%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU290+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.12s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU290+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:38:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(in_type, type, (
% 0.12/0.40 in: ( $i * $i ) > $o)).
% 0.12/0.40 tff(relation_dom_type, type, (
% 0.12/0.40 relation_dom: $i > $i)).
% 0.12/0.40 tff(tptp_fun_D_20_type, type, (
% 0.12/0.40 tptp_fun_D_20: $i)).
% 0.12/0.40 tff(tptp_fun_C_21_type, type, (
% 0.12/0.40 tptp_fun_C_21: $i)).
% 0.12/0.40 tff(tptp_fun_A_23_type, type, (
% 0.12/0.40 tptp_fun_A_23: $i)).
% 0.12/0.40 tff(relation_dom_as_subset_type, type, (
% 0.12/0.40 relation_dom_as_subset: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_B_22_type, type, (
% 0.12/0.40 tptp_fun_B_22: $i)).
% 0.12/0.40 tff(quasi_total_type, type, (
% 0.12/0.40 quasi_total: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(empty_set_type, type, (
% 0.12/0.40 empty_set: $i)).
% 0.12/0.40 tff(relation_of2_as_subset_type, type, (
% 0.12/0.40 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(function_type, type, (
% 0.12/0.40 function: $i > $o)).
% 0.12/0.40 tff(relation_rng_type, type, (
% 0.12/0.40 relation_rng: $i > $i)).
% 0.12/0.40 tff(apply_type, type, (
% 0.12/0.40 apply: ( $i * $i ) > $i)).
% 0.12/0.40 tff(relation_of2_type, type, (
% 0.12/0.40 relation_of2: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_D_0_type, type, (
% 0.12/0.40 tptp_fun_D_0: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_C_1_type, type, (
% 0.12/0.40 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_D_2_type, type, (
% 0.12/0.40 tptp_fun_D_2: ( $i * $i ) > $i)).
% 0.12/0.40 tff(relation_type, type, (
% 0.12/0.40 relation: $i > $o)).
% 0.12/0.40 tff(element_type, type, (
% 0.12/0.40 element: ( $i * $i ) > $o)).
% 0.12/0.40 tff(powerset_type, type, (
% 0.12/0.40 powerset: $i > $i)).
% 0.12/0.40 tff(cartesian_product2_type, type, (
% 0.12/0.40 cartesian_product2: ( $i * $i ) > $i)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 ((~((B!22 = empty_set) | in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, A!23)) | (~(function(D!20) & quasi_total(D!20, A!23, B!22) & relation_of2_as_subset(D!20, A!23, B!22))))) <=> (~((B!22 = empty_set) | in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, A!23)) | (~(function(D!20) & quasi_total(D!20, A!23, B!22) & relation_of2_as_subset(D!20, A!23, B!22)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 ((~![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)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 ((~![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)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 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')).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (~![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))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (~![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))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (~![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))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (~![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))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.40 tff(9,plain,(
% 0.12/0.40 ~((B!22 = empty_set) | in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, A!23)) | (~(function(D!20) & quasi_total(D!20, A!23, B!22) & relation_of2_as_subset(D!20, A!23, B!22))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[8])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (~((B!22 = empty_set) | in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, A!23)) | (~(function(D!20) & quasi_total(D!20, A!23, B!22) & relation_of2_as_subset(D!20, A!23, B!22))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (function(D!20) & quasi_total(D!20, A!23, B!22) & relation_of2_as_subset(D!20, A!23, B!22)),
% 0.12/0.40 inference(or_elim,[status(thm)],[10])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (relation_of2_as_subset(D!20, A!23, B!22)),
% 0.12/0.40 inference(and_elim,[status(thm)],[11])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (^[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))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (^[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))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (![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)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (^[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)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (![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)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.41 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')).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (![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)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 (![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)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.21/0.41 tff(23,plain,(
% 0.21/0.41 ![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)))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[22])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (![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)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (![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)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (((~![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!20, A!23, B!22)) | (~((~((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))) | (~((~(B!22 = empty_set)) | (A!23 = empty_set) | (quasi_total(D!20, A!23, B!22) <=> (D!20 = 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!20, A!23, B!22)) | (~((~((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))) | (~((~(B!22 = empty_set)) | (A!23 = empty_set) | (quasi_total(D!20, A!23, B!22) <=> (D!20 = empty_set)))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (((~relation_of2_as_subset(D!20, A!23, B!22)) | (~((~((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))) | (~((quasi_total(D!20, A!23, B!22) <=> (D!20 = empty_set)) | (A!23 = empty_set) | (~(B!22 = empty_set))))))) <=> ((~relation_of2_as_subset(D!20, A!23, B!22)) | (~((~((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))) | (~((~(B!22 = empty_set)) | (A!23 = empty_set) | (quasi_total(D!20, A!23, B!22) <=> (D!20 = empty_set)))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (((~![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!20, A!23, B!22)) | (~((~((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))) | (~((quasi_total(D!20, A!23, B!22) <=> (D!20 = empty_set)) | (A!23 = empty_set) | (~(B!22 = 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!20, A!23, B!22)) | (~((~((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))) | (~((~(B!22 = empty_set)) | (A!23 = empty_set) | (quasi_total(D!20, A!23, B!22) <=> (D!20 = empty_set))))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[27])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (((~![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!20, A!23, B!22)) | (~((~((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))) | (~((quasi_total(D!20, A!23, B!22) <=> (D!20 = empty_set)) | (A!23 = empty_set) | (~(B!22 = 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!20, A!23, B!22)) | (~((~((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))) | (~((~(B!22 = empty_set)) | (A!23 = empty_set) | (quasi_total(D!20, A!23, B!22) <=> (D!20 = empty_set)))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[28, 26])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 ((~![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!20, A!23, B!22)) | (~((~((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))) | (~((quasi_total(D!20, A!23, B!22) <=> (D!20 = empty_set)) | (A!23 = empty_set) | (~(B!22 = empty_set)))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 ((~![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!20, A!23, B!22)) | (~((~((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))) | (~((~(B!22 = empty_set)) | (A!23 = empty_set) | (quasi_total(D!20, A!23, B!22) <=> (D!20 = empty_set))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (~((~((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))) | (~((~(B!22 = empty_set)) | (A!23 = empty_set) | (quasi_total(D!20, A!23, B!22) <=> (D!20 = empty_set)))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[31, 25, 12])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (((~((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))) | (~((~(B!22 = empty_set)) | (A!23 = empty_set) | (quasi_total(D!20, A!23, B!22) <=> (D!20 = empty_set))))) | ((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 ((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (~(B!22 = empty_set)),
% 0.21/0.41 inference(or_elim,[status(thm)],[10])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (((~(B!22 = empty_set)) | (A!23 = empty_set)) | (B!22 = empty_set)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 ((~(B!22 = empty_set)) | (A!23 = empty_set)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 ((~((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))) | (~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 ((~((~((~(B!22 = empty_set)) | (A!23 = empty_set))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))))) | (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[39, 34])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (quasi_total(D!20, A!23, B!22)),
% 0.21/0.41 inference(and_elim,[status(thm)],[11])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 ((~(quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20)))) | (~quasi_total(D!20, A!23, B!22)) | (A!23 = relation_dom_as_subset(A!23, B!22, D!20))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 ((~(quasi_total(D!20, A!23, B!22) <=> (A!23 = relation_dom_as_subset(A!23, B!22, D!20)))) | (A!23 = relation_dom_as_subset(A!23, B!22, D!20))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (A!23 = relation_dom_as_subset(A!23, B!22, D!20)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (relation_dom_as_subset(A!23, B!22, D!20) = A!23),
% 0.21/0.42 inference(symmetry,[status(thm)],[44])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (relation_dom_as_subset(relation_dom_as_subset(A!23, B!22, D!20), B!22, D!20) = relation_dom_as_subset(A!23, B!22, D!20)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[45])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (relation_of2(D!20, relation_dom_as_subset(A!23, B!22, D!20), B!22) <=> relation_of2(D!20, A!23, B!22)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[45])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 (relation_of2(D!20, A!23, B!22) <=> relation_of2(D!20, relation_dom_as_subset(A!23, B!22, D!20), B!22)),
% 0.21/0.42 inference(symmetry,[status(thm)],[47])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 (^[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)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(52,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')).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.42 tff(54,plain,(
% 0.21/0.42 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.21/0.42 inference(skolemize,[status(sab)],[53])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(D!20, A!23, B!22) <=> relation_of2(D!20, A!23, B!22))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (relation_of2_as_subset(D!20, A!23, B!22) <=> relation_of2(D!20, A!23, B!22)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 ((~(relation_of2_as_subset(D!20, A!23, B!22) <=> relation_of2(D!20, A!23, B!22))) | (~relation_of2_as_subset(D!20, A!23, B!22)) | relation_of2(D!20, A!23, B!22)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 ((~(relation_of2_as_subset(D!20, A!23, B!22) <=> relation_of2(D!20, A!23, B!22))) | relation_of2(D!20, A!23, B!22)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[58, 12])).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 (relation_of2(D!20, A!23, B!22)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[59, 57])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 (relation_of2(D!20, relation_dom_as_subset(A!23, B!22, D!20), B!22)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[60, 48])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(63,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(65,plain,
% 0.21/0.42 (^[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))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 (![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)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.42 tff(67,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')).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.21/0.42 tff(70,plain,(
% 0.21/0.42 ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[69])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | ((~relation_of2(D!20, relation_dom_as_subset(A!23, B!22, D!20), B!22)) | (relation_dom_as_subset(relation_dom_as_subset(A!23, B!22, D!20), B!22, D!20) = relation_dom(D!20)))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | (~relation_of2(D!20, relation_dom_as_subset(A!23, B!22, D!20), B!22)) | (relation_dom_as_subset(relation_dom_as_subset(A!23, B!22, D!20), B!22, D!20) = relation_dom(D!20)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | ((~relation_of2(D!20, relation_dom_as_subset(A!23, B!22, D!20), B!22)) | (relation_dom_as_subset(relation_dom_as_subset(A!23, B!22, D!20), B!22, D!20) = relation_dom(D!20)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | (~relation_of2(D!20, relation_dom_as_subset(A!23, B!22, D!20), B!22)) | (relation_dom_as_subset(relation_dom_as_subset(A!23, B!22, D!20), B!22, D!20) = relation_dom(D!20))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 ((~relation_of2(D!20, relation_dom_as_subset(A!23, B!22, D!20), B!22)) | (relation_dom_as_subset(relation_dom_as_subset(A!23, B!22, D!20), B!22, D!20) = relation_dom(D!20))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (relation_dom_as_subset(relation_dom_as_subset(A!23, B!22, D!20), B!22, D!20) = relation_dom(D!20)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[75, 61])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 (relation_dom(D!20) = relation_dom_as_subset(relation_dom_as_subset(A!23, B!22, D!20), B!22, D!20)),
% 0.21/0.42 inference(symmetry,[status(thm)],[76])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (relation_dom(D!20) = A!23),
% 0.21/0.42 inference(transitivity,[status(thm)],[77, 46, 45])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 (in(C!21, relation_dom(D!20)) <=> in(C!21, A!23)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[78])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (in(C!21, A!23) <=> in(C!21, relation_dom(D!20))),
% 0.21/0.42 inference(symmetry,[status(thm)],[79])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (in(C!21, A!23)),
% 0.21/0.42 inference(or_elim,[status(thm)],[10])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (in(C!21, relation_dom(D!20))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (cartesian_product2(relation_dom_as_subset(A!23, B!22, D!20), B!22) = cartesian_product2(A!23, B!22)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[45])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (powerset(cartesian_product2(relation_dom_as_subset(A!23, B!22, D!20), B!22)) = powerset(cartesian_product2(A!23, B!22))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[83])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (element(D!20, powerset(cartesian_product2(relation_dom_as_subset(A!23, B!22, D!20), B!22))) <=> element(D!20, powerset(cartesian_product2(A!23, B!22)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 (element(D!20, powerset(cartesian_product2(A!23, B!22))) <=> element(D!20, powerset(cartesian_product2(relation_dom_as_subset(A!23, B!22, D!20), B!22)))),
% 0.21/0.42 inference(symmetry,[status(thm)],[85])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (^[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)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[87])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (^[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)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (![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))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.42 tff(92,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')).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.21/0.42 tff(95,plain,(
% 0.21/0.42 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[94])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (((~![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!20, A!23, B!22)) | element(D!20, powerset(cartesian_product2(A!23, B!22))))) <=> ((~![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!20, A!23, B!22)) | element(D!20, powerset(cartesian_product2(A!23, B!22))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 ((~![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!20, A!23, B!22)) | element(D!20, powerset(cartesian_product2(A!23, B!22))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 ((~![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!20, A!23, B!22)) | element(D!20, powerset(cartesian_product2(A!23, B!22)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (element(D!20, powerset(cartesian_product2(A!23, B!22)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[99, 96, 12])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (element(D!20, powerset(cartesian_product2(relation_dom_as_subset(A!23, B!22, D!20), B!22)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[100, 86])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (^[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))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (![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)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[102])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (![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)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (^[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))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (![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)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[105])).
% 0.21/0.42 tff(107,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')).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.21/0.42 tff(110,plain,(
% 0.21/0.42 ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[109])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(D!20) | (~element(D!20, powerset(cartesian_product2(relation_dom_as_subset(A!23, B!22, D!20), B!22)))))) <=> ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(D!20) | (~element(D!20, powerset(cartesian_product2(relation_dom_as_subset(A!23, B!22, D!20), B!22)))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(D!20) | (~element(D!20, powerset(cartesian_product2(relation_dom_as_subset(A!23, B!22, D!20), B!22)))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(D!20) | (~element(D!20, powerset(cartesian_product2(relation_dom_as_subset(A!23, B!22, D!20), B!22))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (relation(D!20) | (~element(D!20, powerset(cartesian_product2(relation_dom_as_subset(A!23, B!22, D!20), B!22))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[114, 111])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (relation(D!20)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[115, 101])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (function(D!20)),
% 0.21/0.42 inference(and_elim,[status(thm)],[11])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, D_24: $i, C: $i, D: $i] : rewrite((~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24)))))))))))) <=> (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))), (![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24)))))))))))) <=> ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24)))))))))))))), rewrite(((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24)))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))), (((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(119,plain,
% 0.21/0.43 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[118])).
% 0.21/0.43 tff(120,plain,
% 0.21/0.43 (^[A: $i] : refl(((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(121,plain,
% 0.21/0.43 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24)))))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[120])).
% 0.21/0.43 tff(122,plain,
% 0.21/0.43 (^[A: $i] : rewrite(((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(123,plain,
% 0.21/0.43 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24)))))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.43 tff(124,plain,
% 0.21/0.43 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))) <=> ![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24)))))))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[123, 121])).
% 0.21/0.43 tff(125,plain,
% 0.21/0.43 (^[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_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(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_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))) <=> (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))), ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) <=> (in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))))), rewrite((in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))) <=> (in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))), ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) <=> (in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))))), rewrite(((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))) <=> ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))), (((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))) <=> ((in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))), rewrite(((in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))) <=> (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))), (((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))) <=> (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))), (((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))), rewrite(((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))), (((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))) <=> ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))), ((((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))) <=> (((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) & ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))), rewrite((((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) & ((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))) <=> (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))), ((((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))) <=> (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))))), (![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))) <=> ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))))) <=> (((~relation(A)) | (~function(A))) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D))))))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))), (((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D))))))))) <=> ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(126,plain,
% 0.21/0.43 (![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(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_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[125])).
% 0.21/0.43 tff(127,plain,
% 0.21/0.43 (![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))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(128,plain,
% 0.21/0.43 (^[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)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(129,plain,
% 0.21/0.43 (![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))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[128])).
% 0.21/0.43 tff(130,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')).
% 0.21/0.43 tff(131,plain,
% 0.21/0.43 (![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))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 (![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))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.21/0.44 tff(133,plain,(
% 0.21/0.44 ![A: $i] : ((~(relation(A) & function(A))) | ![B: $i] : (((~(B = relation_rng(A))) | ![C: $i] : (((~in(C, B)) | (in(tptp_fun_D_0(C, A), relation_dom(A)) & (C = apply(A, tptp_fun_D_0(C, A))))) & (in(C, B) | ![D: $i] : (~(in(D, relation_dom(A)) & (C = apply(A, D))))))) & ((B = relation_rng(A)) | ((in(tptp_fun_C_1(B, A), B) | (in(tptp_fun_D_2(B, A), relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A))))) & ((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : (~(in(D, relation_dom(A)) & (tptp_fun_C_1(B, A) = apply(A, D)))))))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[132])).
% 0.21/0.44 tff(134,plain,
% 0.21/0.44 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i] : (~((~((~(B = relation_rng(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ![D: $i] : ((~in(D, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D)))))))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | ((~in(D, relation_dom(A))) | (~(C = apply(A, D)))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | ((~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24)))))))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[134, 124])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 (![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[135, 119])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))) | (![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24))))))))))) | (~function(D!20)) | (~relation(D!20)))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24))))))))))) | (~function(D!20)) | (~relation(D!20)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 (((~relation(D!20)) | (~function(D!20)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24)))))))))))) <=> (![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24))))))))))) | (~function(D!20)) | (~relation(D!20)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))) | ((~relation(D!20)) | (~function(D!20)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))) | (![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24))))))))))) | (~function(D!20)) | (~relation(D!20))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[138])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 (((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))) | ((~relation(D!20)) | (~function(D!20)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24))))))))))))) <=> ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24))))))))))) | (~function(D!20)) | (~relation(D!20)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[139, 137])).
% 0.21/0.44 tff(141,plain,
% 0.21/0.44 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))) | ((~relation(D!20)) | (~function(D!20)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24))))))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 ((~![A: $i] : ((~relation(A)) | (~function(A)) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(A))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, A), relation_dom(A))) | (~(C = apply(A, tptp_fun_D_0(C, A)))))))) | (~(in(C, B) | (~in(D, relation_dom(A))) | (~(C = apply(A, D))))))))) | (~((B = relation_rng(A)) | (~((~(in(tptp_fun_C_1(B, A), B) | (~((~in(tptp_fun_D_2(B, A), relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, tptp_fun_D_2(B, A)))))))) | (~((~in(tptp_fun_C_1(B, A), B)) | (~in(D_24, relation_dom(A))) | (~(tptp_fun_C_1(B, A) = apply(A, D_24))))))))))))) | ![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24))))))))))) | (~function(D!20)) | (~relation(D!20))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 (![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24))))))))))) | (~relation(D!20))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[142, 136, 117])).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 (![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24)))))))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[143, 116])).
% 0.21/0.44 tff(145,plain,
% 0.21/0.44 (((~![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24)))))))))))) | (~((~((~in(apply(D!20, C!21), relation_rng(D!20))) | (~((~in(tptp_fun_D_0(apply(D!20, C!21), D!20), relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, tptp_fun_D_0(apply(D!20, C!21), D!20)))))))) | (~(in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20)))))))) <=> ((~![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24)))))))))))) | (~((~((~in(apply(D!20, C!21), relation_rng(D!20))) | (~((~in(tptp_fun_D_0(apply(D!20, C!21), D!20), relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, tptp_fun_D_0(apply(D!20, C!21), D!20)))))))) | (~(in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(146,plain,
% 0.21/0.45 ((~((~((~(relation_rng(D!20) = relation_rng(D!20))) | (~((~((~in(apply(D!20, C!21), relation_rng(D!20))) | (~((~in(tptp_fun_D_0(apply(D!20, C!21), D!20), relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, tptp_fun_D_0(apply(D!20, C!21), D!20)))))))) | (~(in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, C!21))))))))) | (~((relation_rng(D!20) = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(relation_rng(D!20), D!20), relation_rng(D!20)) | (~((~in(tptp_fun_D_2(relation_rng(D!20), D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(relation_rng(D!20), D!20) = apply(D!20, tptp_fun_D_2(relation_rng(D!20), D!20)))))))) | (~((~in(tptp_fun_C_1(relation_rng(D!20), D!20), relation_rng(D!20))) | (~in(C!21, relation_dom(D!20))) | (~(tptp_fun_C_1(relation_rng(D!20), D!20) = apply(D!20, C!21))))))))))) <=> (~((~((~in(apply(D!20, C!21), relation_rng(D!20))) | (~((~in(tptp_fun_D_0(apply(D!20, C!21), D!20), relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, tptp_fun_D_0(apply(D!20, C!21), D!20)))))))) | (~(in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20)))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(147,plain,
% 0.21/0.45 (((~![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24)))))))))))) | (~((~((~(relation_rng(D!20) = relation_rng(D!20))) | (~((~((~in(apply(D!20, C!21), relation_rng(D!20))) | (~((~in(tptp_fun_D_0(apply(D!20, C!21), D!20), relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, tptp_fun_D_0(apply(D!20, C!21), D!20)))))))) | (~(in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, C!21))))))))) | (~((relation_rng(D!20) = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(relation_rng(D!20), D!20), relation_rng(D!20)) | (~((~in(tptp_fun_D_2(relation_rng(D!20), D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(relation_rng(D!20), D!20) = apply(D!20, tptp_fun_D_2(relation_rng(D!20), D!20)))))))) | (~((~in(tptp_fun_C_1(relation_rng(D!20), D!20), relation_rng(D!20))) | (~in(C!21, relation_dom(D!20))) | (~(tptp_fun_C_1(relation_rng(D!20), D!20) = apply(D!20, C!21)))))))))))) <=> ((~![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24)))))))))))) | (~((~((~in(apply(D!20, C!21), relation_rng(D!20))) | (~((~in(tptp_fun_D_0(apply(D!20, C!21), D!20), relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, tptp_fun_D_0(apply(D!20, C!21), D!20)))))))) | (~(in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20))))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[146])).
% 0.21/0.45 tff(148,plain,
% 0.21/0.45 (((~![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24)))))))))))) | (~((~((~(relation_rng(D!20) = relation_rng(D!20))) | (~((~((~in(apply(D!20, C!21), relation_rng(D!20))) | (~((~in(tptp_fun_D_0(apply(D!20, C!21), D!20), relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, tptp_fun_D_0(apply(D!20, C!21), D!20)))))))) | (~(in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, C!21))))))))) | (~((relation_rng(D!20) = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(relation_rng(D!20), D!20), relation_rng(D!20)) | (~((~in(tptp_fun_D_2(relation_rng(D!20), D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(relation_rng(D!20), D!20) = apply(D!20, tptp_fun_D_2(relation_rng(D!20), D!20)))))))) | (~((~in(tptp_fun_C_1(relation_rng(D!20), D!20), relation_rng(D!20))) | (~in(C!21, relation_dom(D!20))) | (~(tptp_fun_C_1(relation_rng(D!20), D!20) = apply(D!20, C!21)))))))))))) <=> ((~![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24)))))))))))) | (~((~((~in(apply(D!20, C!21), relation_rng(D!20))) | (~((~in(tptp_fun_D_0(apply(D!20, C!21), D!20), relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, tptp_fun_D_0(apply(D!20, C!21), D!20)))))))) | (~(in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[147, 145])).
% 0.21/0.45 tff(149,plain,
% 0.21/0.45 ((~![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24)))))))))))) | (~((~((~(relation_rng(D!20) = relation_rng(D!20))) | (~((~((~in(apply(D!20, C!21), relation_rng(D!20))) | (~((~in(tptp_fun_D_0(apply(D!20, C!21), D!20), relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, tptp_fun_D_0(apply(D!20, C!21), D!20)))))))) | (~(in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, C!21))))))))) | (~((relation_rng(D!20) = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(relation_rng(D!20), D!20), relation_rng(D!20)) | (~((~in(tptp_fun_D_2(relation_rng(D!20), D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(relation_rng(D!20), D!20) = apply(D!20, tptp_fun_D_2(relation_rng(D!20), D!20)))))))) | (~((~in(tptp_fun_C_1(relation_rng(D!20), D!20), relation_rng(D!20))) | (~in(C!21, relation_dom(D!20))) | (~(tptp_fun_C_1(relation_rng(D!20), D!20) = apply(D!20, C!21)))))))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(150,plain,
% 0.21/0.46 ((~![B: $i, D_24: $i, C: $i, D: $i] : (~((~((~(B = relation_rng(D!20))) | (~((~((~in(C, B)) | (~((~in(tptp_fun_D_0(C, D!20), relation_dom(D!20))) | (~(C = apply(D!20, tptp_fun_D_0(C, D!20)))))))) | (~(in(C, B) | (~in(D, relation_dom(D!20))) | (~(C = apply(D!20, D))))))))) | (~((B = relation_rng(D!20)) | (~((~(in(tptp_fun_C_1(B, D!20), B) | (~((~in(tptp_fun_D_2(B, D!20), relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, tptp_fun_D_2(B, D!20)))))))) | (~((~in(tptp_fun_C_1(B, D!20), B)) | (~in(D_24, relation_dom(D!20))) | (~(tptp_fun_C_1(B, D!20) = apply(D!20, D_24)))))))))))) | (~((~((~in(apply(D!20, C!21), relation_rng(D!20))) | (~((~in(tptp_fun_D_0(apply(D!20, C!21), D!20), relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, tptp_fun_D_0(apply(D!20, C!21), D!20)))))))) | (~(in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.21/0.46 tff(151,plain,
% 0.21/0.46 (~((~((~in(apply(D!20, C!21), relation_rng(D!20))) | (~((~in(tptp_fun_D_0(apply(D!20, C!21), D!20), relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, tptp_fun_D_0(apply(D!20, C!21), D!20)))))))) | (~(in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[150, 144])).
% 0.21/0.46 tff(152,plain,
% 0.21/0.46 (((~((~in(apply(D!20, C!21), relation_rng(D!20))) | (~((~in(tptp_fun_D_0(apply(D!20, C!21), D!20), relation_dom(D!20))) | (~(apply(D!20, C!21) = apply(D!20, tptp_fun_D_0(apply(D!20, C!21), D!20)))))))) | (~(in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20)))))) | (in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(153,plain,
% 0.21/0.46 (in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.21/0.46 tff(154,plain,
% 0.21/0.46 (~in(apply(D!20, C!21), relation_rng(D!20))),
% 0.21/0.46 inference(or_elim,[status(thm)],[10])).
% 0.21/0.46 tff(155,plain,
% 0.21/0.46 ((~(in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20))))) | in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(156,plain,
% 0.21/0.46 ((~(in(apply(D!20, C!21), relation_rng(D!20)) | (~in(C!21, relation_dom(D!20))))) | (~in(C!21, relation_dom(D!20)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.21/0.46 tff(157,plain,
% 0.21/0.46 (~in(C!21, relation_dom(D!20))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[156, 153])).
% 0.21/0.46 tff(158,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[157, 82])).
% 0.21/0.46 % SZS output end Proof
% 0.21/0.46 % E exiting
%------------------------------------------------------------------------------