TSTP Solution File: SEU292+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU292+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 : Tue Sep 20 07:28:43 EDT 2022
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU292+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 12:02:52 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(in_type, type, (
% 0.21/0.43 in: ( $i * $i ) > $o)).
% 0.21/0.43 tff(relation_dom_type, type, (
% 0.21/0.43 relation_dom: $i > $i)).
% 0.21/0.43 tff(tptp_fun_D_17_type, type, (
% 0.21/0.43 tptp_fun_D_17: $i)).
% 0.21/0.43 tff(tptp_fun_C_18_type, type, (
% 0.21/0.43 tptp_fun_C_18: $i)).
% 0.21/0.43 tff(tptp_fun_A_20_type, type, (
% 0.21/0.43 tptp_fun_A_20: $i)).
% 0.21/0.43 tff(relation_dom_as_subset_type, type, (
% 0.21/0.43 relation_dom_as_subset: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_B_19_type, type, (
% 0.21/0.43 tptp_fun_B_19: $i)).
% 0.21/0.43 tff(quasi_total_type, type, (
% 0.21/0.43 quasi_total: ( $i * $i * $i ) > $o)).
% 0.21/0.43 tff(empty_set_type, type, (
% 0.21/0.43 empty_set: $i)).
% 0.21/0.43 tff(relation_of2_as_subset_type, type, (
% 0.21/0.43 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 0.21/0.43 tff(function_type, type, (
% 0.21/0.43 function: $i > $o)).
% 0.21/0.43 tff(tptp_fun_E_21_type, type, (
% 0.21/0.43 tptp_fun_E_21: $i)).
% 0.21/0.43 tff(relation_type, type, (
% 0.21/0.43 relation: $i > $o)).
% 0.21/0.43 tff(apply_type, type, (
% 0.21/0.43 apply: ( $i * $i ) > $i)).
% 0.21/0.43 tff(relation_composition_type, type, (
% 0.21/0.43 relation_composition: ( $i * $i ) > $i)).
% 0.21/0.43 tff(relation_of2_type, type, (
% 0.21/0.43 relation_of2: ( $i * $i * $i ) > $o)).
% 0.21/0.43 tff(element_type, type, (
% 0.21/0.43 element: ( $i * $i ) > $o)).
% 0.21/0.43 tff(powerset_type, type, (
% 0.21/0.43 powerset: $i > $i)).
% 0.21/0.43 tff(cartesian_product2_type, type, (
% 0.21/0.43 cartesian_product2: ( $i * $i ) > $i)).
% 0.21/0.43 tff(1,plain,
% 0.21/0.43 (((function(D!17) & quasi_total(D!17, A!20, B!19) & relation_of2_as_subset(D!17, A!20, B!19)) & (~((B!19 = empty_set) | (~in(C!18, A!20)) | (apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18))) | (~(relation(E!21) & function(E!21)))))) <=> (function(D!17) & quasi_total(D!17, A!20, B!19) & relation_of2_as_subset(D!17, A!20, B!19) & (~((B!19 = empty_set) | (~in(C!18, A!20)) | (apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18))) | (~(relation(E!21) & function(E!21))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 ((~((apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18))) | (B!19 = empty_set) | (~in(C!18, A!20)) | (~(relation(E!21) & function(E!21))))) <=> (~((B!19 = empty_set) | (~in(C!18, A!20)) | (apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18))) | (~(relation(E!21) & function(E!21)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 ((~(~(function(D!17) & quasi_total(D!17, A!20, B!19) & relation_of2_as_subset(D!17, A!20, B!19)))) <=> (function(D!17) & quasi_total(D!17, A!20, B!19) & relation_of2_as_subset(D!17, A!20, B!19))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(4,plain,
% 0.21/0.43 (((~(~(function(D!17) & quasi_total(D!17, A!20, B!19) & relation_of2_as_subset(D!17, A!20, B!19)))) & (~((apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18))) | (B!19 = empty_set) | (~in(C!18, A!20)) | (~(relation(E!21) & function(E!21)))))) <=> ((function(D!17) & quasi_total(D!17, A!20, B!19) & relation_of2_as_subset(D!17, A!20, B!19)) & (~((B!19 = empty_set) | (~in(C!18, A!20)) | (apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18))) | (~(relation(E!21) & function(E!21))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[3, 2])).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (((~(~(function(D!17) & quasi_total(D!17, A!20, B!19) & relation_of2_as_subset(D!17, A!20, B!19)))) & (~((apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18))) | (B!19 = empty_set) | (~in(C!18, A!20)) | (~(relation(E!21) & function(E!21)))))) <=> (function(D!17) & quasi_total(D!17, A!20, B!19) & relation_of2_as_subset(D!17, A!20, B!19) & (~((B!19 = empty_set) | (~in(C!18, A!20)) | (apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18))) | (~(relation(E!21) & function(E!21))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[4, 1])).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : ((~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))) | ![E: $i] : ((apply(relation_composition(D, E), C) = apply(E, apply(D, C))) | (B = empty_set) | (~in(C, A)) | (~(relation(E) & function(E)))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))) | ![E: $i] : ((apply(relation_composition(D, E), C) = apply(E, apply(D, C))) | (B = empty_set) | (~in(C, A)) | (~(relation(E) & function(E))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i, D: $i] : (((function(D) & quasi_total(D, A, B)) & relation_of2_as_subset(D, A, B)) => ![E: $i] : ((relation(E) & function(E)) => (in(C, A) => ((B = empty_set) | (apply(relation_composition(D, E), C) = apply(E, apply(D, C)))))))) <=> (~![A: $i, B: $i, C: $i, D: $i] : ((~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))) | ![E: $i] : ((apply(relation_composition(D, E), C) = apply(E, apply(D, C))) | (B = empty_set) | (~in(C, A)) | (~(relation(E) & function(E))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(8,axiom,(~![A: $i, B: $i, C: $i, D: $i] : (((function(D) & quasi_total(D, A, B)) & relation_of2_as_subset(D, A, B)) => ![E: $i] : ((relation(E) & function(E)) => (in(C, A) => ((B = empty_set) | (apply(relation_composition(D, E), C) = apply(E, apply(D, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t21_funct_2')).
% 0.21/0.43 tff(9,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i, D: $i] : ((~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))) | ![E: $i] : ((apply(relation_composition(D, E), C) = apply(E, apply(D, C))) | (B = empty_set) | (~in(C, A)) | (~(relation(E) & function(E)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i, D: $i] : ((~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))) | ![E: $i] : ((apply(relation_composition(D, E), C) = apply(E, apply(D, C))) | (B = empty_set) | (~in(C, A)) | (~(relation(E) & function(E)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i, D: $i] : ((~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))) | ![E: $i] : ((apply(relation_composition(D, E), C) = apply(E, apply(D, C))) | (B = empty_set) | (~in(C, A)) | (~(relation(E) & function(E)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.21/0.43 tff(12,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i, D: $i] : ((~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))) | ![E: $i] : ((apply(relation_composition(D, E), C) = apply(E, apply(D, C))) | (B = empty_set) | (~in(C, A)) | (~(relation(E) & function(E)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i, D: $i] : ((~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))) | ![E: $i] : ((apply(relation_composition(D, E), C) = apply(E, apply(D, C))) | (B = empty_set) | (~in(C, A)) | (~(relation(E) & function(E)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i, D: $i] : ((~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))) | ![E: $i] : ((apply(relation_composition(D, E), C) = apply(E, apply(D, C))) | (B = empty_set) | (~in(C, A)) | (~(relation(E) & function(E)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 (~![A: $i, B: $i, C: $i, D: $i] : ((~(function(D) & quasi_total(D, A, B) & relation_of2_as_subset(D, A, B))) | ![E: $i] : ((apply(relation_composition(D, E), C) = apply(E, apply(D, C))) | (B = empty_set) | (~in(C, A)) | (~(relation(E) & function(E)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 (function(D!17) & quasi_total(D!17, A!20, B!19) & relation_of2_as_subset(D!17, A!20, B!19) & (~((B!19 = empty_set) | (~in(C!18, A!20)) | (apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18))) | (~(relation(E!21) & function(E!21)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (relation_of2_as_subset(D!17, A!20, B!19)),
% 0.21/0.43 inference(and_elim,[status(thm)],[16])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (^[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))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (![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)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (^[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))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (![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)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (![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)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (^[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)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (![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)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.43 tff(25,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/sandbox2/benchmark/theBenchmark.p','d1_funct_2')).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 (![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)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (![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)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.21/0.43 tff(28,plain,(
% 0.21/0.43 ![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)))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[27])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (![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)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (![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)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[29, 19])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((~(B!19 = empty_set)) | (A!20 = empty_set) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | (~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((~(B!19 = empty_set)) | (A!20 = empty_set) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(32,plain,
% 0.21/0.44 (((~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)) | (A!20 = empty_set) | (~(B!19 = empty_set))))))) <=> ((~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((~(B!19 = empty_set)) | (A!20 = empty_set) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(33,plain,
% 0.21/0.44 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)) | (A!20 = empty_set) | (~(B!19 = empty_set)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((~(B!19 = empty_set)) | (A!20 = empty_set) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set))))))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[32])).
% 0.21/0.44 tff(34,plain,
% 0.21/0.44 (((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)) | (A!20 = empty_set) | (~(B!19 = empty_set)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | (~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((~(B!19 = empty_set)) | (A!20 = empty_set) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[33, 31])).
% 0.21/0.44 tff(35,plain,
% 0.21/0.44 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | ((~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)) | (A!20 = empty_set) | (~(B!19 = empty_set)))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 ((~![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | (~((~((~((~(B = empty_set)) | (A = empty_set))) | (quasi_total(C, A, B) <=> (A = relation_dom_as_subset(A, B, C))))) | (~((quasi_total(C, A, B) <=> (C = empty_set)) | (A = empty_set) | (~(B = empty_set)))))))) | (~relation_of2_as_subset(D!17, A!20, B!19)) | (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((~(B!19 = empty_set)) | (A!20 = empty_set) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.44 tff(37,plain,
% 0.21/0.44 (~((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((~(B!19 = empty_set)) | (A!20 = empty_set) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[36, 30, 17])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((~(B!19 = empty_set)) | (A!20 = empty_set) | (quasi_total(D!17, A!20, B!19) <=> (D!17 = empty_set))))) | ((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 ((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 (~((B!19 = empty_set) | (~in(C!18, A!20)) | (apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18))) | (~(relation(E!21) & function(E!21))))),
% 0.21/0.44 inference(and_elim,[status(thm)],[16])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 (~(B!19 = empty_set)),
% 0.21/0.44 inference(or_elim,[status(thm)],[40])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (((~(B!19 = empty_set)) | (A!20 = empty_set)) | (B!19 = empty_set)),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 ((~(B!19 = empty_set)) | (A!20 = empty_set)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 ((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 ((~((~((~(B!19 = empty_set)) | (A!20 = empty_set))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))))) | (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.21/0.44 tff(46,plain,
% 0.21/0.44 (quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[45, 39])).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (quasi_total(D!17, A!20, B!19)),
% 0.21/0.44 inference(and_elim,[status(thm)],[16])).
% 0.21/0.44 tff(48,plain,
% 0.21/0.44 ((~(quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17)))) | (~quasi_total(D!17, A!20, B!19)) | (A!20 = relation_dom_as_subset(A!20, B!19, D!17))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 ((~(quasi_total(D!17, A!20, B!19) <=> (A!20 = relation_dom_as_subset(A!20, B!19, D!17)))) | (A!20 = relation_dom_as_subset(A!20, B!19, D!17))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (A!20 = relation_dom_as_subset(A!20, B!19, D!17)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 (relation_dom_as_subset(A!20, B!19, D!17) = A!20),
% 0.21/0.44 inference(symmetry,[status(thm)],[50])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 (relation_dom_as_subset(relation_dom_as_subset(A!20, B!19, D!17), B!19, D!17) = relation_dom_as_subset(A!20, B!19, D!17)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[51])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 (relation_of2(D!17, relation_dom_as_subset(A!20, B!19, D!17), B!19) <=> relation_of2(D!17, A!20, B!19)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[51])).
% 0.21/0.45 tff(54,plain,
% 0.21/0.45 (relation_of2(D!17, A!20, B!19) <=> relation_of2(D!17, relation_dom_as_subset(A!20, B!19, D!17), B!19)),
% 0.21/0.45 inference(symmetry,[status(thm)],[53])).
% 0.21/0.45 tff(55,plain,
% 0.21/0.45 (^[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)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(56,plain,
% 0.21/0.45 (![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))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[55])).
% 0.21/0.45 tff(57,plain,
% 0.21/0.45 (![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))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(58,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.21/0.45 tff(59,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.45 tff(60,plain,(
% 0.21/0.45 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.21/0.45 inference(skolemize,[status(sab)],[59])).
% 0.21/0.45 tff(61,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.21/0.45 tff(62,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(D!17, A!20, B!19) <=> relation_of2(D!17, A!20, B!19))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(63,plain,
% 0.21/0.45 (relation_of2_as_subset(D!17, A!20, B!19) <=> relation_of2(D!17, A!20, B!19)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.21/0.45 tff(64,plain,
% 0.21/0.45 ((~(relation_of2_as_subset(D!17, A!20, B!19) <=> relation_of2(D!17, A!20, B!19))) | (~relation_of2_as_subset(D!17, A!20, B!19)) | relation_of2(D!17, A!20, B!19)),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(65,plain,
% 0.21/0.45 ((~(relation_of2_as_subset(D!17, A!20, B!19) <=> relation_of2(D!17, A!20, B!19))) | relation_of2(D!17, A!20, B!19)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[64, 17])).
% 0.21/0.45 tff(66,plain,
% 0.21/0.45 (relation_of2(D!17, A!20, B!19)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[65, 63])).
% 0.21/0.45 tff(67,plain,
% 0.21/0.45 (relation_of2(D!17, relation_dom_as_subset(A!20, B!19, D!17), B!19)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[66, 54])).
% 0.21/0.45 tff(68,plain,
% 0.21/0.45 (^[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))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(69,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.45 tff(70,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(71,plain,
% 0.21/0.45 (^[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))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(72,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.45 tff(73,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/sandbox2/benchmark/theBenchmark.p','redefinition_k4_relset_1')).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.21/0.45 tff(76,plain,(
% 0.21/0.45 ![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[75])).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 (((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | ((~relation_of2(D!17, relation_dom_as_subset(A!20, B!19, D!17), B!19)) | (relation_dom_as_subset(relation_dom_as_subset(A!20, B!19, D!17), B!19, D!17) = relation_dom(D!17)))) <=> ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | (~relation_of2(D!17, relation_dom_as_subset(A!20, B!19, D!17), B!19)) | (relation_dom_as_subset(relation_dom_as_subset(A!20, B!19, D!17), B!19, D!17) = relation_dom(D!17)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(79,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | ((~relation_of2(D!17, relation_dom_as_subset(A!20, B!19, D!17), B!19)) | (relation_dom_as_subset(relation_dom_as_subset(A!20, B!19, D!17), B!19, D!17) = relation_dom(D!17)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i] : ((~relation_of2(C, A, B)) | (relation_dom_as_subset(A, B, C) = relation_dom(C)))) | (~relation_of2(D!17, relation_dom_as_subset(A!20, B!19, D!17), B!19)) | (relation_dom_as_subset(relation_dom_as_subset(A!20, B!19, D!17), B!19, D!17) = relation_dom(D!17))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 ((~relation_of2(D!17, relation_dom_as_subset(A!20, B!19, D!17), B!19)) | (relation_dom_as_subset(relation_dom_as_subset(A!20, B!19, D!17), B!19, D!17) = relation_dom(D!17))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[80, 77])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 (relation_dom_as_subset(relation_dom_as_subset(A!20, B!19, D!17), B!19, D!17) = relation_dom(D!17)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[81, 67])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 (relation_dom(D!17) = relation_dom_as_subset(relation_dom_as_subset(A!20, B!19, D!17), B!19, D!17)),
% 0.21/0.45 inference(symmetry,[status(thm)],[82])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 (relation_dom(D!17) = A!20),
% 0.21/0.45 inference(transitivity,[status(thm)],[83, 52, 51])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (in(C!18, relation_dom(D!17)) <=> in(C!18, A!20)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 (in(C!18, A!20) <=> in(C!18, relation_dom(D!17))),
% 0.21/0.45 inference(symmetry,[status(thm)],[85])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (in(C!18, A!20)),
% 0.21/0.45 inference(or_elim,[status(thm)],[40])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (in(C!18, relation_dom(D!17))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 (cartesian_product2(relation_dom_as_subset(A!20, B!19, D!17), B!19) = cartesian_product2(A!20, B!19)),
% 0.21/0.45 inference(monotonicity,[status(thm)],[51])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 (powerset(cartesian_product2(relation_dom_as_subset(A!20, B!19, D!17), B!19)) = powerset(cartesian_product2(A!20, B!19))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[89])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (element(D!17, powerset(cartesian_product2(relation_dom_as_subset(A!20, B!19, D!17), B!19))) <=> element(D!17, powerset(cartesian_product2(A!20, B!19)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 (element(D!17, powerset(cartesian_product2(A!20, B!19))) <=> element(D!17, powerset(cartesian_product2(relation_dom_as_subset(A!20, B!19, D!17), B!19)))),
% 0.21/0.45 inference(symmetry,[status(thm)],[91])).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 (^[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)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[93])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 (^[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)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 (![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))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.45 tff(98,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) => element(C, powerset(cartesian_product2(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 0.21/0.45 tff(99,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.21/0.45 tff(101,plain,(
% 0.21/0.45 ![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[100])).
% 0.21/0.45 tff(102,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : ((~relation_of2_as_subset(C, A, B)) | element(C, powerset(cartesian_product2(A, B))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.21/0.45 tff(103,plain,
% 0.21/0.45 (((~![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!17, A!20, B!19)) | element(D!17, powerset(cartesian_product2(A!20, B!19))))) <=> ((~![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!17, A!20, B!19)) | element(D!17, powerset(cartesian_product2(A!20, B!19))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(104,plain,
% 0.21/0.45 ((~![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!17, A!20, B!19)) | element(D!17, powerset(cartesian_product2(A!20, B!19))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(105,plain,
% 0.21/0.45 ((~![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!17, A!20, B!19)) | element(D!17, powerset(cartesian_product2(A!20, B!19)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.21/0.45 tff(106,plain,
% 0.21/0.45 (element(D!17, powerset(cartesian_product2(A!20, B!19)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[105, 102, 17])).
% 0.21/0.45 tff(107,plain,
% 0.21/0.45 (element(D!17, powerset(cartesian_product2(relation_dom_as_subset(A!20, B!19, D!17), B!19)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[106, 92])).
% 0.21/0.45 tff(108,plain,
% 0.21/0.45 (^[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))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(109,plain,
% 0.21/0.45 (![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)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[108])).
% 0.21/0.45 tff(110,plain,
% 0.21/0.45 (![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)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(111,plain,
% 0.21/0.45 (^[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))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(112,plain,
% 0.21/0.45 (![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)))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.45 tff(113,axiom,(![A: $i, B: $i, C: $i] : (element(C, powerset(cartesian_product2(A, B))) => relation(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_relset_1')).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.21/0.45 tff(116,plain,(
% 0.21/0.45 ![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[115])).
% 0.21/0.45 tff(117,plain,
% 0.21/0.45 (![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.21/0.45 tff(118,plain,
% 0.21/0.45 (((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(D!17) | (~element(D!17, powerset(cartesian_product2(relation_dom_as_subset(A!20, B!19, D!17), B!19)))))) <=> ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(D!17) | (~element(D!17, powerset(cartesian_product2(relation_dom_as_subset(A!20, B!19, D!17), B!19)))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | (relation(D!17) | (~element(D!17, powerset(cartesian_product2(relation_dom_as_subset(A!20, B!19, D!17), B!19)))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(120,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i] : (relation(C) | (~element(C, powerset(cartesian_product2(A, B)))))) | relation(D!17) | (~element(D!17, powerset(cartesian_product2(relation_dom_as_subset(A!20, B!19, D!17), B!19))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.45 tff(121,plain,
% 0.21/0.45 (relation(D!17) | (~element(D!17, powerset(cartesian_product2(relation_dom_as_subset(A!20, B!19, D!17), B!19))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[120, 117])).
% 0.21/0.45 tff(122,plain,
% 0.21/0.45 (relation(D!17)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[121, 107])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 (^[A: $i, B: $i] : refl(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(124,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[123])).
% 0.21/0.45 tff(125,plain,
% 0.21/0.45 (^[A: $i, B: $i] : rewrite(((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(126,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[125])).
% 0.21/0.45 tff(127,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[126, 124])).
% 0.21/0.45 tff(128,plain,
% 0.21/0.45 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(B) & function(B)) <=> (~((~relation(B)) | (~function(B))))), ((~(relation(B) & function(B))) <=> (~(~((~relation(B)) | (~function(B))))))), rewrite((~(~((~relation(B)) | (~function(B))))) <=> ((~relation(B)) | (~function(B)))), ((~(relation(B) & function(B))) <=> ((~relation(B)) | (~function(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((relation(C) & function(C)) <=> (~((~relation(C)) | (~function(C))))), ((~(relation(C) & function(C))) <=> (~(~((~relation(C)) | (~function(C))))))), rewrite((~(~((~relation(C)) | (~function(C))))) <=> ((~relation(C)) | (~function(C)))), ((~(relation(C) & function(C))) <=> ((~relation(C)) | (~function(C))))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | ((~relation(C)) | (~function(C)))))), rewrite(((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | ((~relation(C)) | (~function(C)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))), (((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))), (![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> (((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))))), rewrite((((~relation(B)) | (~function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C)))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))), (((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(129,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> ![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[128])).
% 0.21/0.46 tff(130,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(131,plain,
% 0.21/0.46 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))) <=> ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), rewrite(((relation(C) & function(C)) => ((~in(A, relation_dom(B))) | (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))), (((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))))), (![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))) <=> ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))))), rewrite(((relation(B) & function(B)) => ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))), (((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(132,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A)))))) <=> ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[131])).
% 0.21/0.46 tff(133,axiom,(![A: $i, B: $i] : ((relation(B) & function(B)) => ![C: $i] : ((relation(C) & function(C)) => (in(A, relation_dom(B)) => (apply(relation_composition(B, C), A) = apply(C, apply(B, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_funct_1')).
% 0.21/0.46 tff(134,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.21/0.46 tff(135,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.21/0.46 tff(136,plain,(
% 0.21/0.46 ![A: $i, B: $i] : ((~(relation(B) & function(B))) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~(relation(C) & function(C)))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[135])).
% 0.21/0.46 tff(137,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.21/0.46 tff(138,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[137, 127])).
% 0.21/0.46 tff(139,plain,
% 0.21/0.46 (function(D!17)),
% 0.21/0.46 inference(and_elim,[status(thm)],[16])).
% 0.21/0.46 tff(140,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(D!17)) | (~function(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17)))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(D!17)) | (~function(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(141,plain,
% 0.21/0.46 (((~relation(D!17)) | (~function(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17))))) <=> ((~relation(D!17)) | (~function(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(142,plain,
% 0.21/0.46 (^[C: $i] : rewrite(((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~in(C!18, relation_dom(D!17))) | (~relation(C)) | (~function(C))) <=> ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(143,plain,
% 0.21/0.46 (![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~in(C!18, relation_dom(D!17))) | (~relation(C)) | (~function(C))) <=> ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[142])).
% 0.21/0.46 tff(144,plain,
% 0.21/0.46 (((~relation(D!17)) | (~function(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~in(C!18, relation_dom(D!17))) | (~relation(C)) | (~function(C)))) <=> ((~relation(D!17)) | (~function(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17)))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[143])).
% 0.21/0.46 tff(145,plain,
% 0.21/0.46 (((~relation(D!17)) | (~function(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~in(C!18, relation_dom(D!17))) | (~relation(C)) | (~function(C)))) <=> ((~relation(D!17)) | (~function(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17)))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[144, 141])).
% 0.21/0.46 tff(146,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(D!17)) | (~function(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~in(C!18, relation_dom(D!17))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(D!17)) | (~function(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[145])).
% 0.21/0.46 tff(147,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(D!17)) | (~function(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~in(C!18, relation_dom(D!17))) | (~relation(C)) | (~function(C))))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(D!17)) | (~function(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17)))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[146, 140])).
% 0.21/0.46 tff(148,plain,
% 0.21/0.46 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | ((~relation(D!17)) | (~function(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~in(C!18, relation_dom(D!17))) | (~relation(C)) | (~function(C))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(149,plain,
% 0.21/0.46 ((~![A: $i, B: $i] : ((~relation(B)) | (~function(B)) | ![C: $i] : ((apply(relation_composition(B, C), A) = apply(C, apply(B, A))) | (~in(A, relation_dom(B))) | (~relation(C)) | (~function(C))))) | (~relation(D!17)) | (~function(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.21/0.46 tff(150,plain,
% 0.21/0.46 ((~relation(D!17)) | ![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[149, 139, 138])).
% 0.21/0.46 tff(151,plain,
% 0.21/0.46 (![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[150, 122])).
% 0.21/0.46 tff(152,plain,
% 0.21/0.46 (relation(E!21) & function(E!21)),
% 0.21/0.46 inference(or_elim,[status(thm)],[40])).
% 0.21/0.46 tff(153,plain,
% 0.21/0.46 (function(E!21)),
% 0.21/0.46 inference(and_elim,[status(thm)],[152])).
% 0.21/0.46 tff(154,plain,
% 0.21/0.46 (relation(E!21)),
% 0.21/0.46 inference(and_elim,[status(thm)],[152])).
% 0.21/0.46 tff(155,plain,
% 0.21/0.46 (~(apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18)))),
% 0.21/0.46 inference(or_elim,[status(thm)],[40])).
% 0.21/0.46 tff(156,plain,
% 0.21/0.46 (((~![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17))))) | ((apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18))) | (~relation(E!21)) | (~function(E!21)) | (~in(C!18, relation_dom(D!17))))) <=> ((~![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17))))) | (apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18))) | (~relation(E!21)) | (~function(E!21)) | (~in(C!18, relation_dom(D!17))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(157,plain,
% 0.21/0.47 ((~![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17))))) | ((apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18))) | (~relation(E!21)) | (~function(E!21)) | (~in(C!18, relation_dom(D!17))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(158,plain,
% 0.21/0.47 ((~![C: $i] : ((apply(relation_composition(D!17, C), C!18) = apply(C, apply(D!17, C!18))) | (~relation(C)) | (~function(C)) | (~in(C!18, relation_dom(D!17))))) | (apply(relation_composition(D!17, E!21), C!18) = apply(E!21, apply(D!17, C!18))) | (~relation(E!21)) | (~function(E!21)) | (~in(C!18, relation_dom(D!17)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.21/0.47 tff(159,plain,
% 0.21/0.47 (~in(C!18, relation_dom(D!17))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[158, 155, 154, 153, 151])).
% 0.21/0.47 tff(160,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[159, 88])).
% 0.21/0.47 % SZS output end Proof
%------------------------------------------------------------------------------