%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU290+2 : 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 38.39s 38.56s
% Output : Proof 38.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU290+2 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.13 % 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 06:38:18 EDT 2025
% 0.13/0.34 % CPUTime :
% 38.39/38.56 % SZS status Theorem
% 38.39/38.56 % SZS output start Proof
% 38.39/38.56 tff(in_type, type, (
% 38.39/38.56 in: ( $i * $i ) > $o)).
% 38.39/38.56 tff(relation_dom_type, type, (
% 38.39/38.56 relation_dom: $i > $i)).
% 38.39/38.56 tff(tptp_fun_D_179_type, type, (
% 38.39/38.56 tptp_fun_D_179: $i)).
% 38.39/38.56 tff(tptp_fun_C_180_type, type, (
% 38.39/38.56 tptp_fun_C_180: $i)).
% 38.39/38.56 tff(tptp_fun_A_182_type, type, (
% 38.39/38.56 tptp_fun_A_182: $i)).
% 38.39/38.56 tff(relation_dom_as_subset_type, type, (
% 38.39/38.56 relation_dom_as_subset: ( $i * $i * $i ) > $i)).
% 38.39/38.56 tff(tptp_fun_B_181_type, type, (
% 38.39/38.56 tptp_fun_B_181: $i)).
% 38.39/38.56 tff(quasi_total_type, type, (
% 38.39/38.56 quasi_total: ( $i * $i * $i ) > $o)).
% 38.39/38.56 tff(empty_set_type, type, (
% 38.39/38.56 empty_set: $i)).
% 38.39/38.56 tff(relation_of2_as_subset_type, type, (
% 38.39/38.56 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 38.39/38.56 tff(function_type, type, (
% 38.39/38.56 function: $i > $o)).
% 38.39/38.56 tff(relation_rng_type, type, (
% 38.39/38.56 relation_rng: $i > $i)).
% 38.39/38.56 tff(apply_type, type, (
% 38.39/38.56 apply: ( $i * $i ) > $i)).
% 38.39/38.56 tff(relation_of2_type, type, (
% 38.39/38.56 relation_of2: ( $i * $i * $i ) > $o)).
% 38.39/38.56 tff(tptp_fun_C_53_type, type, (
% 38.39/38.56 tptp_fun_C_53: ( $i * $i ) > $i)).
% 38.39/38.56 tff(singleton_type, type, (
% 38.39/38.56 singleton: $i > $i)).
% 38.39/38.56 tff(tptp_fun_D_67_type, type, (
% 38.39/38.56 tptp_fun_D_67: ( $i * $i ) > $i)).
% 38.39/38.56 tff(tptp_fun_C_68_type, type, (
% 38.39/38.56 tptp_fun_C_68: ( $i * $i ) > $i)).
% 38.39/38.56 tff(tptp_fun_D_69_type, type, (
% 38.39/38.56 tptp_fun_D_69: ( $i * $i ) > $i)).
% 38.39/38.56 tff(relation_type, type, (
% 38.39/38.56 relation: $i > $o)).
% 38.39/38.56 tff(element_type, type, (
% 38.39/38.56 element: ( $i * $i ) > $o)).
% 38.39/38.56 tff(powerset_type, type, (
% 38.39/38.56 powerset: $i > $i)).
% 38.39/38.56 tff(cartesian_product2_type, type, (
% 38.39/38.56 cartesian_product2: ( $i * $i ) > $i)).
% 38.39/38.56 tff(tptp_fun_C_29_type, type, (
% 38.39/38.56 tptp_fun_C_29: ( $i * $i ) > $i)).
% 38.39/38.56 tff(subset_type, type, (
% 38.39/38.56 subset: ( $i * $i ) > $o)).
% 38.39/38.56 tff(1,plain,
% 38.39/38.56 ((~((B!181 = empty_set) | in(apply(D!179, C!180), relation_rng(D!179)) | (~in(C!180, A!182)) | (~(function(D!179) & quasi_total(D!179, A!182, B!181) & relation_of2_as_subset(D!179, A!182, B!181))))) <=> (~((B!181 = empty_set) | in(apply(D!179, C!180), relation_rng(D!179)) | (~in(C!180, A!182)) | (~(function(D!179) & quasi_total(D!179, A!182, B!181) & relation_of2_as_subset(D!179, A!182, B!181)))))),
% 38.39/38.56 inference(rewrite,[status(thm)],[])).
% 38.39/38.56 tff(2,plain,
% 38.39/38.56 ((~![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | in(apply(D, C), relation_rng(D)) | (~in(C, A)) | (~(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) | in(apply(D, C), relation_rng(D)) | (~in(C, A)) | (~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B)))))),
% 38.39/38.56 inference(rewrite,[status(thm)],[])).
% 38.39/38.56 tff(3,plain,
% 38.39/38.56 ((~![A: $i, B: $i, C: $i, D: $i] : (((function(D) & quasi_total(D, A, B)) & relation_of2_as_subset(D, A, B)) => (in(C, A) => ((B = empty_set) | in(apply(D, C), relation_rng(D)))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | in(apply(D, C), relation_rng(D)) | (~in(C, A)) | (~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B)))))),
% 38.39/38.56 inference(rewrite,[status(thm)],[])).
% 38.39/38.56 tff(4,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (((function(D) & quasi_total(D, A, B)) & relation_of2_as_subset(D, A, B)) => (in(C, A) => ((B = empty_set) | in(apply(D, C), relation_rng(D)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t6_funct_2')).
% 38.39/38.56 tff(5,plain,
% 38.39/38.56 (~![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | in(apply(D, C), relation_rng(D)) | (~in(C, A)) | (~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))))),
% 38.39/38.56 inference(modus_ponens,[status(thm)],[4, 3])).
% 38.39/38.56 tff(6,plain,
% 38.39/38.56 (~![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | in(apply(D, C), relation_rng(D)) | (~in(C, A)) | (~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))))),
% 38.39/38.56 inference(modus_ponens,[status(thm)],[5, 2])).
% 38.39/38.56 tff(7,plain,
% 38.39/38.56 (~![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | in(apply(D, C), relation_rng(D)) | (~in(C, A)) | (~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))))),
% 38.39/38.56 inference(modus_ponens,[status(thm)],[6, 2])).
% 38.39/38.56 tff(8,plain,
% 38.39/38.56 (~![A: $i, B: $i, C: $i, D: $i] : ((B = empty_set) | in(apply(D, C), relation_rng(D)) | (~in(C, A)) | (~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))))),
% 38.39/38.56 inference(modus_ponens,[status(thm)],[7, 2])).
% 38.39/38.56 tff(9,plain,(
% 38.39/38.56 ~((B!181 = empty_set) | in(apply(D!179, C!180), relation_rng(D!179)) | (~in(C!180, A!182)) | (~(function(D!179) & quasi_total(D!179, A!182, B!181) & relation_of2_as_subset(D!179, A!182, B!181))))),
% 38.39/38.56 inference(skolemize,[status(sab)],[8])).
% 38.39/38.56 tff(10,plain,
% 38.39/38.56 (~((B!181 = empty_set) | in(apply(D!179, C!180), relation_rng(D!179)) | (~in(C!180, A!182)) | (~(function(D!179) & quasi_total(D!179, A!182, B!181) & relation_of2_as_subset(D!179, A!182, B!181))))),
% 38.39/38.56 inference(modus_ponens,[status(thm)],[9, 1])).
% 38.39/38.56 tff(11,plain,
% 38.39/38.56 (function(D!179) & quasi_total(D!179, A!182, B!181) & relation_of2_as_subset(D!179, A!182, B!181)),
% 38.39/38.56 inference(or_elim,[status(thm)],[10])).
% 38.39/38.56 tff(12,plain,
% 38.39/38.56 (relation_of2_as_subset(D!179, A!182, B!181)),
% 38.39/38.56 inference(and_elim,[status(thm)],[11])).
% 38.39/38.56 tff(13,plain,
% 38.39/38.56 (^[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))))))))),
% 38.39/38.56 inference(bind,[status(th)],[])).
% 38.39/38.56 tff(14,plain,
% 38.39/38.56 (![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)))))))),
% 38.39/38.56 inference(quant_intro,[status(thm)],[13])).
% 38.39/38.56 tff(15,plain,
% 38.39/38.56 (^[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))))))))),
% 38.39/38.56 inference(bind,[status(th)],[])).
% 38.39/38.56 tff(16,plain,
% 38.39/38.56 (![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)))))))),
% 38.39/38.56 inference(quant_intro,[status(thm)],[15])).
% 38.39/38.56 tff(17,plain,
% 38.39/38.56 (![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)))))),
% 38.39/38.56 inference(rewrite,[status(thm)],[])).
% 38.39/38.56 tff(18,plain,
% 38.39/38.56 (^[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)))))))),
% 38.39/38.56 inference(bind,[status(th)],[])).
% 38.39/38.56 tff(19,plain,
% 38.39/38.56 (![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)))))),
% 38.39/38.56 inference(quant_intro,[status(thm)],[18])).
% 38.39/38.56 tff(20,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')).
% 38.39/38.56 tff(21,plain,
% 38.39/38.56 (![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)))))),
% 38.39/38.56 inference(modus_ponens,[status(thm)],[20, 19])).
% 38.39/38.56 tff(22,plain,
% 38.39/38.56 (![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)))))),
% 38.39/38.56 inference(modus_ponens,[status(thm)],[21, 17])).
% 38.39/38.56 tff(23,plain,(
% 38.39/38.56 ![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)))))),
% 38.39/38.56 inference(skolemize,[status(sab)],[22])).
% 38.39/38.56 tff(24,plain,
% 38.39/38.56 (![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)))))))),
% 38.39/38.56 inference(modus_ponens,[status(thm)],[23, 16])).
% 38.39/38.56 tff(25,plain,
% 38.39/38.56 (![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)))))))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[24, 14])).
% 38.39/38.57 tff(26,plain,
% 38.39/38.57 (((~![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!179, A!182, B!181)) | (~((~((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))) | (~((~(B!181 = empty_set)) | (A!182 = empty_set) | (quasi_total(D!179, A!182, B!181) <=> (D!179 = 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!179, A!182, B!181)) | (~((~((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))) | (~((~(B!181 = empty_set)) | (A!182 = empty_set) | (quasi_total(D!179, A!182, B!181) <=> (D!179 = empty_set)))))))),
% 38.39/38.57 inference(rewrite,[status(thm)],[])).
% 38.39/38.57 tff(27,plain,
% 38.39/38.57 (((~relation_of2_as_subset(D!179, A!182, B!181)) | (~((~((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))) | (~((quasi_total(D!179, A!182, B!181) <=> (D!179 = empty_set)) | (A!182 = empty_set) | (~(B!181 = empty_set))))))) <=> ((~relation_of2_as_subset(D!179, A!182, B!181)) | (~((~((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))) | (~((~(B!181 = empty_set)) | (A!182 = empty_set) | (quasi_total(D!179, A!182, B!181) <=> (D!179 = empty_set)))))))),
% 38.39/38.57 inference(rewrite,[status(thm)],[])).
% 38.39/38.57 tff(28,plain,
% 38.39/38.57 (((~![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!179, A!182, B!181)) | (~((~((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))) | (~((quasi_total(D!179, A!182, B!181) <=> (D!179 = empty_set)) | (A!182 = empty_set) | (~(B!181 = 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!179, A!182, B!181)) | (~((~((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))) | (~((~(B!181 = empty_set)) | (A!182 = empty_set) | (quasi_total(D!179, A!182, B!181) <=> (D!179 = empty_set))))))))),
% 38.39/38.57 inference(monotonicity,[status(thm)],[27])).
% 38.39/38.57 tff(29,plain,
% 38.39/38.57 (((~![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!179, A!182, B!181)) | (~((~((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))) | (~((quasi_total(D!179, A!182, B!181) <=> (D!179 = empty_set)) | (A!182 = empty_set) | (~(B!181 = 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!179, A!182, B!181)) | (~((~((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))) | (~((~(B!181 = empty_set)) | (A!182 = empty_set) | (quasi_total(D!179, A!182, B!181) <=> (D!179 = empty_set)))))))),
% 38.39/38.57 inference(transitivity,[status(thm)],[28, 26])).
% 38.39/38.57 tff(30,plain,
% 38.39/38.57 ((~![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!179, A!182, B!181)) | (~((~((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))) | (~((quasi_total(D!179, A!182, B!181) <=> (D!179 = empty_set)) | (A!182 = empty_set) | (~(B!181 = empty_set)))))))),
% 38.39/38.57 inference(quant_inst,[status(thm)],[])).
% 38.39/38.57 tff(31,plain,
% 38.39/38.57 ((~![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!179, A!182, B!181)) | (~((~((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))) | (~((~(B!181 = empty_set)) | (A!182 = empty_set) | (quasi_total(D!179, A!182, B!181) <=> (D!179 = empty_set))))))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[30, 29])).
% 38.39/38.57 tff(32,plain,
% 38.39/38.57 (~((~((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))) | (~((~(B!181 = empty_set)) | (A!182 = empty_set) | (quasi_total(D!179, A!182, B!181) <=> (D!179 = empty_set)))))),
% 38.39/38.57 inference(unit_resolution,[status(thm)],[31, 25, 12])).
% 38.39/38.57 tff(33,plain,
% 38.39/38.57 (((~((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))) | (~((~(B!181 = empty_set)) | (A!182 = empty_set) | (quasi_total(D!179, A!182, B!181) <=> (D!179 = empty_set))))) | ((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))),
% 38.39/38.57 inference(tautology,[status(thm)],[])).
% 38.39/38.57 tff(34,plain,
% 38.39/38.57 ((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179)))),
% 38.39/38.57 inference(unit_resolution,[status(thm)],[33, 32])).
% 38.39/38.57 tff(35,plain,
% 38.39/38.57 (~(B!181 = empty_set)),
% 38.39/38.57 inference(or_elim,[status(thm)],[10])).
% 38.39/38.57 tff(36,plain,
% 38.39/38.57 (((~(B!181 = empty_set)) | (A!182 = empty_set)) | (B!181 = empty_set)),
% 38.39/38.57 inference(tautology,[status(thm)],[])).
% 38.39/38.57 tff(37,plain,
% 38.39/38.57 ((~(B!181 = empty_set)) | (A!182 = empty_set)),
% 38.39/38.57 inference(unit_resolution,[status(thm)],[36, 35])).
% 38.39/38.57 tff(38,plain,
% 38.39/38.57 ((~((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))) | (~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179)))),
% 38.39/38.57 inference(tautology,[status(thm)],[])).
% 38.39/38.57 tff(39,plain,
% 38.39/38.57 ((~((~((~(B!181 = empty_set)) | (A!182 = empty_set))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))))) | (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179)))),
% 38.39/38.57 inference(unit_resolution,[status(thm)],[38, 37])).
% 38.39/38.57 tff(40,plain,
% 38.39/38.57 (quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179))),
% 38.39/38.57 inference(unit_resolution,[status(thm)],[39, 34])).
% 38.39/38.57 tff(41,plain,
% 38.39/38.57 (quasi_total(D!179, A!182, B!181)),
% 38.39/38.57 inference(and_elim,[status(thm)],[11])).
% 38.39/38.57 tff(42,plain,
% 38.39/38.57 ((~(quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179)))) | (~quasi_total(D!179, A!182, B!181)) | (A!182 = relation_dom_as_subset(A!182, B!181, D!179))),
% 38.39/38.57 inference(tautology,[status(thm)],[])).
% 38.39/38.57 tff(43,plain,
% 38.39/38.57 ((~(quasi_total(D!179, A!182, B!181) <=> (A!182 = relation_dom_as_subset(A!182, B!181, D!179)))) | (A!182 = relation_dom_as_subset(A!182, B!181, D!179))),
% 38.39/38.57 inference(unit_resolution,[status(thm)],[42, 41])).
% 38.39/38.57 tff(44,plain,
% 38.39/38.57 (A!182 = relation_dom_as_subset(A!182, B!181, D!179)),
% 38.39/38.57 inference(unit_resolution,[status(thm)],[43, 40])).
% 38.39/38.57 tff(45,plain,
% 38.39/38.57 (relation_dom_as_subset(A!182, B!181, D!179) = A!182),
% 38.39/38.57 inference(symmetry,[status(thm)],[44])).
% 38.39/38.57 tff(46,plain,
% 38.39/38.57 (^[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)))),
% 38.39/38.57 inference(bind,[status(th)],[])).
% 38.39/38.57 tff(47,plain,
% 38.39/38.57 (![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))),
% 38.39/38.57 inference(quant_intro,[status(thm)],[46])).
% 38.39/38.57 tff(48,plain,
% 38.39/38.57 (![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))),
% 38.39/38.57 inference(rewrite,[status(thm)],[])).
% 38.39/38.57 tff(49,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')).
% 38.39/38.57 tff(50,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[49, 48])).
% 38.39/38.57 tff(51,plain,(
% 38.39/38.57 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 38.39/38.57 inference(skolemize,[status(sab)],[50])).
% 38.39/38.57 tff(52,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[51, 47])).
% 38.39/38.57 tff(53,plain,
% 38.39/38.57 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(D!179, A!182, B!181) <=> relation_of2(D!179, A!182, B!181))),
% 38.39/38.57 inference(quant_inst,[status(thm)],[])).
% 38.39/38.57 tff(54,plain,
% 38.39/38.57 (relation_of2_as_subset(D!179, A!182, B!181) <=> relation_of2(D!179, A!182, B!181)),
% 38.39/38.57 inference(unit_resolution,[status(thm)],[53, 52])).
% 38.39/38.57 tff(55,plain,
% 38.39/38.57 ((~(relation_of2_as_subset(D!179, A!182, B!181) <=> relation_of2(D!179, A!182, B!181))) | (~relation_of2_as_subset(D!179, A!182, B!181)) | relation_of2(D!179, A!182, B!181)),
% 38.39/38.57 inference(tautology,[status(thm)],[])).
% 38.39/38.57 tff(56,plain,
% 38.39/38.57 ((~(relation_of2_as_subset(D!179, A!182, B!181) <=> relation_of2(D!179, A!182, B!181))) | relation_of2(D!179, A!182, B!181)),
% 38.39/38.57 inference(unit_resolution,[status(thm)],[55, 12])).
% 38.39/38.57 tff(57,plain,
% 38.39/38.57 (relation_of2(D!179, A!182, B!181)),
% 38.39/38.57 inference(unit_resolution,[status(thm)],[56, 54])).
% 38.39/38.57 tff(58,plain,
% 38.39/38.57 (^[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))))),
% 38.39/38.57 inference(bind,[status(th)],[])).
% 38.39/38.57 tff(59,plain,
% 38.39/38.57 (![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)))),
% 38.39/38.57 inference(quant_intro,[status(thm)],[58])).
% 38.39/38.57 tff(60,plain,
% 38.39/38.57 (![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)))),
% 38.39/38.57 inference(rewrite,[status(thm)],[])).
% 38.39/38.57 tff(61,plain,
% 38.39/38.57 (^[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))))),
% 38.39/38.57 inference(bind,[status(th)],[])).
% 38.39/38.57 tff(62,plain,
% 38.39/38.57 (![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)))),
% 38.39/38.57 inference(quant_intro,[status(thm)],[61])).
% 38.39/38.57 tff(63,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')).
% 38.39/38.57 tff(64,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[63, 62])).
% 38.39/38.57 tff(65,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[64, 60])).
% 38.39/38.57 tff(66,plain,(
% 38.39/38.57 ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 38.39/38.57 inference(skolemize,[status(sab)],[65])).
% 38.39/38.57 tff(67,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[66, 59])).
% 38.39/38.57 tff(68,plain,
% 38.39/38.57 (((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | ((~relation_of2(D!179, A!182, B!181)) | (relation_dom_as_subset(A!182, B!181, D!179) = relation_dom(D!179)))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | (~relation_of2(D!179, A!182, B!181)) | (relation_dom_as_subset(A!182, B!181, D!179) = relation_dom(D!179)))),
% 38.39/38.57 inference(rewrite,[status(thm)],[])).
% 38.39/38.57 tff(69,plain,
% 38.39/38.57 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | ((~relation_of2(D!179, A!182, B!181)) | (relation_dom_as_subset(A!182, B!181, D!179) = relation_dom(D!179)))),
% 38.39/38.57 inference(quant_inst,[status(thm)],[])).
% 38.39/38.57 tff(70,plain,
% 38.39/38.57 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | (~relation_of2(D!179, A!182, B!181)) | (relation_dom_as_subset(A!182, B!181, D!179) = relation_dom(D!179))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[69, 68])).
% 38.39/38.57 tff(71,plain,
% 38.39/38.57 (relation_dom_as_subset(A!182, B!181, D!179) = relation_dom(D!179)),
% 38.39/38.57 inference(unit_resolution,[status(thm)],[70, 67, 57])).
% 38.39/38.57 tff(72,plain,
% 38.39/38.57 (relation_dom(D!179) = relation_dom_as_subset(A!182, B!181, D!179)),
% 38.39/38.57 inference(symmetry,[status(thm)],[71])).
% 38.39/38.57 tff(73,plain,
% 38.39/38.57 (relation_dom(D!179) = A!182),
% 38.39/38.57 inference(transitivity,[status(thm)],[72, 45])).
% 38.39/38.57 tff(74,plain,
% 38.39/38.57 (in(C!180, relation_dom(D!179)) <=> in(C!180, A!182)),
% 38.39/38.57 inference(monotonicity,[status(thm)],[73])).
% 38.39/38.57 tff(75,plain,
% 38.39/38.57 (in(C!180, A!182) <=> in(C!180, relation_dom(D!179))),
% 38.39/38.57 inference(symmetry,[status(thm)],[74])).
% 38.39/38.57 tff(76,plain,
% 38.39/38.57 (in(C!180, A!182)),
% 38.39/38.57 inference(or_elim,[status(thm)],[10])).
% 38.39/38.57 tff(77,plain,
% 38.39/38.57 (in(C!180, relation_dom(D!179))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[76, 75])).
% 38.39/38.57 tff(78,plain,
% 38.39/38.57 (^[A: $i, B: $i, C: $i] : refl(((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 38.39/38.57 inference(bind,[status(th)],[])).
% 38.39/38.57 tff(79,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 38.39/38.57 inference(quant_intro,[status(thm)],[78])).
% 38.39/38.57 tff(80,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 38.39/38.57 inference(rewrite,[status(thm)],[])).
% 38.39/38.57 tff(81,plain,
% 38.39/38.57 (^[A: $i, B: $i, C: $i] : rewrite((relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B)))))),
% 38.39/38.57 inference(bind,[status(th)],[])).
% 38.39/38.57 tff(82,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 38.39/38.57 inference(quant_intro,[status(thm)],[81])).
% 38.39/38.57 tff(83,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 38.39/38.57 tff(84,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[83, 82])).
% 38.39/38.57 tff(85,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[84, 80])).
% 38.39/38.57 tff(86,plain,(
% 38.39/38.57 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 38.39/38.57 inference(skolemize,[status(sab)],[85])).
% 38.39/38.57 tff(87,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[86, 79])).
% 38.39/38.57 tff(88,plain,
% 38.39/38.57 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(D!179, A!182, B!181)) | element(D!179, powerset(cartesian_product2(A!182, B!181))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(D!179, A!182, B!181)) | element(D!179, powerset(cartesian_product2(A!182, B!181))))),
% 38.39/38.57 inference(rewrite,[status(thm)],[])).
% 38.39/38.57 tff(89,plain,
% 38.39/38.57 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | ((~relation_of2_as_subset(D!179, A!182, B!181)) | element(D!179, powerset(cartesian_product2(A!182, B!181))))),
% 38.39/38.57 inference(quant_inst,[status(thm)],[])).
% 38.39/38.57 tff(90,plain,
% 38.39/38.57 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))) | (~relation_of2_as_subset(D!179, A!182, B!181)) | element(D!179, powerset(cartesian_product2(A!182, B!181)))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[89, 88])).
% 38.39/38.57 tff(91,plain,
% 38.39/38.57 (element(D!179, powerset(cartesian_product2(A!182, B!181)))),
% 38.39/38.57 inference(unit_resolution,[status(thm)],[90, 87, 12])).
% 38.39/38.57 tff(92,plain,
% 38.39/38.57 (^[A: $i, B: $i, C: $i] : refl((relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 38.39/38.57 inference(bind,[status(th)],[])).
% 38.39/38.57 tff(93,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 38.39/38.57 inference(quant_intro,[status(thm)],[92])).
% 38.39/38.57 tff(94,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 38.39/38.57 inference(rewrite,[status(thm)],[])).
% 38.39/38.57 tff(95,plain,
% 38.39/38.57 (^[A: $i, B: $i, C: $i] : rewrite((element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> (relation(C) | (~element(C, powerset(cartesian_product2(A, B))))))),
% 38.39/38.57 inference(bind,[status(th)],[])).
% 38.39/38.57 tff(96,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C)) <=> ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 38.39/38.57 inference(quant_intro,[status(thm)],[95])).
% 38.39/38.57 tff(97,axiom,(![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_relset_1')).
% 38.39/38.57 tff(98,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[97, 96])).
% 38.39/38.57 tff(99,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[98, 94])).
% 38.39/38.57 tff(100,plain,(
% 38.39/38.57 ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 38.39/38.57 inference(skolemize,[status(sab)],[99])).
% 38.39/38.57 tff(101,plain,
% 38.39/38.57 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[100, 93])).
% 38.39/38.57 tff(102,plain,
% 38.39/38.57 (((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(D!179) | (~element(D!179, powerset(cartesian_product2(A!182, B!181)))))) <=> ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(D!179) | (~element(D!179, powerset(cartesian_product2(A!182, B!181)))))),
% 38.39/38.57 inference(rewrite,[status(thm)],[])).
% 38.39/38.57 tff(103,plain,
% 38.39/38.57 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(D!179) | (~element(D!179, powerset(cartesian_product2(A!182, B!181)))))),
% 38.39/38.57 inference(quant_inst,[status(thm)],[])).
% 38.39/38.57 tff(104,plain,
% 38.39/38.57 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(D!179) | (~element(D!179, powerset(cartesian_product2(A!182, B!181))))),
% 38.39/38.57 inference(modus_ponens,[status(thm)],[103, 102])).
% 38.39/38.57 tff(105,plain,
% 38.39/38.57 (relation(D!179)),
% 38.39/38.57 inference(unit_resolution,[status(thm)],[104, 101, 91])).
% 38.39/38.57 tff(106,plain,
% 38.39/38.57 (function(D!179)),
% 38.39/38.57 inference(and_elim,[status(thm)],[11])).
% 38.39/38.57 tff(107,plain,
% 38.39/38.57 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, D_194: $i, C: $i, D: $i] : rewrite((~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ((~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194)))))))))))) <=> (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | (~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))), (![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ((~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194)))))))))))) <=> ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | (~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ((~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | (~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194)))))))))))))), rewrite(((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | (~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194)))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | (~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ((~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | (~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))))),
% 38.39/38.57 inference(bind,[status(th)],[])).
% 38.39/38.57 tff(108,plain,
% 38.39/38.57 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ((~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | (~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))),
% 38.39/38.57 inference(quant_intro,[status(thm)],[107])).
% 38.39/38.57 tff(109,plain,
% 38.39/38.57 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ((~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ((~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))))),
% 38.39/38.57 inference(bind,[status(th)],[])).
% 38.39/38.57 tff(110,plain,
% 38.39/38.57 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ((~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ((~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194)))))))))))))),
% 38.39/38.57 inference(quant_intro,[status(thm)],[109])).
% 38.39/38.57 tff(111,plain,
% 38.39/38.57 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ((~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))))),
% 38.39/38.57 inference(bind,[status(th)],[])).
% 38.39/38.57 tff(112,plain,
% 38.39/38.57 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ((~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194)))))))))))))),
% 38.39/38.57 inference(quant_intro,[status(thm)],[111])).
% 38.39/38.57 tff(113,plain,
% 38.39/38.57 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ((~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194)))))))))))))),
% 38.39/38.57 inference(transitivity,[status(thm)],[112, 110])).
% 38.39/38.57 tff(114,plain,
% 38.39/38.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(A) & function(A)) <=> (~((~relation(A)) | (~function(A))))), ((~(relation(A) & function(A))) <=> (~(~((~relation(A)) | (~function(A))))))), rewrite((~(~((~relation(A)) | (~function(A))))) <=> ((~relation(A)) | (~function(A)))), ((~(relation(A) & function(A))) <=> ((~relation(A)) | (~function(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_67(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_67(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) <=> ((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_69(B, A), relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))) <=> (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))))), ((in(tptp_fun_C_68(B, A), B) | (in(tptp_fun_D_69(B, A), relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))) <=> (in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))))))), rewrite((in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))))) <=> (in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))), ((in(tptp_fun_C_68(B, A), B) | (in(tptp_fun_D_69(B, A), relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))) <=> (in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))))))), rewrite(((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, D))))) <=> ((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D)))))), (((in(tptp_fun_C_68(B, A), B) | (in(tptp_fun_D_69(B, A), relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))) & ((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, D)))))) <=> ((in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))))) & ((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D)))))))), rewrite(((in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))))) & ((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D)))))) <=> (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D))))))))), (((in(tptp_fun_C_68(B, A), B) | (in(tptp_fun_D_69(B, A), relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))) & ((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, D)))))) <=> (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D)))))))))), (((B = relation_rng(A)) | ((in(tptp_fun_C_68(B, A), B) | (in(tptp_fun_D_69(B, A), relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))) & ((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, D))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D))))))))))), rewrite(((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D))))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D)))))))))), (((B = relation_rng(A)) | ((in(tptp_fun_C_68(B, A), B) | (in(tptp_fun_D_69(B, A), relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))) & ((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, D))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D))))))))))), ((((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_67(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_67(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_68(B, A), B) | (in(tptp_fun_D_69(B, A), relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))) & ((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, D)))))))) <=> (((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) & ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D)))))))))))), rewrite((((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) & ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D)))))))))) <=> (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D))))))))))))), ((((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_67(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_67(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_68(B, A), B) | (in(tptp_fun_D_69(B, A), relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))) & ((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, D)))))))) <=> (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D))))))))))))))), (![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_67(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_67(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_68(B, A), B) | (in(tptp_fun_D_69(B, A), relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))) & ((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, D)))))))) <=> ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D)))))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_67(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_67(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_68(B, A), B) | (in(tptp_fun_D_69(B, A), relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))) & ((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, D))))))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D))))))))))))))), rewrite((((~relation(A)) | (~function(A))) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D)))))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_67(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_67(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_68(B, A), B) | (in(tptp_fun_D_69(B, A), relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))) & ((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, D))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D)))))))))))))))),
% 38.39/38.58 inference(bind,[status(th)],[])).
% 38.39/38.58 tff(115,plain,
% 38.39/38.58 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_67(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_67(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_68(B, A), B) | (in(tptp_fun_D_69(B, A), relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))) & ((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, D))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D)))))))))))))),
% 38.39/38.58 inference(quant_intro,[status(thm)],[114])).
% 38.39/38.58 tff(116,plain,
% 38.39/38.58 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 38.39/38.58 inference(rewrite,[status(thm)],[])).
% 38.39/38.58 tff(117,plain,
% 38.39/38.58 (^[A: $i] : rewrite(((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))))),
% 38.39/38.58 inference(bind,[status(th)],[])).
% 38.39/38.58 tff(118,plain,
% 38.39/38.58 (![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D)))))) <=> ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 38.39/38.58 inference(quant_intro,[status(thm)],[117])).
% 38.39/38.58 tff(119,axiom,(![A: $i] : ((relation(A) & function(A)) => ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_funct_1')).
% 38.39/38.58 tff(120,plain,
% 38.39/38.58 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 38.39/38.58 inference(modus_ponens,[status(thm)],[119, 118])).
% 38.39/38.58 tff(121,plain,
% 38.39/38.58 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : ((B = relation_rng(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, relation_dom(A)) & (C = apply(A, D))))))),
% 38.39/38.58 inference(modus_ponens,[status(thm)],[120, 116])).
% 38.39/38.58 tff(122,plain,(
% 38.39/38.58 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_67(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_67(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_68(B, A), B) | (in(tptp_fun_D_69(B, A), relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A))))) & ((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_68(B, A) = apply(A, D)))))))))),
% 38.39/38.58 inference(skolemize,[status(sab)],[121])).
% 38.39/38.58 tff(123,plain,
% 38.39/38.58 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D)))))))))))))),
% 38.39/38.58 inference(modus_ponens,[status(thm)],[122, 115])).
% 38.39/38.58 tff(124,plain,
% 38.39/38.58 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | ((~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194)))))))))))))),
% 38.39/38.58 inference(modus_ponens,[status(thm)],[123, 113])).
% 38.39/38.58 tff(125,plain,
% 38.39/38.58 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | (~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))),
% 38.39/38.58 inference(modus_ponens,[status(thm)],[124, 108])).
% 38.39/38.58 tff(126,plain,
% 38.39/38.58 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | (~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))) | ((~relation(D!179)) | (~function(D!179)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!179))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, D!179), relation_dom(D!179))) | (~(C = apply(D!179, tptp_fun_D_67(C, D!179)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!179))) | (~(C = apply(D!179, D))))))))) | (~((B = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(B, D!179), B) | (~((~in(tptp_fun_D_69(B, D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, tptp_fun_D_69(B, D!179)))))))) | (~((~in(tptp_fun_C_68(B, D!179), B)) | (~in(D_194, relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, D_194))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | (~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))) | (~relation(D!179)) | (~function(D!179)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!179))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, D!179), relation_dom(D!179))) | (~(C = apply(D!179, tptp_fun_D_67(C, D!179)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!179))) | (~(C = apply(D!179, D))))))))) | (~((B = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(B, D!179), B) | (~((~in(tptp_fun_D_69(B, D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, tptp_fun_D_69(B, D!179)))))))) | (~((~in(tptp_fun_C_68(B, D!179), B)) | (~in(D_194, relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, D_194))))))))))))),
% 38.39/38.58 inference(rewrite,[status(thm)],[])).
% 38.39/38.58 tff(127,plain,
% 38.39/38.58 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | (~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))) | ((~relation(D!179)) | (~function(D!179)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!179))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, D!179), relation_dom(D!179))) | (~(C = apply(D!179, tptp_fun_D_67(C, D!179)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!179))) | (~(C = apply(D!179, D))))))))) | (~((B = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(B, D!179), B) | (~((~in(tptp_fun_D_69(B, D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, tptp_fun_D_69(B, D!179)))))))) | (~((~in(tptp_fun_C_68(B, D!179), B)) | (~in(D_194, relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, D_194))))))))))))),
% 38.39/38.58 inference(quant_inst,[status(thm)],[])).
% 38.39/38.58 tff(128,plain,
% 38.39/38.58 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_67(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_68(B, A), B) | (~((~in(tptp_fun_D_69(B, A), relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, tptp_fun_D_69(B, A)))))))) | (~((~in(tptp_fun_C_68(B, A), B)) | (~in(D_194, relation_dom(A))) | (~(tptp_fun_C_68(B, A) = apply(A, D_194))))))))))))) | (~relation(D!179)) | (~function(D!179)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!179))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, D!179), relation_dom(D!179))) | (~(C = apply(D!179, tptp_fun_D_67(C, D!179)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!179))) | (~(C = apply(D!179, D))))))))) | (~((B = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(B, D!179), B) | (~((~in(tptp_fun_D_69(B, D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, tptp_fun_D_69(B, D!179)))))))) | (~((~in(tptp_fun_C_68(B, D!179), B)) | (~in(D_194, relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, D_194)))))))))))),
% 38.39/38.58 inference(modus_ponens,[status(thm)],[127, 126])).
% 38.39/38.58 tff(129,plain,
% 38.39/38.58 ((~relation(D!179)) | ![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!179))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, D!179), relation_dom(D!179))) | (~(C = apply(D!179, tptp_fun_D_67(C, D!179)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!179))) | (~(C = apply(D!179, D))))))))) | (~((B = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(B, D!179), B) | (~((~in(tptp_fun_D_69(B, D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, tptp_fun_D_69(B, D!179)))))))) | (~((~in(tptp_fun_C_68(B, D!179), B)) | (~in(D_194, relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, D_194)))))))))))),
% 38.39/38.58 inference(unit_resolution,[status(thm)],[128, 125, 106])).
% 38.39/38.58 tff(130,plain,
% 38.39/38.58 (![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!179))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, D!179), relation_dom(D!179))) | (~(C = apply(D!179, tptp_fun_D_67(C, D!179)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!179))) | (~(C = apply(D!179, D))))))))) | (~((B = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(B, D!179), B) | (~((~in(tptp_fun_D_69(B, D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, tptp_fun_D_69(B, D!179)))))))) | (~((~in(tptp_fun_C_68(B, D!179), B)) | (~in(D_194, relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, D_194)))))))))))),
% 38.39/38.58 inference(unit_resolution,[status(thm)],[129, 105])).
% 38.39/38.58 tff(131,plain,
% 38.39/38.58 (((~![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!179))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, D!179), relation_dom(D!179))) | (~(C = apply(D!179, tptp_fun_D_67(C, D!179)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!179))) | (~(C = apply(D!179, D))))))))) | (~((B = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(B, D!179), B) | (~((~in(tptp_fun_D_69(B, D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, tptp_fun_D_69(B, D!179)))))))) | (~((~in(tptp_fun_C_68(B, D!179), B)) | (~in(D_194, relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, D_194)))))))))))) | (~((~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))) | (~((~in(tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179), relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179)))))))) | (~((~in(C!180, relation_dom(D!179))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))))))) <=> ((~![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!179))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, D!179), relation_dom(D!179))) | (~(C = apply(D!179, tptp_fun_D_67(C, D!179)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!179))) | (~(C = apply(D!179, D))))))))) | (~((B = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(B, D!179), B) | (~((~in(tptp_fun_D_69(B, D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, tptp_fun_D_69(B, D!179)))))))) | (~((~in(tptp_fun_C_68(B, D!179), B)) | (~in(D_194, relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, D_194)))))))))))) | (~((~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))) | (~((~in(tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179), relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179)))))))) | (~((~in(C!180, relation_dom(D!179))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))))))),
% 38.39/38.58 inference(rewrite,[status(thm)],[])).
% 38.39/38.58 tff(132,plain,
% 38.39/38.58 ((~((~((~(relation_rng(D!179) = relation_rng(D!179))) | (~((~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))) | (~((~in(tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179), relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179)))))))) | (~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~in(C!180, relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))))))) | (~((relation_rng(D!179) = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(relation_rng(D!179), D!179), relation_rng(D!179)) | (~((~in(tptp_fun_D_69(relation_rng(D!179), D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(relation_rng(D!179), D!179) = apply(D!179, tptp_fun_D_69(relation_rng(D!179), D!179)))))))) | (~((~in(tptp_fun_C_68(relation_rng(D!179), D!179), relation_rng(D!179))) | (~in(C!180, relation_dom(D!179))) | (~(tptp_fun_C_68(relation_rng(D!179), D!179) = apply(D!179, C!180))))))))))) <=> (~((~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))) | (~((~in(tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179), relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179)))))))) | (~((~in(C!180, relation_dom(D!179))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))))))),
% 38.39/38.58 inference(rewrite,[status(thm)],[])).
% 38.39/38.58 tff(133,plain,
% 38.39/38.58 (((~![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!179))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, D!179), relation_dom(D!179))) | (~(C = apply(D!179, tptp_fun_D_67(C, D!179)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!179))) | (~(C = apply(D!179, D))))))))) | (~((B = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(B, D!179), B) | (~((~in(tptp_fun_D_69(B, D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, tptp_fun_D_69(B, D!179)))))))) | (~((~in(tptp_fun_C_68(B, D!179), B)) | (~in(D_194, relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, D_194)))))))))))) | (~((~((~(relation_rng(D!179) = relation_rng(D!179))) | (~((~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))) | (~((~in(tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179), relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179)))))))) | (~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~in(C!180, relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))))))) | (~((relation_rng(D!179) = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(relation_rng(D!179), D!179), relation_rng(D!179)) | (~((~in(tptp_fun_D_69(relation_rng(D!179), D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(relation_rng(D!179), D!179) = apply(D!179, tptp_fun_D_69(relation_rng(D!179), D!179)))))))) | (~((~in(tptp_fun_C_68(relation_rng(D!179), D!179), relation_rng(D!179))) | (~in(C!180, relation_dom(D!179))) | (~(tptp_fun_C_68(relation_rng(D!179), D!179) = apply(D!179, C!180)))))))))))) <=> ((~![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!179))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, D!179), relation_dom(D!179))) | (~(C = apply(D!179, tptp_fun_D_67(C, D!179)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!179))) | (~(C = apply(D!179, D))))))))) | (~((B = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(B, D!179), B) | (~((~in(tptp_fun_D_69(B, D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, tptp_fun_D_69(B, D!179)))))))) | (~((~in(tptp_fun_C_68(B, D!179), B)) | (~in(D_194, relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, D_194)))))))))))) | (~((~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))) | (~((~in(tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179), relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179)))))))) | (~((~in(C!180, relation_dom(D!179))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))))))),
% 38.39/38.58 inference(monotonicity,[status(thm)],[132])).
% 38.39/38.58 tff(134,plain,
% 38.39/38.58 (((~![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!179))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, D!179), relation_dom(D!179))) | (~(C = apply(D!179, tptp_fun_D_67(C, D!179)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!179))) | (~(C = apply(D!179, D))))))))) | (~((B = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(B, D!179), B) | (~((~in(tptp_fun_D_69(B, D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, tptp_fun_D_69(B, D!179)))))))) | (~((~in(tptp_fun_C_68(B, D!179), B)) | (~in(D_194, relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, D_194)))))))))))) | (~((~((~(relation_rng(D!179) = relation_rng(D!179))) | (~((~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))) | (~((~in(tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179), relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179)))))))) | (~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~in(C!180, relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))))))) | (~((relation_rng(D!179) = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(relation_rng(D!179), D!179), relation_rng(D!179)) | (~((~in(tptp_fun_D_69(relation_rng(D!179), D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(relation_rng(D!179), D!179) = apply(D!179, tptp_fun_D_69(relation_rng(D!179), D!179)))))))) | (~((~in(tptp_fun_C_68(relation_rng(D!179), D!179), relation_rng(D!179))) | (~in(C!180, relation_dom(D!179))) | (~(tptp_fun_C_68(relation_rng(D!179), D!179) = apply(D!179, C!180)))))))))))) <=> ((~![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!179))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, D!179), relation_dom(D!179))) | (~(C = apply(D!179, tptp_fun_D_67(C, D!179)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!179))) | (~(C = apply(D!179, D))))))))) | (~((B = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(B, D!179), B) | (~((~in(tptp_fun_D_69(B, D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, tptp_fun_D_69(B, D!179)))))))) | (~((~in(tptp_fun_C_68(B, D!179), B)) | (~in(D_194, relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, D_194)))))))))))) | (~((~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))) | (~((~in(tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179), relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179)))))))) | (~((~in(C!180, relation_dom(D!179))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))))))),
% 38.39/38.58 inference(transitivity,[status(thm)],[133, 131])).
% 38.39/38.58 tff(135,plain,
% 38.39/38.58 ((~![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!179))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, D!179), relation_dom(D!179))) | (~(C = apply(D!179, tptp_fun_D_67(C, D!179)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!179))) | (~(C = apply(D!179, D))))))))) | (~((B = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(B, D!179), B) | (~((~in(tptp_fun_D_69(B, D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, tptp_fun_D_69(B, D!179)))))))) | (~((~in(tptp_fun_C_68(B, D!179), B)) | (~in(D_194, relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, D_194)))))))))))) | (~((~((~(relation_rng(D!179) = relation_rng(D!179))) | (~((~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))) | (~((~in(tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179), relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179)))))))) | (~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~in(C!180, relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))))))) | (~((relation_rng(D!179) = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(relation_rng(D!179), D!179), relation_rng(D!179)) | (~((~in(tptp_fun_D_69(relation_rng(D!179), D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(relation_rng(D!179), D!179) = apply(D!179, tptp_fun_D_69(relation_rng(D!179), D!179)))))))) | (~((~in(tptp_fun_C_68(relation_rng(D!179), D!179), relation_rng(D!179))) | (~in(C!180, relation_dom(D!179))) | (~(tptp_fun_C_68(relation_rng(D!179), D!179) = apply(D!179, C!180)))))))))))),
% 38.39/38.59 inference(quant_inst,[status(thm)],[])).
% 38.39/38.59 tff(136,plain,
% 38.39/38.59 ((~![B: $i, D_194: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!179))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_67(C, D!179), relation_dom(D!179))) | (~(C = apply(D!179, tptp_fun_D_67(C, D!179)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!179))) | (~(C = apply(D!179, D))))))))) | (~((B = relation_rng(D!179)) | (~((~(in(tptp_fun_C_68(B, D!179), B) | (~((~in(tptp_fun_D_69(B, D!179), relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, tptp_fun_D_69(B, D!179)))))))) | (~((~in(tptp_fun_C_68(B, D!179), B)) | (~in(D_194, relation_dom(D!179))) | (~(tptp_fun_C_68(B, D!179) = apply(D!179, D_194)))))))))))) | (~((~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))) | (~((~in(tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179), relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179)))))))) | (~((~in(C!180, relation_dom(D!179))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))))))),
% 38.39/38.59 inference(modus_ponens,[status(thm)],[135, 134])).
% 38.39/38.59 tff(137,plain,
% 38.39/38.59 (~((~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))) | (~((~in(tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179), relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179)))))))) | (~((~in(C!180, relation_dom(D!179))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))))),
% 38.39/38.59 inference(unit_resolution,[status(thm)],[136, 130])).
% 38.39/38.59 tff(138,plain,
% 38.39/38.59 (((~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))) | (~((~in(tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179), relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, tptp_fun_D_67(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), D!179)))))))) | (~((~in(C!180, relation_dom(D!179))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))))) | ((~in(C!180, relation_dom(D!179))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))),
% 38.39/38.59 inference(tautology,[status(thm)],[])).
% 38.39/38.59 tff(139,plain,
% 38.39/38.59 ((~in(C!180, relation_dom(D!179))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))),
% 38.39/38.59 inference(unit_resolution,[status(thm)],[138, 137])).
% 38.39/38.59 tff(140,plain,
% 38.39/38.59 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))))),
% 38.39/38.59 inference(bind,[status(th)],[])).
% 38.39/38.59 tff(141,plain,
% 38.39/38.59 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))),
% 38.39/38.59 inference(quant_intro,[status(thm)],[140])).
% 38.39/38.59 tff(142,plain,
% 38.39/38.59 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))),
% 38.39/38.59 inference(pull_quant,[status(thm)],[])).
% 38.39/38.59 tff(143,plain,
% 38.39/38.59 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))))),
% 38.39/38.59 inference(bind,[status(th)],[])).
% 38.39/38.59 tff(144,plain,
% 38.39/38.59 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))),
% 38.39/38.59 inference(quant_intro,[status(thm)],[143])).
% 38.39/38.59 tff(145,plain,
% 38.39/38.59 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))),
% 38.39/38.59 inference(transitivity,[status(thm)],[144, 142])).
% 38.39/38.59 tff(146,plain,
% 38.39/38.59 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))),
% 38.39/38.59 inference(transitivity,[status(thm)],[145, 141])).
% 38.39/38.59 tff(147,plain,
% 38.39/38.59 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))))),
% 38.39/38.59 inference(bind,[status(th)],[])).
% 38.39/38.59 tff(148,plain,
% 38.39/38.59 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))),
% 38.39/38.59 inference(quant_intro,[status(thm)],[147])).
% 38.39/38.59 tff(149,plain,
% 38.39/38.59 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))),
% 38.39/38.59 inference(transitivity,[status(thm)],[148, 146])).
% 38.39/38.59 tff(150,plain,
% 38.39/38.59 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), trans(monotonicity(rewrite((~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))) <=> (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))), (((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))), rewrite(((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))), (((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))))),
% 38.39/38.59 inference(bind,[status(th)],[])).
% 38.39/38.59 tff(151,plain,
% 38.39/38.59 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))),
% 38.39/38.59 inference(quant_intro,[status(thm)],[150])).
% 38.39/38.59 tff(152,plain,
% 38.39/38.59 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 38.39/38.59 inference(rewrite,[status(thm)],[])).
% 38.39/38.59 tff(153,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 38.39/38.59 tff(154,plain,
% 38.39/38.59 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 38.39/38.59 inference(modus_ponens,[status(thm)],[153, 152])).
% 38.39/38.59 tff(155,plain,(
% 38.39/38.59 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))),
% 38.39/38.59 inference(skolemize,[status(sab)],[154])).
% 38.39/38.59 tff(156,plain,
% 38.39/38.59 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))),
% 38.39/38.59 inference(modus_ponens,[status(thm)],[155, 151])).
% 38.39/38.59 tff(157,plain,
% 38.39/38.59 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))),
% 38.39/38.59 inference(modus_ponens,[status(thm)],[156, 149])).
% 38.39/38.59 tff(158,plain,
% 38.39/38.59 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))),
% 38.39/38.59 inference(rewrite,[status(thm)],[])).
% 38.39/38.59 tff(159,plain,
% 38.39/38.59 ((~(~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))) <=> (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))),
% 38.39/38.59 inference(rewrite,[status(thm)],[])).
% 38.39/38.59 tff(160,plain,
% 38.39/38.59 (((~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))) | $false) <=> (~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))),
% 38.39/38.59 inference(rewrite,[status(thm)],[])).
% 38.39/38.59 tff(161,plain,
% 38.39/38.59 ((~$true) <=> $false),
% 38.39/38.59 inference(rewrite,[status(thm)],[])).
% 38.39/38.59 tff(162,plain,
% 38.39/38.59 (($true | (~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180))))) <=> $true),
% 38.39/38.59 inference(rewrite,[status(thm)],[])).
% 38.39/38.59 tff(163,plain,
% 38.39/38.59 ((~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180)))) <=> (~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180))))),
% 38.39/38.59 inference(rewrite,[status(thm)],[])).
% 38.39/38.59 tff(164,plain,
% 38.39/38.59 ((singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180))) <=> $true),
% 38.39/38.59 inference(rewrite,[status(thm)],[])).
% 38.39/38.59 tff(165,plain,
% 38.39/38.59 (((singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180))) | (~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180))))) <=> ($true | (~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180)))))),
% 38.39/38.59 inference(monotonicity,[status(thm)],[164, 163])).
% 38.39/38.59 tff(166,plain,
% 38.39/38.59 (((singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180))) | (~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180))))) <=> $true),
% 38.39/38.59 inference(transitivity,[status(thm)],[165, 162])).
% 38.39/38.59 tff(167,plain,
% 38.39/38.59 ((~((singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180))) | (~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180)))))) <=> (~$true)),
% 38.39/38.59 inference(monotonicity,[status(thm)],[166])).
% 38.39/38.59 tff(168,plain,
% 38.39/38.59 ((~((singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180))) | (~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180)))))) <=> $false),
% 38.39/38.59 inference(transitivity,[status(thm)],[167, 161])).
% 38.39/38.59 tff(169,plain,
% 38.39/38.59 ((~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))) <=> (~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))),
% 38.39/38.59 inference(rewrite,[status(thm)],[])).
% 38.39/38.59 tff(170,plain,
% 38.39/38.59 (($false | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))) <=> (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))),
% 38.39/38.59 inference(rewrite,[status(thm)],[])).
% 38.39/38.59 tff(171,plain,
% 38.39/38.59 ((~(singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180)))) <=> (~$true)),
% 38.39/38.59 inference(monotonicity,[status(thm)],[164])).
% 38.39/38.59 tff(172,plain,
% 38.39/38.59 ((~(singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180)))) <=> $false),
% 38.39/38.59 inference(transitivity,[status(thm)],[171, 161])).
% 38.39/38.59 tff(173,plain,
% 38.39/38.59 (((~(singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180)))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))) <=> ($false | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))),
% 38.39/38.59 inference(monotonicity,[status(thm)],[172])).
% 38.39/38.59 tff(174,plain,
% 38.39/38.59 (((~(singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180)))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))) <=> (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))),
% 38.39/38.59 inference(transitivity,[status(thm)],[173, 170])).
% 38.39/38.59 tff(175,plain,
% 38.39/38.59 ((~((~(singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180)))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))) <=> (~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))),
% 38.39/38.59 inference(monotonicity,[status(thm)],[174])).
% 38.39/38.59 tff(176,plain,
% 38.39/38.59 ((~((~(singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180)))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))) <=> (~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))),
% 38.39/38.59 inference(transitivity,[status(thm)],[175, 169])).
% 38.39/38.59 tff(177,plain,
% 38.39/38.59 (((~((~(singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180)))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))) | (~((singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180))) | (~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180))))))) <=> ((~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))) | $false)),
% 38.39/38.59 inference(monotonicity,[status(thm)],[176, 168])).
% 38.39/38.59 tff(178,plain,
% 38.39/38.59 (((~((~(singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180)))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))) | (~((singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180))) | (~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180))))))) <=> (~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))),
% 38.39/38.59 inference(transitivity,[status(thm)],[177, 160])).
% 38.39/38.59 tff(179,plain,
% 38.39/38.59 ((~((~((~(singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180)))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))) | (~((singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180))) | (~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180)))))))) <=> (~(~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))))),
% 38.39/38.59 inference(monotonicity,[status(thm)],[178])).
% 38.39/38.59 tff(180,plain,
% 38.39/38.59 ((~((~((~(singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180)))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))) | (~((singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180))) | (~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180)))))))) <=> (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))),
% 38.39/38.59 inference(transitivity,[status(thm)],[179, 159])).
% 38.39/38.59 tff(181,plain,
% 38.39/38.59 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))) | (~((~((~(singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180)))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))) | (~((singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180))) | (~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180))))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))),
% 38.39/38.59 inference(monotonicity,[status(thm)],[180])).
% 38.39/38.59 tff(182,plain,
% 38.39/38.59 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))) | (~((~((~(singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180)))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))) | (~((singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180))) | (~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180))))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))),
% 38.39/38.59 inference(transitivity,[status(thm)],[181, 158])).
% 38.39/38.59 tff(183,plain,
% 38.39/38.59 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))) | (~((~((~(singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180)))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))) | (~((singleton(apply(D!179, C!180)) = singleton(apply(D!179, C!180))) | (~(in(tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_29(singleton(apply(D!179, C!180)), apply(D!179, C!180)) = apply(D!179, C!180))))))))),
% 38.39/38.59 inference(quant_inst,[status(thm)],[])).
% 38.39/38.59 tff(184,plain,
% 38.39/38.59 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_29(B, A), B) <=> (tptp_fun_C_29(B, A) = A)))))))) | (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))),
% 38.39/38.59 inference(modus_ponens,[status(thm)],[183, 182])).
% 38.39/38.59 tff(185,plain,
% 38.39/38.59 (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))),
% 38.39/38.59 inference(unit_resolution,[status(thm)],[184, 157])).
% 38.39/38.59 tff(186,plain,
% 38.39/38.59 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B))))))))),
% 38.39/38.59 inference(bind,[status(th)],[])).
% 38.39/38.59 tff(187,plain,
% 38.39/38.59 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B)))))))),
% 38.39/38.59 inference(quant_intro,[status(thm)],[186])).
% 38.39/38.59 tff(188,plain,
% 38.39/38.59 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B))))))))),
% 38.39/38.59 inference(bind,[status(th)],[])).
% 38.39/38.59 tff(189,plain,
% 38.39/38.59 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B)))))))),
% 38.39/38.59 inference(quant_intro,[status(thm)],[188])).
% 38.39/38.59 tff(190,plain,
% 38.39/38.59 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B)))))))),
% 38.39/38.59 inference(transitivity,[status(thm)],[189, 187])).
% 38.39/38.59 tff(191,plain,
% 38.39/38.59 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B)))))))))),
% 38.39/38.59 inference(bind,[status(th)],[])).
% 38.39/38.59 tff(192,plain,
% 38.39/38.59 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B)))))))),
% 38.39/38.59 inference(quant_intro,[status(thm)],[191])).
% 38.39/38.59 tff(193,plain,
% 38.39/38.59 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 38.39/38.60 inference(rewrite,[status(thm)],[])).
% 38.39/38.60 tff(194,plain,
% 38.39/38.60 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 38.39/38.60 inference(bind,[status(th)],[])).
% 38.39/38.60 tff(195,plain,
% 38.39/38.60 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 38.39/38.60 inference(quant_intro,[status(thm)],[194])).
% 38.39/38.60 tff(196,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 38.39/38.60 tff(197,plain,
% 38.39/38.60 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 38.39/38.60 inference(modus_ponens,[status(thm)],[196, 195])).
% 38.39/38.60 tff(198,plain,
% 38.39/38.60 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 38.39/38.60 inference(modus_ponens,[status(thm)],[197, 193])).
% 38.39/38.60 tff(199,plain,(
% 38.39/38.60 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B)))))),
% 38.39/38.60 inference(skolemize,[status(sab)],[198])).
% 38.39/38.60 tff(200,plain,
% 38.39/38.60 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B)))))))),
% 38.39/38.60 inference(modus_ponens,[status(thm)],[199, 192])).
% 38.39/38.60 tff(201,plain,
% 38.39/38.60 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B)))))))),
% 38.39/38.60 inference(modus_ponens,[status(thm)],[200, 190])).
% 38.39/38.60 tff(202,plain,
% 38.39/38.60 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_53(B, A), A)) | in(tptp_fun_C_53(B, A), B)))))))) | (~((~((~subset(singleton(apply(D!179, C!180)), relation_rng(D!179))) | ![C: $i] : ((~in(C, singleton(apply(D!179, C!180)))) | in(C, relation_rng(D!179))))) | (~(subset(singleton(apply(D!179, C!180)), relation_rng(D!179)) | (~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))))))))),
% 38.39/38.60 inference(quant_inst,[status(thm)],[])).
% 38.39/38.60 tff(203,plain,
% 38.39/38.60 (~((~((~subset(singleton(apply(D!179, C!180)), relation_rng(D!179))) | ![C: $i] : ((~in(C, singleton(apply(D!179, C!180)))) | in(C, relation_rng(D!179))))) | (~(subset(singleton(apply(D!179, C!180)), relation_rng(D!179)) | (~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)))))))),
% 38.39/38.60 inference(unit_resolution,[status(thm)],[202, 201])).
% 38.39/38.60 tff(204,plain,
% 38.39/38.60 (((~((~subset(singleton(apply(D!179, C!180)), relation_rng(D!179))) | ![C: $i] : ((~in(C, singleton(apply(D!179, C!180)))) | in(C, relation_rng(D!179))))) | (~(subset(singleton(apply(D!179, C!180)), relation_rng(D!179)) | (~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))))))) | (subset(singleton(apply(D!179, C!180)), relation_rng(D!179)) | (~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)))))),
% 38.39/38.60 inference(tautology,[status(thm)],[])).
% 38.39/38.60 tff(205,plain,
% 38.39/38.60 (subset(singleton(apply(D!179, C!180)), relation_rng(D!179)) | (~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))))),
% 38.39/38.60 inference(unit_resolution,[status(thm)],[204, 203])).
% 38.39/38.60 tff(206,plain,
% 38.39/38.60 (^[A: $i, B: $i] : refl((subset(singleton(A), B) <=> in(A, B)) <=> (subset(singleton(A), B) <=> in(A, B)))),
% 38.39/38.60 inference(bind,[status(th)],[])).
% 38.39/38.60 tff(207,plain,
% 38.39/38.60 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 38.39/38.60 inference(quant_intro,[status(thm)],[206])).
% 38.39/38.60 tff(208,plain,
% 38.39/38.60 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 38.39/38.60 inference(rewrite,[status(thm)],[])).
% 38.39/38.60 tff(209,axiom,(![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l2_zfmisc_1')).
% 38.39/38.60 tff(210,plain,
% 38.39/38.60 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 38.39/38.60 inference(modus_ponens,[status(thm)],[209, 208])).
% 38.39/38.60 tff(211,plain,(
% 38.39/38.60 ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 38.39/38.60 inference(skolemize,[status(sab)],[210])).
% 38.39/38.60 tff(212,plain,
% 38.39/38.60 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 38.39/38.60 inference(modus_ponens,[status(thm)],[211, 207])).
% 38.39/38.60 tff(213,plain,
% 38.39/38.60 ((~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))) | (subset(singleton(apply(D!179, C!180)), relation_rng(D!179)) <=> in(apply(D!179, C!180), relation_rng(D!179)))),
% 38.39/38.60 inference(quant_inst,[status(thm)],[])).
% 38.39/38.60 tff(214,plain,
% 38.39/38.60 (subset(singleton(apply(D!179, C!180)), relation_rng(D!179)) <=> in(apply(D!179, C!180), relation_rng(D!179))),
% 38.39/38.60 inference(unit_resolution,[status(thm)],[213, 212])).
% 38.39/38.60 tff(215,plain,
% 38.39/38.60 (~in(apply(D!179, C!180), relation_rng(D!179))),
% 38.39/38.60 inference(or_elim,[status(thm)],[10])).
% 38.39/38.60 tff(216,plain,
% 38.39/38.60 ((~(subset(singleton(apply(D!179, C!180)), relation_rng(D!179)) <=> in(apply(D!179, C!180), relation_rng(D!179)))) | (~subset(singleton(apply(D!179, C!180)), relation_rng(D!179))) | in(apply(D!179, C!180), relation_rng(D!179))),
% 38.39/38.60 inference(tautology,[status(thm)],[])).
% 38.39/38.60 tff(217,plain,
% 38.39/38.60 ((~(subset(singleton(apply(D!179, C!180)), relation_rng(D!179)) <=> in(apply(D!179, C!180), relation_rng(D!179)))) | (~subset(singleton(apply(D!179, C!180)), relation_rng(D!179)))),
% 38.39/38.60 inference(unit_resolution,[status(thm)],[216, 215])).
% 38.39/38.60 tff(218,plain,
% 38.39/38.60 (~subset(singleton(apply(D!179, C!180)), relation_rng(D!179))),
% 38.39/38.60 inference(unit_resolution,[status(thm)],[217, 214])).
% 38.39/38.60 tff(219,plain,
% 38.39/38.60 ((~(subset(singleton(apply(D!179, C!180)), relation_rng(D!179)) | (~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)))))) | subset(singleton(apply(D!179, C!180)), relation_rng(D!179)) | (~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))))),
% 38.39/38.60 inference(tautology,[status(thm)],[])).
% 38.39/38.60 tff(220,plain,
% 38.39/38.60 ((~(subset(singleton(apply(D!179, C!180)), relation_rng(D!179)) | (~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)))))) | (~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))))),
% 38.39/38.60 inference(unit_resolution,[status(thm)],[219, 218])).
% 38.39/38.60 tff(221,plain,
% 38.39/38.60 (~((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)))),
% 38.39/38.60 inference(unit_resolution,[status(thm)],[220, 205])).
% 38.39/38.60 tff(222,plain,
% 38.39/38.60 (((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))),
% 38.39/38.60 inference(tautology,[status(thm)],[])).
% 38.39/38.60 tff(223,plain,
% 38.47/38.65 (in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))),
% 38.47/38.65 inference(unit_resolution,[status(thm)],[222, 221])).
% 38.47/38.65 tff(224,plain,
% 38.47/38.65 ((~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))) | (~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))) | (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))),
% 38.47/38.65 inference(tautology,[status(thm)],[])).
% 38.47/38.65 tff(225,plain,
% 38.47/38.65 ((~(in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180))) <=> (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))) | (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))),
% 38.47/38.65 inference(unit_resolution,[status(thm)],[224, 223])).
% 38.47/38.65 tff(226,plain,
% 38.47/38.65 (tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)),
% 38.47/38.65 inference(unit_resolution,[status(thm)],[225, 185])).
% 38.47/38.65 tff(227,plain,
% 38.47/38.65 (((~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), singleton(apply(D!179, C!180)))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))) | (~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)))),
% 38.47/38.65 inference(tautology,[status(thm)],[])).
% 38.47/38.65 tff(228,plain,
% 38.47/38.65 (~in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179))),
% 38.47/38.65 inference(unit_resolution,[status(thm)],[227, 221])).
% 38.47/38.65 tff(229,plain,
% 38.47/38.65 ((~((~in(C!180, relation_dom(D!179))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))) | (~in(C!180, relation_dom(D!179))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))),
% 38.47/38.65 inference(tautology,[status(thm)],[])).
% 38.47/38.65 tff(230,plain,
% 38.47/38.65 ((~((~in(C!180, relation_dom(D!179))) | in(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))), relation_rng(D!179)) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180))))) | (~in(C!180, relation_dom(D!179))) | (~(tptp_fun_C_53(relation_rng(D!179), singleton(apply(D!179, C!180))) = apply(D!179, C!180)))),
% 38.47/38.65 inference(unit_resolution,[status(thm)],[229, 228])).
% 38.47/38.65 tff(231,plain,
% 38.47/38.65 (~in(C!180, relation_dom(D!179))),
% 38.47/38.65 inference(unit_resolution,[status(thm)],[230, 226, 139])).
% 38.47/38.65 tff(232,plain,
% 38.47/38.65 ($false),
% 38.47/38.65 inference(unit_resolution,[status(thm)],[231, 77])).
% 38.47/38.65 % SZS output end Proof
% 38.56/38.71 % E exiting
%------------------------------------------------------------------------------