% 1.74/1.92 tff(67,plain,
% 1.74/1.92 ((A!20 = relation_dom_as_subset(A!20, C!18, D!17)) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[66])).
% 1.74/1.92 tff(68,plain,
% 1.74/1.92 ((A!20 = relation_dom_as_subset(A!20, B!19, D!17)) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))),
% 1.74/1.92 inference(symmetry,[status(thm)],[67])).
% 1.74/1.92 tff(69,assumption,(~(B!19 = empty_set)), introduced(assumption)).
% 1.74/1.92 tff(70,plain,
% 1.74/1.92 (((~(B!19 = empty_set)) | (A!20 = empty_set)) | (B!19 = empty_set)),
% 1.74/1.92 inference(tautology,[status(thm)],[])).
% 1.74/1.92 tff(71,plain,
% 1.74/1.92 ((~(B!19 = empty_set)) | (A!20 = empty_set)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[70, 69])).
% 1.74/1.92 tff(72,plain,
% 1.74/1.92 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set))))))) <=> ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set))))))))),
% 1.74/1.92 inference(bind,[status(th)],[])).
% 1.74/1.92 tff(73,plain,
% 1.74/1.92 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set))))))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))),
% 1.74/1.92 inference(quant_intro,[status(thm)],[72])).
% 1.74/1.92 tff(74,plain,
% 1.74/1.92 (^[A: $i, B: $i, C: $i] : rewrite(((~relation_of2_as_subset(C, A, B)) | (((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set))))) <=> ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set))))))))),
% 1.74/1.92 inference(bind,[status(th)],[])).
% 1.74/1.92 tff(75,plain,
% 1.74/1.92 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set))))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))),
% 1.74/1.92 inference(quant_intro,[status(thm)],[74])).
% 1.74/1.92 tff(76,plain,
% 1.74/1.92 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set))))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(77,plain,
% 1.74/1.92 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((((B = empty_set) => (A = empty_set)) => (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((B = empty_set) => ((A = empty_set) | (quasi_total(C, A, B) <=> (C = empty_set))))) <=> (((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set))))), ((relation_of2_as_subset(C, A, B) => ((((B = empty_set) => (A = empty_set)) => (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((B = empty_set) => ((A = empty_set) | (quasi_total(C, A, B) <=> (C = empty_set)))))) <=> (relation_of2_as_subset(C, A, B) => (((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set))))))), rewrite((relation_of2_as_subset(C, A, B) => (((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set))))) <=> ((~relation_of2_as_subset(C, A, B)) | (((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))), ((relation_of2_as_subset(C, A, B) => ((((B = empty_set) => (A = empty_set)) => (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((B = empty_set) => ((A = empty_set) | (quasi_total(C, A, B) <=> (C = empty_set)))))) <=> ((~relation_of2_as_subset(C, A, B)) | (((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))),
% 1.74/1.92 inference(bind,[status(th)],[])).
% 1.74/1.92 tff(78,plain,
% 1.74/1.92 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => ((((B = empty_set) => (A = empty_set)) => (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((B = empty_set) => ((A = empty_set) | (quasi_total(C, A, B) <=> (C = empty_set)))))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))),
% 1.74/1.92 inference(quant_intro,[status(thm)],[77])).
% 1.74/1.92 tff(79,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => ((((B = empty_set) => (A = empty_set)) => (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((B = empty_set) => ((A = empty_set) | (quasi_total(C, A, B) <=> (C = empty_set))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_funct_2')).
% 1.74/1.92 tff(80,plain,
% 1.74/1.92 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[79, 78])).
% 1.74/1.92 tff(81,plain,
% 1.74/1.92 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[80, 76])).
% 1.74/1.92 tff(82,plain,(
% 1.74/1.92 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C)))) & ((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))),
% 1.74/1.92 inference(skolemize,[status(sab)],[81])).
% 1.74/1.92 tff(83,plain,
% 1.74/1.92 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[82, 75])).
% 1.74/1.92 tff(84,plain,
% 1.74/1.92 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[83, 73])).
% 1.74/1.92 tff(85,plain,
% 1.74/1.92 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((A!20 = empty_set) | (~(B!19 = empty_set)) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | (~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((A!20 = empty_set) | (~(B!19 = empty_set)) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(86,plain,
% 1.74/1.92 (((~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)) | (A!20 = empty_set) | (~(B!19 = empty_set))))))) <=> ((~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((A!20 = empty_set) | (~(B!19 = empty_set)) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(87,plain,
% 1.74/1.92 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)) | (A!20 = empty_set) | (~(B!19 = empty_set)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((A!20 = empty_set) | (~(B!19 = empty_set)) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[86])).
% 1.74/1.92 tff(88,plain,
% 1.74/1.92 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)) | (A!20 = empty_set) | (~(B!19 = empty_set)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | (~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((A!20 = empty_set) | (~(B!19 = empty_set)) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[87, 85])).
% 1.74/1.92 tff(89,plain,
% 1.74/1.92 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)) | (A!20 = empty_set) | (~(B!19 = empty_set)))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(90,plain,
% 1.74/1.92 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | (~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((A!20 = empty_set) | (~(B!19 = empty_set)) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set))))))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[89, 88])).
% 1.74/1.92 tff(91,plain,
% 1.74/1.92 (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((A!20 = empty_set) | (~(B!19 = empty_set)) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[90, 84, 21])).
% 1.74/1.92 tff(92,plain,
% 1.74/1.92 (((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((A!20 = empty_set) | (~(B!19 = empty_set)) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set))))) | ((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))),
% 1.74/1.92 inference(tautology,[status(thm)],[])).
% 1.74/1.92 tff(93,plain,
% 1.74/1.92 ((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[92, 91])).
% 1.74/1.92 tff(94,plain,
% 1.74/1.92 ((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17)))),
% 1.74/1.92 inference(tautology,[status(thm)],[])).
% 1.74/1.92 tff(95,plain,
% 1.74/1.92 ((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[94, 93])).
% 1.74/1.92 tff(96,plain,
% 1.74/1.92 (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[95, 71])).
% 1.74/1.92 tff(97,plain,
% 1.74/1.92 (quasi_total(D!17, A!20, B!19)),
% 1.74/1.92 inference(and_elim,[status(thm)],[20])).
% 1.74/1.92 tff(98,plain,
% 1.74/1.92 ((~(quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17)))) | (~quasi_total(D!17, A!20, B!19)) | (A!20 = relation_dom_as_subset(A!20, B!19, D!17))),
% 1.74/1.92 inference(tautology,[status(thm)],[])).
% 1.74/1.92 tff(99,plain,
% 1.74/1.92 ((~(quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17)))) | (A!20 = relation_dom_as_subset(A!20, B!19, D!17))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[98, 97])).
% 1.74/1.92 tff(100,plain,
% 1.74/1.92 (A!20 = relation_dom_as_subset(A!20, B!19, D!17)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[99, 96])).
% 1.74/1.92 tff(101,plain,
% 1.74/1.92 (A!20 = relation_dom_as_subset(A!20, C!18, D!17)),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[100, 68])).
% 1.74/1.92 tff(102,plain,
% 1.74/1.92 (function(D!17)),
% 1.74/1.92 inference(and_elim,[status(thm)],[20])).
% 1.74/1.92 tff(103,plain,
% 1.74/1.92 ((~(~((~function(D!17)) | (~quasi_total(D!17, A!20, C!18)) | (~relation_of2_as_subset(D!17, A!20, C!18))))) <=> ((~function(D!17)) | (~quasi_total(D!17, A!20, C!18)) | (~relation_of2_as_subset(D!17, A!20, C!18)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(104,plain,
% 1.74/1.92 ((function(D!17) & quasi_total(D!17, A!20, C!18) & relation_of2_as_subset(D!17, A!20, C!18)) <=> (~((~function(D!17)) | (~quasi_total(D!17, A!20, C!18)) | (~relation_of2_as_subset(D!17, A!20, C!18))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(105,plain,
% 1.74/1.92 ((~(function(D!17) & quasi_total(D!17, A!20, C!18) & relation_of2_as_subset(D!17, A!20, C!18))) <=> (~(~((~function(D!17)) | (~quasi_total(D!17, A!20, C!18)) | (~relation_of2_as_subset(D!17, A!20, C!18)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[104])).
% 1.74/1.92 tff(106,plain,
% 1.74/1.92 ((~(function(D!17) & quasi_total(D!17, A!20, C!18) & relation_of2_as_subset(D!17, A!20, C!18))) <=> ((~function(D!17)) | (~quasi_total(D!17, A!20, C!18)) | (~relation_of2_as_subset(D!17, A!20, C!18)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[105, 103])).
% 1.74/1.92 tff(107,plain,
% 1.74/1.92 (~(function(D!17) & quasi_total(D!17, A!20, C!18) & relation_of2_as_subset(D!17, A!20, C!18))),
% 1.74/1.92 inference(or_elim,[status(thm)],[19])).
% 1.74/1.92 tff(108,plain,
% 1.74/1.92 ((~function(D!17)) | (~quasi_total(D!17, A!20, C!18)) | (~relation_of2_as_subset(D!17, A!20, C!18))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[107, 106])).
% 1.74/1.92 tff(109,plain,
% 1.74/1.92 ((~quasi_total(D!17, A!20, C!18)) | (~relation_of2_as_subset(D!17, A!20, C!18))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[108, 102])).
% 1.74/1.92 tff(110,plain,
% 1.74/1.92 (~quasi_total(D!17, A!20, C!18)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[109, 58])).
% 1.74/1.92 tff(111,plain,
% 1.74/1.92 ((~(quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17)))) | quasi_total(D!17, A!20, C!18) | (~(A!20 = relation_dom_as_subset(A!20, C!18, D!17)))),
% 1.74/1.92 inference(tautology,[status(thm)],[])).
% 1.74/1.92 tff(112,plain,
% 1.74/1.92 ((~(quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17)))) | (~(A!20 = relation_dom_as_subset(A!20, C!18, D!17)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[111, 110])).
% 1.74/1.92 tff(113,plain,
% 1.74/1.92 (~(quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[112, 101])).
% 1.74/1.92 tff(114,plain,
% 1.74/1.92 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, C!18)) | (~((~((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))))) | (~((A!20 = empty_set) | (~(C!18 = empty_set)) | (quasi_total(D!17, A!20, C!18) <=> (D!17 = empty_set)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | (~relation_of2_as_subset(D!17, A!20, C!18)) | (~((~((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))))) | (~((A!20 = empty_set) | (~(C!18 = empty_set)) | (quasi_total(D!17, A!20, C!18) <=> (D!17 = empty_set)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(115,plain,
% 1.74/1.92 (((~relation_of2_as_subset(D!17, A!20, C!18)) | (~((~((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))))) | (~((quasi_total(D!17, A!20, C!18) <=> (D!17 = empty_set)) | (A!20 = empty_set) | (~(C!18 = empty_set))))))) <=> ((~relation_of2_as_subset(D!17, A!20, C!18)) | (~((~((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))))) | (~((A!20 = empty_set) | (~(C!18 = empty_set)) | (quasi_total(D!17, A!20, C!18) <=> (D!17 = empty_set)))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(116,plain,
% 1.74/1.92 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, C!18)) | (~((~((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))))) | (~((quasi_total(D!17, A!20, C!18) <=> (D!17 = empty_set)) | (A!20 = empty_set) | (~(C!18 = empty_set)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, C!18)) | (~((~((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))))) | (~((A!20 = empty_set) | (~(C!18 = empty_set)) | (quasi_total(D!17, A!20, C!18) <=> (D!17 = empty_set))))))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[115])).
% 1.74/1.92 tff(117,plain,
% 1.74/1.92 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, C!18)) | (~((~((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))))) | (~((quasi_total(D!17, A!20, C!18) <=> (D!17 = empty_set)) | (A!20 = empty_set) | (~(C!18 = empty_set)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | (~relation_of2_as_subset(D!17, A!20, C!18)) | (~((~((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))))) | (~((A!20 = empty_set) | (~(C!18 = empty_set)) | (quasi_total(D!17, A!20, C!18) <=> (D!17 = empty_set)))))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[116, 114])).
% 1.74/1.92 tff(118,plain,
% 1.74/1.92 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, C!18)) | (~((~((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))))) | (~((quasi_total(D!17, A!20, C!18) <=> (D!17 = empty_set)) | (A!20 = empty_set) | (~(C!18 = empty_set)))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(119,plain,
% 1.74/1.93 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | (~relation_of2_as_subset(D!17, A!20, C!18)) | (~((~((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))))) | (~((A!20 = empty_set) | (~(C!18 = empty_set)) | (quasi_total(D!17, A!20, C!18) <=> (D!17 = empty_set))))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.74/1.93 tff(120,plain,
% 1.74/1.93 (~((~((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))))) | (~((A!20 = empty_set) | (~(C!18 = empty_set)) | (quasi_total(D!17, A!20, C!18) <=> (D!17 = empty_set)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[119, 84, 58])).
% 1.74/1.93 tff(121,plain,
% 1.74/1.93 (((~((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))))) | (~((A!20 = empty_set) | (~(C!18 = empty_set)) | (quasi_total(D!17, A!20, C!18) <=> (D!17 = empty_set))))) | ((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))))),
% 1.74/1.93 inference(tautology,[status(thm)],[])).
% 1.74/1.93 tff(122,plain,
% 1.74/1.93 ((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[121, 120])).
% 1.74/1.93 tff(123,plain,
% 1.74/1.93 ((~((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))))) | (~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17)))),
% 1.74/1.93 inference(tautology,[status(thm)],[])).
% 1.74/1.93 tff(124,plain,
% 1.74/1.93 ((~((~(C!18 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17)))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[123, 122])).
% 1.74/1.93 tff(125,plain,
% 1.74/1.93 (~((~(C!18 = empty_set)) | (A!20 = empty_set))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[124, 113])).
% 1.74/1.93 tff(126,plain,
% 1.74/1.93 (((~(C!18 = empty_set)) | (A!20 = empty_set)) | (C!18 = empty_set)),
% 1.74/1.93 inference(tautology,[status(thm)],[])).
% 1.74/1.93 tff(127,plain,
% 1.74/1.93 (C!18 = empty_set),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[126, 125])).
% 1.74/1.93 tff(128,plain,
% 1.74/1.93 (empty_set = C!18),
% 1.74/1.93 inference(symmetry,[status(thm)],[127])).
% 1.74/1.93 tff(129,plain,
% 1.74/1.93 (subset(B!19, empty_set) <=> subset(B!19, C!18)),
% 1.74/1.93 inference(monotonicity,[status(thm)],[128])).
% 1.74/1.93 tff(130,plain,
% 1.74/1.93 (subset(B!19, C!18) <=> subset(B!19, empty_set)),
% 1.74/1.93 inference(symmetry,[status(thm)],[129])).
% 1.74/1.93 tff(131,plain,
% 1.74/1.93 (subset(B!19, empty_set)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[42, 130])).
% 1.74/1.93 tff(132,plain,
% 1.74/1.93 (^[A: $i] : refl(((~subset(A, empty_set)) | (A = empty_set)) <=> ((~subset(A, empty_set)) | (A = empty_set)))),
% 1.74/1.93 inference(bind,[status(th)],[])).
% 1.74/1.93 tff(133,plain,
% 1.74/1.93 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set)) <=> ![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 1.74/1.93 inference(quant_intro,[status(thm)],[132])).
% 1.74/1.93 tff(134,plain,
% 1.74/1.93 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set)) <=> ![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(135,plain,
% 1.74/1.93 (^[A: $i] : rewrite((subset(A, empty_set) => (A = empty_set)) <=> ((~subset(A, empty_set)) | (A = empty_set)))),
% 1.74/1.93 inference(bind,[status(th)],[])).
% 1.74/1.93 tff(136,plain,
% 1.74/1.93 (![A: $i] : (subset(A, empty_set) => (A = empty_set)) <=> ![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 1.74/1.93 inference(quant_intro,[status(thm)],[135])).
% 1.74/1.93 tff(137,axiom,(![A: $i] : (subset(A, empty_set) => (A = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_xboole_1')).
% 1.74/1.93 tff(138,plain,
% 1.74/1.93 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.74/1.93 tff(139,plain,
% 1.74/1.93 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[138, 134])).
% 1.74/1.93 tff(140,plain,(
% 1.74/1.93 ![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 1.74/1.93 inference(skolemize,[status(sab)],[139])).
% 1.74/1.93 tff(141,plain,
% 1.74/1.93 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[140, 133])).
% 1.74/1.93 tff(142,plain,
% 1.74/1.93 (((~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))) | ((~subset(B!19, empty_set)) | (B!19 = empty_set))) <=> ((~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))) | (~subset(B!19, empty_set)) | (B!19 = empty_set))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(143,plain,
% 1.74/1.93 ((~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))) | ((~subset(B!19, empty_set)) | (B!19 = empty_set))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(144,plain,
% 1.74/1.93 ((~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))) | (~subset(B!19, empty_set)) | (B!19 = empty_set)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.74/1.93 tff(145,plain,
% 1.74/1.93 (~subset(B!19, empty_set)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[144, 141, 69])).
% 1.74/1.93 tff(146,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[145, 131])).
% 1.74/1.93 tff(147,plain,(B!19 = empty_set), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(148,plain,
% 1.74/1.93 ((~(~((~(B!19 = empty_set)) | (A!20 = empty_set)))) <=> ((~(B!19 = empty_set)) | (A!20 = empty_set))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(149,plain,
% 1.74/1.93 (((B!19 = empty_set) & (~(A!20 = empty_set))) <=> (~((~(B!19 = empty_set)) | (A!20 = empty_set)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(150,plain,
% 1.74/1.93 ((~((B!19 = empty_set) & (~(A!20 = empty_set)))) <=> (~(~((~(B!19 = empty_set)) | (A!20 = empty_set))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[149])).
% 1.74/1.93 tff(151,plain,
% 1.74/1.93 ((~((B!19 = empty_set) & (~(A!20 = empty_set)))) <=> ((~(B!19 = empty_set)) | (A!20 = empty_set))),
% 1.74/1.93 inference(transitivity,[status(thm)],[150, 148])).
% 1.74/1.93 tff(152,plain,
% 1.74/1.93 (~((B!19 = empty_set) & (~(A!20 = empty_set)))),
% 1.74/1.93 inference(or_elim,[status(thm)],[19])).
% 1.74/1.93 tff(153,plain,
% 1.74/1.93 ((~(B!19 = empty_set)) | (A!20 = empty_set)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.74/1.93 tff(154,plain,
% 1.74/1.93 (A!20 = empty_set),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[153, 147])).
% 1.74/1.93 tff(155,plain,
% 1.74/1.93 (((~(B!19 = empty_set)) | (A!20 = empty_set)) | (~(A!20 = empty_set))),
% 1.74/1.93 inference(tautology,[status(thm)],[])).
% 1.74/1.93 tff(156,plain,
% 1.74/1.93 ((~(B!19 = empty_set)) | (A!20 = empty_set)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[155, 154])).
% 1.74/1.93 tff(157,plain,
% 1.74/1.93 (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[95, 156])).
% 1.74/1.93 tff(158,plain,
% 1.74/1.93 (A!20 = relation_dom_as_subset(A!20, B!19, D!17)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[99, 157])).
% 1.74/1.93 tff(159,plain,
% 1.74/1.93 (A!20 = relation_dom_as_subset(A!20, C!18, D!17)),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[158, 68])).
% 1.74/1.93 tff(160,plain,
% 1.74/1.93 (((~(C!18 = empty_set)) | (A!20 = empty_set)) | (~(A!20 = empty_set))),
% 1.74/1.93 inference(tautology,[status(thm)],[])).
% 1.74/1.93 tff(161,plain,
% 1.74/1.93 ((~(C!18 = empty_set)) | (A!20 = empty_set)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[160, 154])).
% 1.74/1.93 tff(162,plain,
% 1.74/1.93 (quasi_total(D!17, A!20, C!18) <=> (A!20 = relation_dom_as_subset(A!20, C!18, D!17))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[124, 161])).
% 1.74/1.93 tff(163,plain,
% 1.74/1.93 (~(A!20 = relation_dom_as_subset(A!20, C!18, D!17))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[112, 162])).
% 1.74/1.94 tff(164,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[163, 159])).
% 1.74/1.94 % SZS output end Proof
% 1.74/1.94 % E exiting
%------------------------------------------------------------------------------