TSTP Solution File: ITP013_2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP013_2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 Sep 17 04:15:04 EDT 2022
% Result : Theorem 4.82s 3.38s
% Output : Proof 4.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ITP013_2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 02:40:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 4.82/3.38 % SZS status Theorem
% 4.82/3.38 % SZS output start Proof
% 4.82/3.38 tff(ap_type, type, (
% 4.82/3.38 ap: ( $i * $i ) > $i)).
% 4.82/3.38 tff(inj__ty_2Enum_2Enum_type, type, (
% 4.82/3.38 inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i)).
% 4.82/3.38 tff(tptp_fun_V1b_2_type, type, (
% 4.82/3.38 tptp_fun_V1b_2: tp__ty_2Enum_2Enum)).
% 4.82/3.38 tff(c_2Ewords_2En2w_type, type, (
% 4.82/3.38 c_2Ewords_2En2w: del > $i)).
% 4.82/3.38 tff(tptp_fun_A_27a_4_type, type, (
% 4.82/3.38 tptp_fun_A_27a_4: del)).
% 4.82/3.38 tff(tptp_fun_V0a_3_type, type, (
% 4.82/3.38 tptp_fun_V0a_3: tp__ty_2Enum_2Enum)).
% 4.82/3.38 tff(c_2Ewords_2Eword__sub_type, type, (
% 4.82/3.38 c_2Ewords_2Eword__sub: del > $i)).
% 4.82/3.38 tff(c_2Earithmetic_2E_2D_type, type, (
% 4.82/3.38 c_2Earithmetic_2E_2D: $i)).
% 4.82/3.38 tff(c_2Ewords_2Eword__2comp_type, type, (
% 4.82/3.38 c_2Ewords_2Eword__2comp: del > $i)).
% 4.82/3.38 tff(c_2Ewords_2Eword__add_type, type, (
% 4.82/3.38 c_2Ewords_2Eword__add: del > $i)).
% 4.82/3.38 tff(mem_type, type, (
% 4.82/3.38 mem: ( $i * del ) > $o)).
% 4.82/3.38 tff(ty_2Efcp_2Ecart_type, type, (
% 4.82/3.38 ty_2Efcp_2Ecart: ( del * del ) > del)).
% 4.82/3.38 tff(bool_type, type, (
% 4.82/3.38 bool: del)).
% 4.82/3.38 tff(ty_2Enum_2Enum_type, type, (
% 4.82/3.38 ty_2Enum_2Enum: del)).
% 4.82/3.38 tff(arr_type, type, (
% 4.82/3.38 arr: ( del * del ) > del)).
% 4.82/3.38 tff(c_2Earithmetic_2E_3C_3D_type, type, (
% 4.82/3.38 c_2Earithmetic_2E_3C_3D: $i)).
% 4.82/3.38 tff(c_2Ebool_2ECOND_type, type, (
% 4.82/3.38 c_2Ebool_2ECOND: del > $i)).
% 4.82/3.38 tff(c_2Earithmetic_2E_2B_type, type, (
% 4.82/3.38 c_2Earithmetic_2E_2B: $i)).
% 4.82/3.38 tff(inj__o_type, type, (
% 4.82/3.38 inj__o: tp__o > $i)).
% 4.82/3.38 tff(fo__c_2Ebool_2ET_type, type, (
% 4.82/3.38 fo__c_2Ebool_2ET: tp__o)).
% 4.82/3.38 tff(fo__c_2Ebool_2EF_type, type, (
% 4.82/3.38 fo__c_2Ebool_2EF: tp__o)).
% 4.82/3.38 tff(c_2Ebool_2E_7E_type, type, (
% 4.82/3.38 c_2Ebool_2E_7E: $i)).
% 4.82/3.38 tff(p_type, type, (
% 4.82/3.38 p: $i > $o)).
% 4.82/3.38 tff(c_2Ebool_2EF_type, type, (
% 4.82/3.38 c_2Ebool_2EF: $i)).
% 4.82/3.38 tff(c_2Ebool_2ET_type, type, (
% 4.82/3.38 c_2Ebool_2ET: $i)).
% 4.82/3.38 tff(fo__c_2Earithmetic_2E_3C_3D_type, type, (
% 4.82/3.38 fo__c_2Earithmetic_2E_3C_3D: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__o)).
% 4.82/3.38 tff(fo__c_2Earithmetic_2E_2D_type, type, (
% 4.82/3.38 fo__c_2Earithmetic_2E_2D: ( tp__ty_2Enum_2Enum * tp__ty_2Enum_2Enum ) > tp__ty_2Enum_2Enum)).
% 4.82/3.38 tff(1,plain,
% 4.82/3.38 (^[A_27a: del] : refl(mem(c_2Ewords_2En2w(A_27a), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a))) <=> mem(c_2Ewords_2En2w(A_27a), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a))))),
% 4.82/3.38 inference(bind,[status(th)],[])).
% 4.82/3.38 tff(2,plain,
% 4.82/3.38 (![A_27a: del] : mem(c_2Ewords_2En2w(A_27a), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a))) <=> ![A_27a: del] : mem(c_2Ewords_2En2w(A_27a), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a)))),
% 4.82/3.38 inference(quant_intro,[status(thm)],[1])).
% 4.82/3.38 tff(3,plain,
% 4.82/3.38 (![A_27a: del] : mem(c_2Ewords_2En2w(A_27a), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a))) <=> ![A_27a: del] : mem(c_2Ewords_2En2w(A_27a), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a)))),
% 4.82/3.38 inference(rewrite,[status(thm)],[])).
% 4.82/3.38 tff(4,axiom,(![A_27a: del] : mem(c_2Ewords_2En2w(A_27a), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Ewords_2En2w')).
% 4.82/3.38 tff(5,plain,
% 4.82/3.38 (![A_27a: del] : mem(c_2Ewords_2En2w(A_27a), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a)))),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 4.82/3.38 tff(6,plain,(
% 4.82/3.38 ![A_27a: del] : mem(c_2Ewords_2En2w(A_27a), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a)))),
% 4.82/3.38 inference(skolemize,[status(sab)],[5])).
% 4.82/3.38 tff(7,plain,
% 4.82/3.38 (![A_27a: del] : mem(c_2Ewords_2En2w(A_27a), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a)))),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 4.82/3.38 tff(8,plain,
% 4.82/3.38 ((~![A_27a: del] : mem(c_2Ewords_2En2w(A_27a), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a)))) | mem(c_2Ewords_2En2w(A_27a!4), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.82/3.38 inference(quant_inst,[status(thm)],[])).
% 4.82/3.38 tff(9,plain,
% 4.82/3.38 (mem(c_2Ewords_2En2w(A_27a!4), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.82/3.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 4.82/3.38 tff(10,plain,
% 4.82/3.38 (^[A: del, B: del, F: $i] : refl(((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))),
% 4.82/3.38 inference(bind,[status(th)],[])).
% 4.82/3.38 tff(11,plain,
% 4.82/3.38 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 4.82/3.38 inference(quant_intro,[status(thm)],[10])).
% 4.82/3.38 tff(12,plain,
% 4.82/3.38 (^[A: del, B: del, F: $i] : rewrite(((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))),
% 4.82/3.38 inference(bind,[status(th)],[])).
% 4.82/3.38 tff(13,plain,
% 4.82/3.38 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 4.82/3.38 inference(quant_intro,[status(thm)],[12])).
% 4.82/3.38 tff(14,plain,
% 4.82/3.38 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 4.82/3.38 inference(transitivity,[status(thm)],[13, 11])).
% 4.82/3.38 tff(15,plain,
% 4.82/3.38 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 4.82/3.38 inference(rewrite,[status(thm)],[])).
% 4.82/3.38 tff(16,plain,
% 4.82/3.38 (^[A: del, B: del, F: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite((mem(X, A) => mem(ap(F, X), B)) <=> ((~mem(X, A)) | mem(ap(F, X), B)))), (![X: $i] : (mem(X, A) => mem(ap(F, X), B)) <=> ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))), ((mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> (mem(F, arr(A, B)) => ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))), rewrite((mem(F, arr(A, B)) => ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))), ((mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))))),
% 4.82/3.38 inference(bind,[status(th)],[])).
% 4.82/3.38 tff(17,plain,
% 4.82/3.38 (![A: del, B: del, F: $i] : (mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 4.82/3.38 inference(quant_intro,[status(thm)],[16])).
% 4.82/3.38 tff(18,axiom,(![A: del, B: del, F: $i] : (mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B)))), file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001_2.ax','ap_tp')).
% 4.82/3.38 tff(19,plain,
% 4.82/3.38 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 4.82/3.38 tff(20,plain,
% 4.82/3.38 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 4.82/3.38 tff(21,plain,(
% 4.82/3.38 ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 4.82/3.38 inference(skolemize,[status(sab)],[20])).
% 4.82/3.38 tff(22,plain,
% 4.82/3.38 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 4.82/3.38 tff(23,plain,
% 4.82/3.38 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ewords_2En2w(A_27a!4), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a!4)))) | ![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4))))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Ewords_2En2w(A_27a!4), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a!4)))) | ![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4))))),
% 4.82/3.38 inference(rewrite,[status(thm)],[])).
% 4.82/3.38 tff(24,plain,
% 4.82/3.38 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ewords_2En2w(A_27a!4), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a!4)))) | ![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4))))),
% 4.82/3.38 inference(quant_inst,[status(thm)],[])).
% 4.82/3.38 tff(25,plain,
% 4.82/3.38 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Ewords_2En2w(A_27a!4), arr(ty_2Enum_2Enum, ty_2Efcp_2Ecart(bool, A_27a!4)))) | ![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 4.82/3.38 tff(26,plain,
% 4.82/3.38 (![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.82/3.38 inference(unit_resolution,[status(thm)],[25, 22, 9])).
% 4.82/3.38 tff(27,plain,
% 4.82/3.38 (^[X: tp__ty_2Enum_2Enum] : refl(mem(inj__ty_2Enum_2Enum(X), ty_2Enum_2Enum) <=> mem(inj__ty_2Enum_2Enum(X), ty_2Enum_2Enum))),
% 4.82/3.38 inference(bind,[status(th)],[])).
% 4.82/3.38 tff(28,plain,
% 4.82/3.38 (![X: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X), ty_2Enum_2Enum) <=> ![X: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X), ty_2Enum_2Enum)),
% 4.82/3.38 inference(quant_intro,[status(thm)],[27])).
% 4.82/3.38 tff(29,plain,
% 4.82/3.38 (![X: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X), ty_2Enum_2Enum) <=> ![X: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X), ty_2Enum_2Enum)),
% 4.82/3.38 inference(rewrite,[status(thm)],[])).
% 4.82/3.38 tff(30,axiom,(![X: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X), ty_2Enum_2Enum)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','stp_inj_mem_ty_2Enum_2Enum')).
% 4.82/3.38 tff(31,plain,
% 4.82/3.38 (![X: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X), ty_2Enum_2Enum)),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[30, 29])).
% 4.82/3.38 tff(32,plain,(
% 4.82/3.38 ![X: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X), ty_2Enum_2Enum)),
% 4.82/3.38 inference(skolemize,[status(sab)],[31])).
% 4.82/3.38 tff(33,plain,
% 4.82/3.38 (![X: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X), ty_2Enum_2Enum)),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[32, 28])).
% 4.82/3.38 tff(34,plain,
% 4.82/3.38 ((~![X: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X), ty_2Enum_2Enum)) | mem(inj__ty_2Enum_2Enum(V1b!2), ty_2Enum_2Enum)),
% 4.82/3.38 inference(quant_inst,[status(thm)],[])).
% 4.82/3.38 tff(35,plain,
% 4.82/3.38 (mem(inj__ty_2Enum_2Enum(V1b!2), ty_2Enum_2Enum)),
% 4.82/3.38 inference(unit_resolution,[status(thm)],[34, 33])).
% 4.82/3.38 tff(36,plain,
% 4.82/3.38 (((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | ((~mem(inj__ty_2Enum_2Enum(V1b!2), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)), ty_2Efcp_2Ecart(bool, A_27a!4)))) <=> ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | (~mem(inj__ty_2Enum_2Enum(V1b!2), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.82/3.38 inference(rewrite,[status(thm)],[])).
% 4.82/3.38 tff(37,plain,
% 4.82/3.38 ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | ((~mem(inj__ty_2Enum_2Enum(V1b!2), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.82/3.38 inference(quant_inst,[status(thm)],[])).
% 4.82/3.38 tff(38,plain,
% 4.82/3.38 ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | (~mem(inj__ty_2Enum_2Enum(V1b!2), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)), ty_2Efcp_2Ecart(bool, A_27a!4))),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 4.82/3.38 tff(39,plain,
% 4.82/3.38 (mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)), ty_2Efcp_2Ecart(bool, A_27a!4))),
% 4.82/3.38 inference(unit_resolution,[status(thm)],[38, 35, 26])).
% 4.82/3.38 tff(40,plain,
% 4.82/3.38 ((~![X: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X), ty_2Enum_2Enum)) | mem(inj__ty_2Enum_2Enum(V0a!3), ty_2Enum_2Enum)),
% 4.82/3.38 inference(quant_inst,[status(thm)],[])).
% 4.82/3.38 tff(41,plain,
% 4.82/3.38 (mem(inj__ty_2Enum_2Enum(V0a!3), ty_2Enum_2Enum)),
% 4.82/3.38 inference(unit_resolution,[status(thm)],[40, 33])).
% 4.82/3.38 tff(42,plain,
% 4.82/3.38 (((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | ((~mem(inj__ty_2Enum_2Enum(V0a!3), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3)), ty_2Efcp_2Ecart(bool, A_27a!4)))) <=> ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | (~mem(inj__ty_2Enum_2Enum(V0a!3), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3)), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.82/3.38 inference(rewrite,[status(thm)],[])).
% 4.82/3.38 tff(43,plain,
% 4.82/3.38 ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | ((~mem(inj__ty_2Enum_2Enum(V0a!3), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3)), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.82/3.38 inference(quant_inst,[status(thm)],[])).
% 4.82/3.38 tff(44,plain,
% 4.82/3.38 ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | (~mem(inj__ty_2Enum_2Enum(V0a!3), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3)), ty_2Efcp_2Ecart(bool, A_27a!4))),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 4.82/3.38 tff(45,plain,
% 4.82/3.38 (mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3)), ty_2Efcp_2Ecart(bool, A_27a!4))),
% 4.82/3.38 inference(unit_resolution,[status(thm)],[44, 41, 26])).
% 4.82/3.38 tff(46,plain,
% 4.82/3.38 (^[A_27a: del, V0v: $i] : refl(((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w))))) <=> ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w))))))),
% 4.82/3.38 inference(bind,[status(th)],[])).
% 4.82/3.38 tff(47,plain,
% 4.82/3.38 (![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w))))) <=> ![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))),
% 4.82/3.38 inference(quant_intro,[status(thm)],[46])).
% 4.82/3.38 tff(48,plain,
% 4.82/3.38 (^[A_27a: del, V0v: $i] : rewrite(((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w))))) <=> ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w))))))),
% 4.82/3.38 inference(bind,[status(th)],[])).
% 4.82/3.38 tff(49,plain,
% 4.82/3.38 (![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w))))) <=> ![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))),
% 4.82/3.38 inference(quant_intro,[status(thm)],[48])).
% 4.82/3.38 tff(50,plain,
% 4.82/3.38 (![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w))))) <=> ![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))),
% 4.82/3.38 inference(transitivity,[status(thm)],[49, 47])).
% 4.82/3.38 tff(51,plain,
% 4.82/3.38 (![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w))))) <=> ![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))),
% 4.82/3.38 inference(rewrite,[status(thm)],[])).
% 4.82/3.38 tff(52,plain,
% 4.82/3.38 (^[A_27a: del, V0v: $i] : trans(monotonicity(quant_intro(proof_bind(^[V1w: $i] : rewrite((mem(V1w, ty_2Efcp_2Ecart(bool, A_27a)) => (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))) <=> ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))), (![V1w: $i] : (mem(V1w, ty_2Efcp_2Ecart(bool, A_27a)) => (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))) <=> ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))), ((mem(V0v, ty_2Efcp_2Ecart(bool, A_27a)) => ![V1w: $i] : (mem(V1w, ty_2Efcp_2Ecart(bool, A_27a)) => (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w))))) <=> (mem(V0v, ty_2Efcp_2Ecart(bool, A_27a)) => ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w))))))), rewrite((mem(V0v, ty_2Efcp_2Ecart(bool, A_27a)) => ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w))))) <=> ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))), ((mem(V0v, ty_2Efcp_2Ecart(bool, A_27a)) => ![V1w: $i] : (mem(V1w, ty_2Efcp_2Ecart(bool, A_27a)) => (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w))))) <=> ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))))),
% 4.82/3.38 inference(bind,[status(th)],[])).
% 4.82/3.38 tff(53,plain,
% 4.82/3.38 (![A_27a: del, V0v: $i] : (mem(V0v, ty_2Efcp_2Ecart(bool, A_27a)) => ![V1w: $i] : (mem(V1w, ty_2Efcp_2Ecart(bool, A_27a)) => (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w))))) <=> ![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))),
% 4.82/3.38 inference(quant_intro,[status(thm)],[52])).
% 4.82/3.38 tff(54,axiom,(![A_27a: del, V0v: $i] : (mem(V0v, ty_2Efcp_2Ecart(bool, A_27a)) => ![V1w: $i] : (mem(V1w, ty_2Efcp_2Ecart(bool, A_27a)) => (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax_thm_2Ewords_2Eword__sub__def')).
% 4.82/3.38 tff(55,plain,
% 4.82/3.38 (![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 4.82/3.38 tff(56,plain,
% 4.82/3.38 (![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[55, 51])).
% 4.82/3.38 tff(57,plain,(
% 4.82/3.38 ![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))),
% 4.82/3.38 inference(skolemize,[status(sab)],[56])).
% 4.82/3.38 tff(58,plain,
% 4.82/3.38 (![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[57, 50])).
% 4.82/3.38 tff(59,plain,
% 4.82/3.38 (((~![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))) | ((~mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3)), ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), V1w)))))) <=> ((~![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))) | (~mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3)), ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), V1w)))))),
% 4.82/3.38 inference(rewrite,[status(thm)],[])).
% 4.82/3.38 tff(60,plain,
% 4.82/3.38 ((~![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))) | ((~mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3)), ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), V1w)))))),
% 4.82/3.38 inference(quant_inst,[status(thm)],[])).
% 4.82/3.38 tff(61,plain,
% 4.82/3.38 ((~![A_27a: del, V0v: $i] : ((~mem(V0v, ty_2Efcp_2Ecart(bool, A_27a))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a), V0v), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a), V0v), ap(c_2Ewords_2Eword__2comp(A_27a), V1w)))))) | (~mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3)), ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), V1w))))),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[60, 59])).
% 4.82/3.38 tff(62,plain,
% 4.82/3.38 ((~mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3)), ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), V1w))))),
% 4.82/3.38 inference(unit_resolution,[status(thm)],[61, 58])).
% 4.82/3.38 tff(63,plain,
% 4.82/3.38 (![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), V1w))))),
% 4.82/3.38 inference(unit_resolution,[status(thm)],[62, 45])).
% 4.82/3.38 tff(64,plain,
% 4.82/3.38 (((~![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), V1w))))) | ((~mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)), ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2))) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2))))))) <=> ((~![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), V1w))))) | (~mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)), ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2))) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2))))))),
% 4.82/3.38 inference(rewrite,[status(thm)],[])).
% 4.82/3.38 tff(65,plain,
% 4.82/3.38 ((~![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), V1w))))) | ((~mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)), ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2))) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2))))))),
% 4.82/3.38 inference(quant_inst,[status(thm)],[])).
% 4.82/3.38 tff(66,plain,
% 4.82/3.38 ((~![V1w: $i] : ((~mem(V1w, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), V1w) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), V1w))))) | (~mem(ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)), ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2))) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)))))),
% 4.82/3.38 inference(modus_ponens,[status(thm)],[65, 64])).
% 4.82/3.38 tff(67,plain,
% 4.82/3.38 (ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2))) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2))))),
% 4.82/3.38 inference(unit_resolution,[status(thm)],[66, 63, 39])).
% 4.82/3.38 tff(68,plain,
% 4.82/3.38 (ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)))) = ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)))),
% 4.82/3.38 inference(symmetry,[status(thm)],[67])).
% 4.82/3.38 tff(69,plain,
% 4.82/3.38 (^[A_27a: del, A_27b: del] : refl((~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))))) <=> (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))))))),
% 4.82/3.38 inference(bind,[status(th)],[])).
% 4.82/3.38 tff(70,plain,
% 4.82/3.38 (![A_27a: del, A_27b: del] : (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))))) <=> ![A_27a: del, A_27b: del] : (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m)))))))))),
% 4.82/3.38 inference(quant_intro,[status(thm)],[69])).
% 4.82/3.38 tff(71,plain,
% 4.82/3.38 (^[A_27a: del, A_27b: del] : rewrite((~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))))) <=> (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))))))),
% 4.82/3.38 inference(bind,[status(th)],[])).
% 4.82/3.38 tff(72,plain,
% 4.82/3.38 (![A_27a: del, A_27b: del] : (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))))) <=> ![A_27a: del, A_27b: del] : (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m)))))))))),
% 4.82/3.38 inference(quant_intro,[status(thm)],[71])).
% 4.82/3.38 tff(73,plain,
% 4.82/3.38 (![A_27a: del, A_27b: del] : (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))))) <=> ![A_27a: del, A_27b: del] : (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m)))))))))),
% 4.82/3.38 inference(transitivity,[status(thm)],[72, 70])).
% 4.82/3.38 tff(74,plain,
% 4.82/3.38 (^[A_27a: del, A_27b: del] : rewrite((![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n))))) & ![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))) <=> (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))))))),
% 4.82/3.38 inference(bind,[status(th)],[])).
% 4.82/3.38 tff(75,plain,
% 4.82/3.38 (![A_27a: del, A_27b: del] : (![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n))))) & ![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))) <=> ![A_27a: del, A_27b: del] : (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m)))))))))),
% 4.82/3.39 inference(quant_intro,[status(thm)],[74])).
% 4.82/3.39 tff(76,plain,
% 4.82/3.39 (![A_27a: del, A_27b: del] : (![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n))))) & ![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))) <=> ![A_27a: del, A_27b: del] : (![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n))))) & ![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m)))))))),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(77,axiom,(![A_27a: del, A_27b: del] : (![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n))))) & ![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Ewords_2EWORD__LITERAL__ADD')).
% 4.82/3.39 tff(78,plain,
% 4.82/3.39 (![A_27a: del, A_27b: del] : (![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n))))) & ![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m)))))))),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[77, 76])).
% 4.82/3.39 tff(79,plain,(
% 4.82/3.39 ![A_27a: del, A_27b: del] : (![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n))))) & ![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m)))))))),
% 4.82/3.39 inference(skolemize,[status(sab)],[78])).
% 4.82/3.39 tff(80,plain,
% 4.82/3.39 (![A_27a: del, A_27b: del] : (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m)))))))))),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[79, 75])).
% 4.82/3.39 tff(81,plain,
% 4.82/3.39 (![A_27a: del, A_27b: del] : (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m)))))))))),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[80, 73])).
% 4.82/3.39 tff(82,plain,
% 4.82/3.39 ((~![A_27a: del, A_27b: del] : (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a), ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27b)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27b), ap(c_2Ewords_2En2w(A_27b), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m)))))))))) | (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m)))))))))),
% 4.82/3.39 inference(quant_inst,[status(thm)],[])).
% 4.82/3.39 tff(83,plain,
% 4.82/3.39 (~((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))))),
% 4.82/3.39 inference(unit_resolution,[status(thm)],[82, 81])).
% 4.82/3.39 tff(84,plain,
% 4.82/3.39 (((~![V0m: tp__ty_2Enum_2Enum, V1n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0m)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1n)))) = ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2B, inj__ty_2Enum_2Enum(V0m)), inj__ty_2Enum_2Enum(V1n)))))) | (~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m)))))))) | ![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))),
% 4.82/3.39 inference(tautology,[status(thm)],[])).
% 4.82/3.39 tff(85,plain,
% 4.82/3.39 (![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))),
% 4.82/3.39 inference(unit_resolution,[status(thm)],[84, 83])).
% 4.82/3.39 tff(86,plain,
% 4.82/3.39 ((~![V2m: tp__ty_2Enum_2Enum, V3n: tp__ty_2Enum_2Enum] : (ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V3n)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V2m)), inj__ty_2Enum_2Enum(V3n)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V3n)), inj__ty_2Enum_2Enum(V2m))))))) | (ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))))))),
% 4.82/3.39 inference(quant_inst,[status(thm)],[])).
% 4.82/3.39 tff(87,plain,
% 4.82/3.39 (ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))))),
% 4.82/3.39 inference(unit_resolution,[status(thm)],[86, 85])).
% 4.82/3.39 tff(88,plain,
% 4.82/3.39 (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))))) = ap(ap(c_2Ewords_2Eword__add(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2))))),
% 4.82/3.39 inference(symmetry,[status(thm)],[87])).
% 4.82/3.39 tff(89,plain,
% 4.82/3.39 (mem(c_2Ebool_2EF, bool) <=> mem(inj__o(fo__c_2Ebool_2EF), bool)),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(90,plain,
% 4.82/3.39 (mem(c_2Ebool_2EF, bool) <=> mem(c_2Ebool_2EF, bool)),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(91,axiom,(mem(c_2Ebool_2EF, bool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Ebool_2EF')).
% 4.82/3.39 tff(92,plain,
% 4.82/3.39 (mem(c_2Ebool_2EF, bool)),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[91, 90])).
% 4.82/3.39 tff(93,plain,
% 4.82/3.39 (mem(inj__o(fo__c_2Ebool_2EF), bool)),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[92, 89])).
% 4.82/3.39 tff(94,plain,
% 4.82/3.39 (^[Q: $i] : refl(((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q)))) <=> ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q)))))),
% 4.82/3.39 inference(bind,[status(th)],[])).
% 4.82/3.39 tff(95,plain,
% 4.82/3.39 (![Q: $i] : ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q)))) <=> ![Q: $i] : ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q))))),
% 4.82/3.39 inference(quant_intro,[status(thm)],[94])).
% 4.82/3.39 tff(96,plain,
% 4.82/3.39 (![Q: $i] : ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q)))) <=> ![Q: $i] : ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q))))),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(97,plain,
% 4.82/3.39 (^[Q: $i] : rewrite((mem(Q, bool) => (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q)))) <=> ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q)))))),
% 4.82/3.39 inference(bind,[status(th)],[])).
% 4.82/3.39 tff(98,plain,
% 4.82/3.39 (![Q: $i] : (mem(Q, bool) => (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q)))) <=> ![Q: $i] : ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q))))),
% 4.82/3.39 inference(quant_intro,[status(thm)],[97])).
% 4.82/3.39 tff(99,axiom,(![Q: $i] : (mem(Q, bool) => (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax_neg_p')).
% 4.82/3.39 tff(100,plain,
% 4.82/3.39 (![Q: $i] : ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q))))),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[99, 98])).
% 4.82/3.39 tff(101,plain,
% 4.82/3.39 (![Q: $i] : ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q))))),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[100, 96])).
% 4.82/3.39 tff(102,plain,(
% 4.82/3.39 ![Q: $i] : ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q))))),
% 4.82/3.39 inference(skolemize,[status(sab)],[101])).
% 4.82/3.39 tff(103,plain,
% 4.82/3.39 (![Q: $i] : ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q))))),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[102, 95])).
% 4.82/3.39 tff(104,plain,
% 4.82/3.39 (((~![Q: $i] : ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q))))) | ((~mem(inj__o(fo__c_2Ebool_2EF), bool)) | (p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))) <=> (~p(inj__o(fo__c_2Ebool_2EF)))))) <=> ((~![Q: $i] : ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q))))) | (~mem(inj__o(fo__c_2Ebool_2EF), bool)) | (p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))) <=> (~p(inj__o(fo__c_2Ebool_2EF)))))),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(105,plain,
% 4.82/3.39 ((~![Q: $i] : ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q))))) | ((~mem(inj__o(fo__c_2Ebool_2EF), bool)) | (p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))) <=> (~p(inj__o(fo__c_2Ebool_2EF)))))),
% 4.82/3.39 inference(quant_inst,[status(thm)],[])).
% 4.82/3.39 tff(106,plain,
% 4.82/3.39 ((~![Q: $i] : ((~mem(Q, bool)) | (p(ap(c_2Ebool_2E_7E, Q)) <=> (~p(Q))))) | (~mem(inj__o(fo__c_2Ebool_2EF), bool)) | (p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))) <=> (~p(inj__o(fo__c_2Ebool_2EF))))),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[105, 104])).
% 4.82/3.39 tff(107,plain,
% 4.82/3.39 (p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))) <=> (~p(inj__o(fo__c_2Ebool_2EF)))),
% 4.82/3.39 inference(unit_resolution,[status(thm)],[106, 103, 93])).
% 4.82/3.39 tff(108,plain,
% 4.82/3.39 ((~p(c_2Ebool_2EF)) <=> (~p(inj__o(fo__c_2Ebool_2EF)))),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(109,plain,
% 4.82/3.39 ((~p(c_2Ebool_2EF)) <=> (~p(c_2Ebool_2EF))),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(110,axiom,(~p(c_2Ebool_2EF)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax_false_p')).
% 4.82/3.39 tff(111,plain,
% 4.82/3.39 (~p(c_2Ebool_2EF)),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[110, 109])).
% 4.82/3.39 tff(112,plain,
% 4.82/3.39 (~p(inj__o(fo__c_2Ebool_2EF))),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[111, 108])).
% 4.82/3.39 tff(113,plain,
% 4.82/3.39 ((~(p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))) <=> (~p(inj__o(fo__c_2Ebool_2EF))))) | p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))) | p(inj__o(fo__c_2Ebool_2EF))),
% 4.82/3.39 inference(tautology,[status(thm)],[])).
% 4.82/3.39 tff(114,plain,
% 4.82/3.39 ((~(p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))) <=> (~p(inj__o(fo__c_2Ebool_2EF))))) | p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))),
% 4.82/3.39 inference(unit_resolution,[status(thm)],[113, 112])).
% 4.82/3.39 tff(115,plain,
% 4.82/3.39 (p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))),
% 4.82/3.39 inference(unit_resolution,[status(thm)],[114, 107])).
% 4.82/3.39 tff(116,plain,
% 4.82/3.39 (p(c_2Ebool_2ET) <=> p(inj__o(fo__c_2Ebool_2ET))),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(117,plain,
% 4.82/3.39 (p(c_2Ebool_2ET) <=> p(c_2Ebool_2ET)),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(118,axiom,(p(c_2Ebool_2ET)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ax_true_p')).
% 4.82/3.39 tff(119,plain,
% 4.82/3.39 (p(c_2Ebool_2ET)),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[118, 117])).
% 4.82/3.39 tff(120,plain,
% 4.82/3.39 (p(inj__o(fo__c_2Ebool_2ET))),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[119, 116])).
% 4.82/3.39 tff(121,plain,
% 4.82/3.39 ((~((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))))) | (~p(inj__o(fo__c_2Ebool_2ET))) | (~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))))),
% 4.82/3.39 inference(tautology,[status(thm)],[])).
% 4.82/3.39 tff(122,plain,
% 4.82/3.39 (~((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))))),
% 4.82/3.39 inference(unit_resolution,[status(thm)],[121, 120, 115])).
% 4.82/3.39 tff(123,plain,
% 4.82/3.39 (mem(c_2Ebool_2E_7E, arr(bool, bool)) <=> mem(c_2Ebool_2E_7E, arr(bool, bool))),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(124,axiom,(mem(c_2Ebool_2E_7E, arr(bool, bool))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Ebool_2E_7E')).
% 4.82/3.39 tff(125,plain,
% 4.82/3.39 (mem(c_2Ebool_2E_7E, arr(bool, bool))),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[124, 123])).
% 4.82/3.39 tff(126,plain,
% 4.82/3.39 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ebool_2E_7E, arr(bool, bool))) | ![X: $i] : ((~mem(X, bool)) | mem(ap(c_2Ebool_2E_7E, X), bool)))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Ebool_2E_7E, arr(bool, bool))) | ![X: $i] : ((~mem(X, bool)) | mem(ap(c_2Ebool_2E_7E, X), bool)))),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(127,plain,
% 4.82/3.39 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ebool_2E_7E, arr(bool, bool))) | ![X: $i] : ((~mem(X, bool)) | mem(ap(c_2Ebool_2E_7E, X), bool)))),
% 4.82/3.39 inference(quant_inst,[status(thm)],[])).
% 4.82/3.39 tff(128,plain,
% 4.82/3.39 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Ebool_2E_7E, arr(bool, bool))) | ![X: $i] : ((~mem(X, bool)) | mem(ap(c_2Ebool_2E_7E, X), bool))),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[127, 126])).
% 4.82/3.39 tff(129,plain,
% 4.82/3.39 (![X: $i] : ((~mem(X, bool)) | mem(ap(c_2Ebool_2E_7E, X), bool))),
% 4.82/3.39 inference(unit_resolution,[status(thm)],[128, 22, 125])).
% 4.82/3.39 tff(130,plain,
% 4.82/3.39 (((~![X: $i] : ((~mem(X, bool)) | mem(ap(c_2Ebool_2E_7E, X), bool))) | ((~mem(inj__o(fo__c_2Ebool_2EF), bool)) | mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool))) <=> ((~![X: $i] : ((~mem(X, bool)) | mem(ap(c_2Ebool_2E_7E, X), bool))) | (~mem(inj__o(fo__c_2Ebool_2EF), bool)) | mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool))),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(131,plain,
% 4.82/3.39 ((~![X: $i] : ((~mem(X, bool)) | mem(ap(c_2Ebool_2E_7E, X), bool))) | ((~mem(inj__o(fo__c_2Ebool_2EF), bool)) | mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool))),
% 4.82/3.39 inference(quant_inst,[status(thm)],[])).
% 4.82/3.39 tff(132,plain,
% 4.82/3.39 ((~![X: $i] : ((~mem(X, bool)) | mem(ap(c_2Ebool_2E_7E, X), bool))) | (~mem(inj__o(fo__c_2Ebool_2EF), bool)) | mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[131, 130])).
% 4.82/3.39 tff(133,plain,
% 4.82/3.39 (mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)),
% 4.82/3.39 inference(unit_resolution,[status(thm)],[132, 93, 129])).
% 4.82/3.39 tff(134,plain,
% 4.82/3.39 (mem(c_2Ebool_2ET, bool) <=> mem(inj__o(fo__c_2Ebool_2ET), bool)),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(135,plain,
% 4.82/3.39 (mem(c_2Ebool_2ET, bool) <=> mem(c_2Ebool_2ET, bool)),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(136,axiom,(mem(c_2Ebool_2ET, bool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Ebool_2ET')).
% 4.82/3.39 tff(137,plain,
% 4.82/3.39 (mem(c_2Ebool_2ET, bool)),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[136, 135])).
% 4.82/3.39 tff(138,plain,
% 4.82/3.39 (mem(inj__o(fo__c_2Ebool_2ET), bool)),
% 4.82/3.39 inference(modus_ponens,[status(thm)],[137, 134])).
% 4.82/3.39 tff(139,plain,
% 4.82/3.39 (^[Q: $i] : refl(((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool)))) <=> ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool)))))),
% 4.82/3.39 inference(bind,[status(th)],[])).
% 4.82/3.39 tff(140,plain,
% 4.82/3.39 (![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool)))) <=> ![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))),
% 4.82/3.39 inference(quant_intro,[status(thm)],[139])).
% 4.82/3.39 tff(141,plain,
% 4.82/3.39 (^[Q: $i] : rewrite(((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool)))) <=> ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool)))))),
% 4.82/3.39 inference(bind,[status(th)],[])).
% 4.82/3.39 tff(142,plain,
% 4.82/3.39 (![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool)))) <=> ![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))),
% 4.82/3.39 inference(quant_intro,[status(thm)],[141])).
% 4.82/3.39 tff(143,plain,
% 4.82/3.39 (![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool)))) <=> ![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))),
% 4.82/3.39 inference(transitivity,[status(thm)],[142, 140])).
% 4.82/3.39 tff(144,plain,
% 4.82/3.39 (![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool)))) <=> ![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))),
% 4.82/3.39 inference(rewrite,[status(thm)],[])).
% 4.82/3.39 tff(145,plain,
% 4.82/3.39 (^[Q: $i] : trans(monotonicity(quant_intro(proof_bind(^[R: $i] : trans(monotonicity(rewrite(((p(Q) <=> p(R)) => (Q = R)) <=> ((Q = R) | ((~p(Q)) <=> p(R)))), ((mem(R, bool) => ((p(Q) <=> p(R)) => (Q = R))) <=> (mem(R, bool) => ((Q = R) | ((~p(Q)) <=> p(R)))))), rewrite((mem(R, bool) => ((Q = R) | ((~p(Q)) <=> p(R)))) <=> ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool)))), ((mem(R, bool) => ((p(Q) <=> p(R)) => (Q = R))) <=> ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool)))))), (![R: $i] : (mem(R, bool) => ((p(Q) <=> p(R)) => (Q = R))) <=> ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))), ((mem(Q, bool) => ![R: $i] : (mem(R, bool) => ((p(Q) <=> p(R)) => (Q = R)))) <=> (mem(Q, bool) => ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool)))))), rewrite((mem(Q, bool) => ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool)))) <=> ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))), ((mem(Q, bool) => ![R: $i] : (mem(R, bool) => ((p(Q) <=> p(R)) => (Q = R)))) <=> ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))))),
% 4.82/3.39 inference(bind,[status(th)],[])).
% 4.82/3.39 tff(146,plain,
% 4.82/3.39 (![Q: $i] : (mem(Q, bool) => ![R: $i] : (mem(R, bool) => ((p(Q) <=> p(R)) => (Q = R)))) <=> ![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))),
% 4.96/3.39 inference(quant_intro,[status(thm)],[145])).
% 4.96/3.39 tff(147,axiom,(![Q: $i] : (mem(Q, bool) => ![R: $i] : (mem(R, bool) => ((p(Q) <=> p(R)) => (Q = R))))), file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001_2.ax','boolext')).
% 4.96/3.39 tff(148,plain,
% 4.96/3.39 (![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))),
% 4.96/3.39 inference(modus_ponens,[status(thm)],[147, 146])).
% 4.96/3.39 tff(149,plain,
% 4.96/3.39 (![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))),
% 4.96/3.39 inference(modus_ponens,[status(thm)],[148, 144])).
% 4.96/3.39 tff(150,plain,(
% 4.96/3.39 ![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))),
% 4.96/3.39 inference(skolemize,[status(sab)],[149])).
% 4.96/3.39 tff(151,plain,
% 4.96/3.39 (![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))),
% 4.96/3.39 inference(modus_ponens,[status(thm)],[150, 143])).
% 4.96/3.39 tff(152,plain,
% 4.96/3.39 (((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | ((~mem(inj__o(fo__c_2Ebool_2ET), bool)) | ![R: $i] : ((~mem(R, bool)) | (inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R))))) <=> ((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | (~mem(inj__o(fo__c_2Ebool_2ET), bool)) | ![R: $i] : ((~mem(R, bool)) | (inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R))))),
% 4.96/3.39 inference(rewrite,[status(thm)],[])).
% 4.96/3.39 tff(153,plain,
% 4.96/3.39 (((~mem(inj__o(fo__c_2Ebool_2ET), bool)) | ![R: $i] : ((inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R)) | (~mem(R, bool)))) <=> ((~mem(inj__o(fo__c_2Ebool_2ET), bool)) | ![R: $i] : ((~mem(R, bool)) | (inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R))))),
% 4.96/3.39 inference(rewrite,[status(thm)],[])).
% 4.96/3.39 tff(154,plain,
% 4.96/3.39 (((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | ((~mem(inj__o(fo__c_2Ebool_2ET), bool)) | ![R: $i] : ((inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R)) | (~mem(R, bool))))) <=> ((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | ((~mem(inj__o(fo__c_2Ebool_2ET), bool)) | ![R: $i] : ((~mem(R, bool)) | (inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R)))))),
% 4.96/3.39 inference(monotonicity,[status(thm)],[153])).
% 4.96/3.39 tff(155,plain,
% 4.96/3.39 (((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | ((~mem(inj__o(fo__c_2Ebool_2ET), bool)) | ![R: $i] : ((inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R)) | (~mem(R, bool))))) <=> ((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | (~mem(inj__o(fo__c_2Ebool_2ET), bool)) | ![R: $i] : ((~mem(R, bool)) | (inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R))))),
% 4.96/3.39 inference(transitivity,[status(thm)],[154, 152])).
% 4.96/3.39 tff(156,plain,
% 4.96/3.39 ((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | ((~mem(inj__o(fo__c_2Ebool_2ET), bool)) | ![R: $i] : ((inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R)) | (~mem(R, bool))))),
% 4.96/3.39 inference(quant_inst,[status(thm)],[])).
% 4.96/3.39 tff(157,plain,
% 4.96/3.39 ((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | (~mem(inj__o(fo__c_2Ebool_2ET), bool)) | ![R: $i] : ((~mem(R, bool)) | (inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R)))),
% 4.96/3.39 inference(modus_ponens,[status(thm)],[156, 155])).
% 4.96/3.39 tff(158,plain,
% 4.96/3.39 (![R: $i] : ((~mem(R, bool)) | (inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R)))),
% 4.96/3.39 inference(unit_resolution,[status(thm)],[157, 151, 138])).
% 4.96/3.39 tff(159,plain,
% 4.96/3.39 (((~![R: $i] : ((~mem(R, bool)) | (inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R)))) | ((~mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)) | (inj__o(fo__c_2Ebool_2ET) = ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))))) <=> ((~![R: $i] : ((~mem(R, bool)) | (inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R)))) | (~mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)) | (inj__o(fo__c_2Ebool_2ET) = ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))))),
% 4.96/3.39 inference(rewrite,[status(thm)],[])).
% 4.96/3.39 tff(160,plain,
% 4.96/3.39 ((~![R: $i] : ((~mem(R, bool)) | (inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R)))) | ((~mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)) | (inj__o(fo__c_2Ebool_2ET) = ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))))),
% 4.96/3.39 inference(quant_inst,[status(thm)],[])).
% 4.96/3.39 tff(161,plain,
% 4.96/3.39 ((~![R: $i] : ((~mem(R, bool)) | (inj__o(fo__c_2Ebool_2ET) = R) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(R)))) | (~mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)) | (inj__o(fo__c_2Ebool_2ET) = ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))) | ((~p(inj__o(fo__c_2Ebool_2ET))) <=> p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))))),
% 4.96/3.39 inference(modus_ponens,[status(thm)],[160, 159])).
% 4.96/3.39 tff(162,plain,
% 4.96/3.39 (inj__o(fo__c_2Ebool_2ET) = ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))),
% 4.96/3.39 inference(unit_resolution,[status(thm)],[161, 158, 133, 122])).
% 4.96/3.39 tff(163,plain,
% 4.96/3.39 (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = inj__o(fo__c_2Ebool_2ET)),
% 4.96/3.39 inference(symmetry,[status(thm)],[162])).
% 4.96/3.39 tff(164,plain,
% 4.96/3.39 ((~![A_27a: del, V0a: tp__ty_2Enum_2Enum, V1b: tp__ty_2Enum_2Enum] : ((~p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b)), inj__ty_2Enum_2Enum(V0a)))) | (ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a)), inj__ty_2Enum_2Enum(V1b))) = ap(ap(c_2Ewords_2Eword__sub(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0a))), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1b)))))) <=> (~![A_27a: del, V0a: tp__ty_2Enum_2Enum, V1b: tp__ty_2Enum_2Enum] : ((~p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b)), inj__ty_2Enum_2Enum(V0a)))) | (ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a)), inj__ty_2Enum_2Enum(V1b))) = ap(ap(c_2Ewords_2Eword__sub(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0a))), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1b))))))),
% 4.96/3.39 inference(rewrite,[status(thm)],[])).
% 4.96/3.39 tff(165,plain,
% 4.96/3.39 ((~![A_27a: del, V0a: tp__ty_2Enum_2Enum, V1b: tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b)), inj__ty_2Enum_2Enum(V0a))) => (ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a)), inj__ty_2Enum_2Enum(V1b))) = ap(ap(c_2Ewords_2Eword__sub(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0a))), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1b)))))) <=> (~![A_27a: del, V0a: tp__ty_2Enum_2Enum, V1b: tp__ty_2Enum_2Enum] : ((~p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b)), inj__ty_2Enum_2Enum(V0a)))) | (ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a)), inj__ty_2Enum_2Enum(V1b))) = ap(ap(c_2Ewords_2Eword__sub(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0a))), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1b))))))),
% 4.96/3.39 inference(rewrite,[status(thm)],[])).
% 4.96/3.39 tff(166,axiom,(~![A_27a: del, V0a: tp__ty_2Enum_2Enum, V1b: tp__ty_2Enum_2Enum] : (p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b)), inj__ty_2Enum_2Enum(V0a))) => (ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a)), inj__ty_2Enum_2Enum(V1b))) = ap(ap(c_2Ewords_2Eword__sub(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0a))), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1b)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Ewords_2En2w__sub')).
% 4.96/3.39 tff(167,plain,
% 4.96/3.39 (~![A_27a: del, V0a: tp__ty_2Enum_2Enum, V1b: tp__ty_2Enum_2Enum] : ((~p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b)), inj__ty_2Enum_2Enum(V0a)))) | (ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a)), inj__ty_2Enum_2Enum(V1b))) = ap(ap(c_2Ewords_2Eword__sub(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0a))), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1b)))))),
% 4.96/3.39 inference(modus_ponens,[status(thm)],[166, 165])).
% 4.96/3.39 tff(168,plain,
% 4.96/3.39 (~![A_27a: del, V0a: tp__ty_2Enum_2Enum, V1b: tp__ty_2Enum_2Enum] : ((~p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b)), inj__ty_2Enum_2Enum(V0a)))) | (ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a)), inj__ty_2Enum_2Enum(V1b))) = ap(ap(c_2Ewords_2Eword__sub(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0a))), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1b)))))),
% 4.96/3.39 inference(modus_ponens,[status(thm)],[167, 164])).
% 4.96/3.39 tff(169,plain,
% 4.96/3.39 (~![A_27a: del, V0a: tp__ty_2Enum_2Enum, V1b: tp__ty_2Enum_2Enum] : ((~p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b)), inj__ty_2Enum_2Enum(V0a)))) | (ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a)), inj__ty_2Enum_2Enum(V1b))) = ap(ap(c_2Ewords_2Eword__sub(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0a))), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1b)))))),
% 4.96/3.39 inference(modus_ponens,[status(thm)],[168, 164])).
% 4.96/3.39 tff(170,plain,
% 4.96/3.39 (~![A_27a: del, V0a: tp__ty_2Enum_2Enum, V1b: tp__ty_2Enum_2Enum] : ((~p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b)), inj__ty_2Enum_2Enum(V0a)))) | (ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a)), inj__ty_2Enum_2Enum(V1b))) = ap(ap(c_2Ewords_2Eword__sub(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0a))), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1b)))))),
% 4.96/3.39 inference(modus_ponens,[status(thm)],[169, 164])).
% 4.96/3.39 tff(171,plain,
% 4.96/3.39 (~![A_27a: del, V0a: tp__ty_2Enum_2Enum, V1b: tp__ty_2Enum_2Enum] : ((~p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b)), inj__ty_2Enum_2Enum(V0a)))) | (ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a)), inj__ty_2Enum_2Enum(V1b))) = ap(ap(c_2Ewords_2Eword__sub(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0a))), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1b)))))),
% 4.96/3.39 inference(modus_ponens,[status(thm)],[170, 164])).
% 4.96/3.39 tff(172,plain,
% 4.96/3.39 (~![A_27a: del, V0a: tp__ty_2Enum_2Enum, V1b: tp__ty_2Enum_2Enum] : ((~p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b)), inj__ty_2Enum_2Enum(V0a)))) | (ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a)), inj__ty_2Enum_2Enum(V1b))) = ap(ap(c_2Ewords_2Eword__sub(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0a))), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1b)))))),
% 4.96/3.39 inference(modus_ponens,[status(thm)],[171, 164])).
% 4.96/3.39 tff(173,plain,
% 4.96/3.39 (~![A_27a: del, V0a: tp__ty_2Enum_2Enum, V1b: tp__ty_2Enum_2Enum] : ((~p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b)), inj__ty_2Enum_2Enum(V0a)))) | (ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a)), inj__ty_2Enum_2Enum(V1b))) = ap(ap(c_2Ewords_2Eword__sub(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0a))), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1b)))))),
% 4.96/3.39 inference(modus_ponens,[status(thm)],[172, 164])).
% 4.96/3.39 tff(174,plain,
% 4.96/3.39 (~![A_27a: del, V0a: tp__ty_2Enum_2Enum, V1b: tp__ty_2Enum_2Enum] : ((~p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b)), inj__ty_2Enum_2Enum(V0a)))) | (ap(c_2Ewords_2En2w(A_27a), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a)), inj__ty_2Enum_2Enum(V1b))) = ap(ap(c_2Ewords_2Eword__sub(A_27a), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V0a))), ap(c_2Ewords_2En2w(A_27a), inj__ty_2Enum_2Enum(V1b)))))),
% 4.96/3.39 inference(modus_ponens,[status(thm)],[173, 164])).
% 4.96/3.39 tff(175,plain,(
% 4.96/3.39 ~((~p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))) | (ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))) = ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)))))),
% 4.97/3.40 inference(skolemize,[status(sab)],[174])).
% 4.97/3.40 tff(176,plain,
% 4.97/3.40 (p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))),
% 4.97/3.40 inference(or_elim,[status(thm)],[175])).
% 4.97/3.40 tff(177,plain,
% 4.97/3.40 ((~((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))))) | (~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) | (~p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))))),
% 4.97/3.40 inference(tautology,[status(thm)],[])).
% 4.97/3.40 tff(178,plain,
% 4.97/3.40 (~((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))))),
% 4.97/3.40 inference(unit_resolution,[status(thm)],[177, 176, 115])).
% 4.97/3.40 tff(179,plain,
% 4.97/3.40 (((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | ((~mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)) | ![R: $i] : ((~mem(R, bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R))))) <=> ((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | (~mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)) | ![R: $i] : ((~mem(R, bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R))))),
% 4.97/3.40 inference(rewrite,[status(thm)],[])).
% 4.97/3.40 tff(180,plain,
% 4.97/3.40 (((~mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)) | ![R: $i] : ((ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R)) | (~mem(R, bool)))) <=> ((~mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)) | ![R: $i] : ((~mem(R, bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R))))),
% 4.97/3.40 inference(rewrite,[status(thm)],[])).
% 4.97/3.40 tff(181,plain,
% 4.97/3.40 (((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | ((~mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)) | ![R: $i] : ((ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R)) | (~mem(R, bool))))) <=> ((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | ((~mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)) | ![R: $i] : ((~mem(R, bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R)))))),
% 4.97/3.40 inference(monotonicity,[status(thm)],[180])).
% 4.97/3.40 tff(182,plain,
% 4.97/3.40 (((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | ((~mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)) | ![R: $i] : ((ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R)) | (~mem(R, bool))))) <=> ((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | (~mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)) | ![R: $i] : ((~mem(R, bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R))))),
% 4.97/3.40 inference(transitivity,[status(thm)],[181, 179])).
% 4.97/3.40 tff(183,plain,
% 4.97/3.40 ((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | ((~mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)) | ![R: $i] : ((ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R)) | (~mem(R, bool))))),
% 4.97/3.40 inference(quant_inst,[status(thm)],[])).
% 4.97/3.40 tff(184,plain,
% 4.97/3.40 ((~![Q: $i] : ((~mem(Q, bool)) | ![R: $i] : ((Q = R) | ((~p(Q)) <=> p(R)) | (~mem(R, bool))))) | (~mem(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)), bool)) | ![R: $i] : ((~mem(R, bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R)))),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[183, 182])).
% 4.97/3.40 tff(185,plain,
% 4.97/3.40 (![R: $i] : ((~mem(R, bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R)))),
% 4.97/3.40 inference(unit_resolution,[status(thm)],[184, 151, 133])).
% 4.97/3.40 tff(186,plain,
% 4.97/3.40 (^[X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : refl((inj__o(fo__c_2Earithmetic_2E_3C_3D(X0, X1)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1))) <=> (inj__o(fo__c_2Earithmetic_2E_3C_3D(X0, X1)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1))))),
% 4.97/3.40 inference(bind,[status(th)],[])).
% 4.97/3.40 tff(187,plain,
% 4.97/3.40 (![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Earithmetic_2E_3C_3D(X0, X1)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1))) <=> ![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Earithmetic_2E_3C_3D(X0, X1)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1)))),
% 4.97/3.40 inference(quant_intro,[status(thm)],[186])).
% 4.97/3.40 tff(188,plain,
% 4.97/3.40 (![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Earithmetic_2E_3C_3D(X0, X1)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1))) <=> ![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Earithmetic_2E_3C_3D(X0, X1)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1)))),
% 4.97/3.40 inference(rewrite,[status(thm)],[])).
% 4.97/3.40 tff(189,axiom,(![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Earithmetic_2E_3C_3D(X0, X1)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','stp_eq_fo_c_2Earithmetic_2E_3C_3D')).
% 4.97/3.40 tff(190,plain,
% 4.97/3.40 (![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Earithmetic_2E_3C_3D(X0, X1)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1)))),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[189, 188])).
% 4.97/3.40 tff(191,plain,(
% 4.97/3.40 ![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Earithmetic_2E_3C_3D(X0, X1)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1)))),
% 4.97/3.40 inference(skolemize,[status(sab)],[190])).
% 4.97/3.40 tff(192,plain,
% 4.97/3.40 (![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Earithmetic_2E_3C_3D(X0, X1)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1)))),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[191, 187])).
% 4.97/3.40 tff(193,plain,
% 4.97/3.40 ((~![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__o(fo__c_2Earithmetic_2E_3C_3D(X0, X1)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1)))) | (inj__o(fo__c_2Earithmetic_2E_3C_3D(V1b!2, V0a!3)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))),
% 4.97/3.40 inference(quant_inst,[status(thm)],[])).
% 4.97/3.40 tff(194,plain,
% 4.97/3.40 (inj__o(fo__c_2Earithmetic_2E_3C_3D(V1b!2, V0a!3)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))),
% 4.97/3.40 inference(unit_resolution,[status(thm)],[193, 192])).
% 4.97/3.40 tff(195,plain,
% 4.97/3.40 (mem(inj__o(fo__c_2Earithmetic_2E_3C_3D(V1b!2, V0a!3)), bool) <=> mem(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), bool)),
% 4.97/3.40 inference(monotonicity,[status(thm)],[194])).
% 4.97/3.40 tff(196,plain,
% 4.97/3.40 (^[X: tp__o] : refl(mem(inj__o(X), bool) <=> mem(inj__o(X), bool))),
% 4.97/3.40 inference(bind,[status(th)],[])).
% 4.97/3.40 tff(197,plain,
% 4.97/3.40 (![X: tp__o] : mem(inj__o(X), bool) <=> ![X: tp__o] : mem(inj__o(X), bool)),
% 4.97/3.40 inference(quant_intro,[status(thm)],[196])).
% 4.97/3.40 tff(198,plain,
% 4.97/3.40 (![X: tp__o] : mem(inj__o(X), bool) <=> ![X: tp__o] : mem(inj__o(X), bool)),
% 4.97/3.40 inference(rewrite,[status(thm)],[])).
% 4.97/3.40 tff(199,axiom,(![X: tp__o] : mem(inj__o(X), bool)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','stp_inj_mem_o')).
% 4.97/3.40 tff(200,plain,
% 4.97/3.40 (![X: tp__o] : mem(inj__o(X), bool)),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[199, 198])).
% 4.97/3.40 tff(201,plain,(
% 4.97/3.40 ![X: tp__o] : mem(inj__o(X), bool)),
% 4.97/3.40 inference(skolemize,[status(sab)],[200])).
% 4.97/3.40 tff(202,plain,
% 4.97/3.40 (![X: tp__o] : mem(inj__o(X), bool)),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[201, 197])).
% 4.97/3.40 tff(203,plain,
% 4.97/3.40 ((~![X: tp__o] : mem(inj__o(X), bool)) | mem(inj__o(fo__c_2Earithmetic_2E_3C_3D(V1b!2, V0a!3)), bool)),
% 4.97/3.40 inference(quant_inst,[status(thm)],[])).
% 4.97/3.40 tff(204,plain,
% 4.97/3.40 (mem(inj__o(fo__c_2Earithmetic_2E_3C_3D(V1b!2, V0a!3)), bool)),
% 4.97/3.40 inference(unit_resolution,[status(thm)],[203, 202])).
% 4.97/3.40 tff(205,plain,
% 4.97/3.40 (mem(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), bool)),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[204, 195])).
% 4.97/3.40 tff(206,plain,
% 4.97/3.40 (((~![R: $i] : ((~mem(R, bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R)))) | ((~mem(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))))) <=> ((~![R: $i] : ((~mem(R, bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R)))) | (~mem(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))))),
% 4.97/3.40 inference(rewrite,[status(thm)],[])).
% 4.97/3.40 tff(207,plain,
% 4.97/3.40 ((~![R: $i] : ((~mem(R, bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R)))) | ((~mem(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))))),
% 4.97/3.40 inference(quant_inst,[status(thm)],[])).
% 4.97/3.40 tff(208,plain,
% 4.97/3.40 ((~![R: $i] : ((~mem(R, bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = R) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(R)))) | (~mem(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), bool)) | (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))) | ((~p(ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)))) <=> p(ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))))),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[207, 206])).
% 4.97/3.40 tff(209,plain,
% 4.97/3.40 (ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF)) = ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))),
% 4.97/3.40 inference(unit_resolution,[status(thm)],[208, 205, 185, 178])).
% 4.97/3.40 tff(210,plain,
% 4.97/3.40 (ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)) = ap(c_2Ebool_2E_7E, inj__o(fo__c_2Ebool_2EF))),
% 4.97/3.40 inference(symmetry,[status(thm)],[209])).
% 4.97/3.40 tff(211,plain,
% 4.97/3.40 (ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)) = inj__o(fo__c_2Ebool_2ET)),
% 4.97/3.40 inference(transitivity,[status(thm)],[210, 163])).
% 4.97/3.40 tff(212,plain,
% 4.97/3.40 (ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))) = ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET))),
% 4.97/3.40 inference(monotonicity,[status(thm)],[211])).
% 4.97/3.40 tff(213,plain,
% 4.97/3.40 (ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)) = ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))),
% 4.97/3.40 inference(symmetry,[status(thm)],[212])).
% 4.97/3.40 tff(214,plain,
% 4.97/3.40 (ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))) = ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))))),
% 4.97/3.40 inference(monotonicity,[status(thm)],[213])).
% 4.97/3.40 tff(215,plain,
% 4.97/3.40 (ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))) = ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))))),
% 4.97/3.40 inference(symmetry,[status(thm)],[214])).
% 4.97/3.40 tff(216,plain,
% 4.97/3.40 (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))))),
% 4.97/3.40 inference(monotonicity,[status(thm)],[215])).
% 4.97/3.40 tff(217,plain,
% 4.97/3.40 (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), ap(ap(c_2Earithmetic_2E_3C_3D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))))),
% 4.97/3.40 inference(symmetry,[status(thm)],[216])).
% 4.97/3.40 tff(218,plain,
% 4.97/3.40 (mem(c_2Earithmetic_2E_2D, arr(ty_2Enum_2Enum, arr(ty_2Enum_2Enum, ty_2Enum_2Enum))) <=> mem(c_2Earithmetic_2E_2D, arr(ty_2Enum_2Enum, arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))),
% 4.97/3.40 inference(rewrite,[status(thm)],[])).
% 4.97/3.40 tff(219,axiom,(mem(c_2Earithmetic_2E_2D, arr(ty_2Enum_2Enum, arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Earithmetic_2E_2D')).
% 4.97/3.40 tff(220,plain,
% 4.97/3.40 (mem(c_2Earithmetic_2E_2D, arr(ty_2Enum_2Enum, arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[219, 218])).
% 4.97/3.40 tff(221,plain,
% 4.97/3.40 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Earithmetic_2E_2D, arr(ty_2Enum_2Enum, arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))) | ![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Earithmetic_2E_2D, X), arr(ty_2Enum_2Enum, ty_2Enum_2Enum))))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Earithmetic_2E_2D, arr(ty_2Enum_2Enum, arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))) | ![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Earithmetic_2E_2D, X), arr(ty_2Enum_2Enum, ty_2Enum_2Enum))))),
% 4.97/3.40 inference(rewrite,[status(thm)],[])).
% 4.97/3.40 tff(222,plain,
% 4.97/3.40 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Earithmetic_2E_2D, arr(ty_2Enum_2Enum, arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))) | ![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Earithmetic_2E_2D, X), arr(ty_2Enum_2Enum, ty_2Enum_2Enum))))),
% 4.97/3.40 inference(quant_inst,[status(thm)],[])).
% 4.97/3.40 tff(223,plain,
% 4.97/3.40 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Earithmetic_2E_2D, arr(ty_2Enum_2Enum, arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))) | ![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Earithmetic_2E_2D, X), arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[222, 221])).
% 4.97/3.40 tff(224,plain,
% 4.97/3.40 (![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Earithmetic_2E_2D, X), arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))),
% 4.97/3.40 inference(unit_resolution,[status(thm)],[223, 22, 220])).
% 4.97/3.40 tff(225,plain,
% 4.97/3.40 (((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Earithmetic_2E_2D, X), arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))) | ((~mem(inj__ty_2Enum_2Enum(V1b!2), ty_2Enum_2Enum)) | mem(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))) <=> ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Earithmetic_2E_2D, X), arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))) | (~mem(inj__ty_2Enum_2Enum(V1b!2), ty_2Enum_2Enum)) | mem(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))),
% 4.97/3.40 inference(rewrite,[status(thm)],[])).
% 4.97/3.40 tff(226,plain,
% 4.97/3.40 ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Earithmetic_2E_2D, X), arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))) | ((~mem(inj__ty_2Enum_2Enum(V1b!2), ty_2Enum_2Enum)) | mem(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))),
% 4.97/3.40 inference(quant_inst,[status(thm)],[])).
% 4.97/3.40 tff(227,plain,
% 4.97/3.40 ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Earithmetic_2E_2D, X), arr(ty_2Enum_2Enum, ty_2Enum_2Enum)))) | (~mem(inj__ty_2Enum_2Enum(V1b!2), ty_2Enum_2Enum)) | mem(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), arr(ty_2Enum_2Enum, ty_2Enum_2Enum))),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[226, 225])).
% 4.97/3.40 tff(228,plain,
% 4.97/3.40 (mem(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), arr(ty_2Enum_2Enum, ty_2Enum_2Enum))),
% 4.97/3.40 inference(unit_resolution,[status(thm)],[227, 224, 35])).
% 4.97/3.40 tff(229,plain,
% 4.97/3.40 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), arr(ty_2Enum_2Enum, ty_2Enum_2Enum))) | ![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), X), ty_2Enum_2Enum)))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), arr(ty_2Enum_2Enum, ty_2Enum_2Enum))) | ![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), X), ty_2Enum_2Enum)))),
% 4.97/3.40 inference(rewrite,[status(thm)],[])).
% 4.97/3.40 tff(230,plain,
% 4.97/3.40 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), arr(ty_2Enum_2Enum, ty_2Enum_2Enum))) | ![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), X), ty_2Enum_2Enum)))),
% 4.97/3.40 inference(quant_inst,[status(thm)],[])).
% 4.97/3.40 tff(231,plain,
% 4.97/3.40 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), arr(ty_2Enum_2Enum, ty_2Enum_2Enum))) | ![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), X), ty_2Enum_2Enum))),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[230, 229])).
% 4.97/3.40 tff(232,plain,
% 4.97/3.40 (![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), X), ty_2Enum_2Enum))),
% 4.97/3.40 inference(unit_resolution,[status(thm)],[231, 22, 228])).
% 4.97/3.40 tff(233,plain,
% 4.97/3.40 (((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), X), ty_2Enum_2Enum))) | ((~mem(inj__ty_2Enum_2Enum(V0a!3), ty_2Enum_2Enum)) | mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), ty_2Enum_2Enum))) <=> ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), X), ty_2Enum_2Enum))) | (~mem(inj__ty_2Enum_2Enum(V0a!3), ty_2Enum_2Enum)) | mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), ty_2Enum_2Enum))),
% 4.97/3.40 inference(rewrite,[status(thm)],[])).
% 4.97/3.40 tff(234,plain,
% 4.97/3.40 ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), X), ty_2Enum_2Enum))) | ((~mem(inj__ty_2Enum_2Enum(V0a!3), ty_2Enum_2Enum)) | mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), ty_2Enum_2Enum))),
% 4.97/3.40 inference(quant_inst,[status(thm)],[])).
% 4.97/3.40 tff(235,plain,
% 4.97/3.40 ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), X), ty_2Enum_2Enum))) | (~mem(inj__ty_2Enum_2Enum(V0a!3), ty_2Enum_2Enum)) | mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), ty_2Enum_2Enum)),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[234, 233])).
% 4.97/3.40 tff(236,plain,
% 4.97/3.40 (mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), ty_2Enum_2Enum)),
% 4.97/3.40 inference(unit_resolution,[status(thm)],[235, 41, 232])).
% 4.97/3.40 tff(237,plain,
% 4.97/3.40 (((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | ((~mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ty_2Efcp_2Ecart(bool, A_27a!4)))) <=> ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | (~mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.97/3.40 inference(rewrite,[status(thm)],[])).
% 4.97/3.40 tff(238,plain,
% 4.97/3.40 ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | ((~mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.97/3.40 inference(quant_inst,[status(thm)],[])).
% 4.97/3.40 tff(239,plain,
% 4.97/3.40 ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | (~mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ty_2Efcp_2Ecart(bool, A_27a!4))),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[238, 237])).
% 4.97/3.40 tff(240,plain,
% 4.97/3.40 (mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ty_2Efcp_2Ecart(bool, A_27a!4))),
% 4.97/3.40 inference(unit_resolution,[status(thm)],[239, 26, 236])).
% 4.97/3.40 tff(241,plain,
% 4.97/3.40 (^[A_27a: del] : refl(mem(c_2Ewords_2Eword__2comp(A_27a), arr(ty_2Efcp_2Ecart(bool, A_27a), ty_2Efcp_2Ecart(bool, A_27a))) <=> mem(c_2Ewords_2Eword__2comp(A_27a), arr(ty_2Efcp_2Ecart(bool, A_27a), ty_2Efcp_2Ecart(bool, A_27a))))),
% 4.97/3.40 inference(bind,[status(th)],[])).
% 4.97/3.40 tff(242,plain,
% 4.97/3.40 (![A_27a: del] : mem(c_2Ewords_2Eword__2comp(A_27a), arr(ty_2Efcp_2Ecart(bool, A_27a), ty_2Efcp_2Ecart(bool, A_27a))) <=> ![A_27a: del] : mem(c_2Ewords_2Eword__2comp(A_27a), arr(ty_2Efcp_2Ecart(bool, A_27a), ty_2Efcp_2Ecart(bool, A_27a)))),
% 4.97/3.40 inference(quant_intro,[status(thm)],[241])).
% 4.97/3.40 tff(243,plain,
% 4.97/3.40 (![A_27a: del] : mem(c_2Ewords_2Eword__2comp(A_27a), arr(ty_2Efcp_2Ecart(bool, A_27a), ty_2Efcp_2Ecart(bool, A_27a))) <=> ![A_27a: del] : mem(c_2Ewords_2Eword__2comp(A_27a), arr(ty_2Efcp_2Ecart(bool, A_27a), ty_2Efcp_2Ecart(bool, A_27a)))),
% 4.97/3.40 inference(rewrite,[status(thm)],[])).
% 4.97/3.40 tff(244,axiom,(![A_27a: del] : mem(c_2Ewords_2Eword__2comp(A_27a), arr(ty_2Efcp_2Ecart(bool, A_27a), ty_2Efcp_2Ecart(bool, A_27a)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mem_c_2Ewords_2Eword__2comp')).
% 4.97/3.40 tff(245,plain,
% 4.97/3.40 (![A_27a: del] : mem(c_2Ewords_2Eword__2comp(A_27a), arr(ty_2Efcp_2Ecart(bool, A_27a), ty_2Efcp_2Ecart(bool, A_27a)))),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[244, 243])).
% 4.97/3.40 tff(246,plain,(
% 4.97/3.40 ![A_27a: del] : mem(c_2Ewords_2Eword__2comp(A_27a), arr(ty_2Efcp_2Ecart(bool, A_27a), ty_2Efcp_2Ecart(bool, A_27a)))),
% 4.97/3.40 inference(skolemize,[status(sab)],[245])).
% 4.97/3.40 tff(247,plain,
% 4.97/3.40 (![A_27a: del] : mem(c_2Ewords_2Eword__2comp(A_27a), arr(ty_2Efcp_2Ecart(bool, A_27a), ty_2Efcp_2Ecart(bool, A_27a)))),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[246, 242])).
% 4.97/3.40 tff(248,plain,
% 4.97/3.40 ((~![A_27a: del] : mem(c_2Ewords_2Eword__2comp(A_27a), arr(ty_2Efcp_2Ecart(bool, A_27a), ty_2Efcp_2Ecart(bool, A_27a)))) | mem(c_2Ewords_2Eword__2comp(A_27a!4), arr(ty_2Efcp_2Ecart(bool, A_27a!4), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.97/3.40 inference(quant_inst,[status(thm)],[])).
% 4.97/3.40 tff(249,plain,
% 4.97/3.40 (mem(c_2Ewords_2Eword__2comp(A_27a!4), arr(ty_2Efcp_2Ecart(bool, A_27a!4), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.97/3.40 inference(unit_resolution,[status(thm)],[248, 247])).
% 4.97/3.40 tff(250,plain,
% 4.97/3.40 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ewords_2Eword__2comp(A_27a!4), arr(ty_2Efcp_2Ecart(bool, A_27a!4), ty_2Efcp_2Ecart(bool, A_27a!4)))) | ![X: $i] : ((~mem(X, ty_2Efcp_2Ecart(bool, A_27a!4))) | mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4))))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Ewords_2Eword__2comp(A_27a!4), arr(ty_2Efcp_2Ecart(bool, A_27a!4), ty_2Efcp_2Ecart(bool, A_27a!4)))) | ![X: $i] : ((~mem(X, ty_2Efcp_2Ecart(bool, A_27a!4))) | mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4))))),
% 4.97/3.40 inference(rewrite,[status(thm)],[])).
% 4.97/3.40 tff(251,plain,
% 4.97/3.40 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(c_2Ewords_2Eword__2comp(A_27a!4), arr(ty_2Efcp_2Ecart(bool, A_27a!4), ty_2Efcp_2Ecart(bool, A_27a!4)))) | ![X: $i] : ((~mem(X, ty_2Efcp_2Ecart(bool, A_27a!4))) | mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4))))),
% 4.97/3.40 inference(quant_inst,[status(thm)],[])).
% 4.97/3.40 tff(252,plain,
% 4.97/3.40 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(c_2Ewords_2Eword__2comp(A_27a!4), arr(ty_2Efcp_2Ecart(bool, A_27a!4), ty_2Efcp_2Ecart(bool, A_27a!4)))) | ![X: $i] : ((~mem(X, ty_2Efcp_2Ecart(bool, A_27a!4))) | mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[251, 250])).
% 4.97/3.40 tff(253,plain,
% 4.97/3.40 (![X: $i] : ((~mem(X, ty_2Efcp_2Ecart(bool, A_27a!4))) | mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.97/3.40 inference(unit_resolution,[status(thm)],[252, 22, 249])).
% 4.97/3.40 tff(254,plain,
% 4.97/3.40 (((~![X: $i] : ((~mem(X, ty_2Efcp_2Ecart(bool, A_27a!4))) | mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | ((~mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ty_2Efcp_2Ecart(bool, A_27a!4))) | mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))), ty_2Efcp_2Ecart(bool, A_27a!4)))) <=> ((~![X: $i] : ((~mem(X, ty_2Efcp_2Ecart(bool, A_27a!4))) | mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | (~mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ty_2Efcp_2Ecart(bool, A_27a!4))) | mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.97/3.40 inference(rewrite,[status(thm)],[])).
% 4.97/3.40 tff(255,plain,
% 4.97/3.40 ((~![X: $i] : ((~mem(X, ty_2Efcp_2Ecart(bool, A_27a!4))) | mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | ((~mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ty_2Efcp_2Ecart(bool, A_27a!4))) | mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.97/3.40 inference(quant_inst,[status(thm)],[])).
% 4.97/3.40 tff(256,plain,
% 4.97/3.40 ((~![X: $i] : ((~mem(X, ty_2Efcp_2Ecart(bool, A_27a!4))) | mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | (~mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))), ty_2Efcp_2Ecart(bool, A_27a!4))) | mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))), ty_2Efcp_2Ecart(bool, A_27a!4))),
% 4.97/3.40 inference(modus_ponens,[status(thm)],[255, 254])).
% 4.97/3.40 tff(257,plain,
% 4.97/3.40 (mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))), ty_2Efcp_2Ecart(bool, A_27a!4))),
% 4.97/3.40 inference(unit_resolution,[status(thm)],[256, 253, 240])).
% 4.97/3.40 tff(258,plain,
% 4.97/3.40 (^[A_27a: del] : refl((~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))))) <=> (~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))))))),
% 4.97/3.40 inference(bind,[status(th)],[])).
% 4.97/3.40 tff(259,plain,
% 4.97/3.40 (![A_27a: del] : (~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))))) <=> ![A_27a: del] : (~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))))),
% 4.97/3.40 inference(quant_intro,[status(thm)],[258])).
% 4.97/3.40 tff(260,plain,
% 4.97/3.40 (^[A_27a: del] : rewrite((~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))))) <=> (~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))))))),
% 4.97/3.41 inference(bind,[status(th)],[])).
% 4.97/3.41 tff(261,plain,
% 4.97/3.41 (![A_27a: del] : (~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))))) <=> ![A_27a: del] : (~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))))),
% 4.97/3.41 inference(quant_intro,[status(thm)],[260])).
% 4.97/3.41 tff(262,plain,
% 4.97/3.41 (![A_27a: del] : (~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))))) <=> ![A_27a: del] : (~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))))),
% 4.97/3.41 inference(transitivity,[status(thm)],[261, 259])).
% 4.97/3.41 tff(263,plain,
% 4.97/3.41 (^[A_27a: del] : rewrite((![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1))) & ![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))) <=> (~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))))))),
% 4.97/3.41 inference(bind,[status(th)],[])).
% 4.97/3.41 tff(264,plain,
% 4.97/3.41 (![A_27a: del] : (![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1))) & ![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))) <=> ![A_27a: del] : (~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))))),
% 4.97/3.41 inference(quant_intro,[status(thm)],[263])).
% 4.97/3.41 tff(265,plain,
% 4.97/3.41 (![A_27a: del] : (![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1))) & ![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))) <=> ![A_27a: del] : (![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1))) & ![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))),
% 4.97/3.41 inference(rewrite,[status(thm)],[])).
% 4.97/3.41 tff(266,plain,
% 4.97/3.41 (^[A_27a: del] : rewrite((![V0t1: $i] : (mem(V0t1, A_27a) => ![V1t2: $i] : (mem(V1t2, A_27a) => (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1))) & ![V2t1: $i] : (mem(V2t1, A_27a) => ![V3t2: $i] : (mem(V3t2, A_27a) => (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))) <=> (![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1))) & ![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))))),
% 4.97/3.41 inference(bind,[status(th)],[])).
% 4.97/3.41 tff(267,plain,
% 4.97/3.41 (![A_27a: del] : (![V0t1: $i] : (mem(V0t1, A_27a) => ![V1t2: $i] : (mem(V1t2, A_27a) => (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1))) & ![V2t1: $i] : (mem(V2t1, A_27a) => ![V3t2: $i] : (mem(V3t2, A_27a) => (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))) <=> ![A_27a: del] : (![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1))) & ![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))),
% 4.97/3.41 inference(quant_intro,[status(thm)],[266])).
% 4.97/3.41 tff(268,axiom,(![A_27a: del] : (![V0t1: $i] : (mem(V0t1, A_27a) => ![V1t2: $i] : (mem(V1t2, A_27a) => (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1))) & ![V2t1: $i] : (mem(V2t1, A_27a) => ![V3t2: $i] : (mem(V3t2, A_27a) => (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_thm_2Ebool_2Ebool__case__thm')).
% 4.97/3.41 tff(269,plain,
% 4.97/3.41 (![A_27a: del] : (![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1))) & ![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))),
% 4.97/3.41 inference(modus_ponens,[status(thm)],[268, 267])).
% 4.97/3.41 tff(270,plain,
% 4.97/3.41 (![A_27a: del] : (![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1))) & ![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))),
% 4.97/3.41 inference(modus_ponens,[status(thm)],[269, 265])).
% 4.97/3.41 tff(271,plain,(
% 4.97/3.41 ![A_27a: del] : (![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1))) & ![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))),
% 4.97/3.41 inference(skolemize,[status(sab)],[270])).
% 4.97/3.41 tff(272,plain,
% 4.97/3.41 (![A_27a: del] : (~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))))),
% 4.97/3.41 inference(modus_ponens,[status(thm)],[271, 264])).
% 4.97/3.41 tff(273,plain,
% 4.97/3.41 (![A_27a: del] : (~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))))),
% 4.97/3.41 inference(modus_ponens,[status(thm)],[272, 262])).
% 4.97/3.41 tff(274,plain,
% 4.97/3.41 ((~![A_27a: del] : (~((~![V0t1: $i] : ((~mem(V0t1, A_27a)) | ![V1t2: $i] : ((~mem(V1t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, A_27a)) | ![V3t2: $i] : ((~mem(V3t2, A_27a)) | (ap(ap(ap(c_2Ebool_2ECOND(A_27a), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))))) | (~((~![V0t1: $i] : ((~mem(V0t1, ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V3t2: $i] : ((~mem(V3t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))))),
% 4.97/3.41 inference(quant_inst,[status(thm)],[])).
% 4.97/3.41 tff(275,plain,
% 4.97/3.41 (~((~![V0t1: $i] : ((~mem(V0t1, ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V3t2: $i] : ((~mem(V3t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2)))))),
% 4.97/3.41 inference(unit_resolution,[status(thm)],[274, 273])).
% 4.97/3.41 tff(276,plain,
% 4.97/3.41 (((~![V0t1: $i] : ((~mem(V0t1, ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~![V2t1: $i] : ((~mem(V2t1, ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V3t2: $i] : ((~mem(V3t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2EF)), V2t1), V3t2) = V3t2))))) | ![V0t1: $i] : ((~mem(V0t1, ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))),
% 4.97/3.41 inference(tautology,[status(thm)],[])).
% 4.97/3.41 tff(277,plain,
% 4.97/3.41 (![V0t1: $i] : ((~mem(V0t1, ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))),
% 4.97/3.41 inference(unit_resolution,[status(thm)],[276, 275])).
% 4.97/3.41 tff(278,plain,
% 4.97/3.41 (^[X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : refl((inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(X0, X1)) = ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1))) <=> (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(X0, X1)) = ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1))))),
% 4.97/3.41 inference(bind,[status(th)],[])).
% 4.97/3.41 tff(279,plain,
% 4.97/3.41 (![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(X0, X1)) = ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1))) <=> ![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(X0, X1)) = ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1)))),
% 4.97/3.41 inference(quant_intro,[status(thm)],[278])).
% 4.97/3.41 tff(280,plain,
% 4.97/3.41 (![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(X0, X1)) = ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1))) <=> ![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(X0, X1)) = ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1)))),
% 4.97/3.41 inference(rewrite,[status(thm)],[])).
% 4.97/3.41 tff(281,axiom,(![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(X0, X1)) = ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','stp_eq_fo_c_2Earithmetic_2E_2D')).
% 4.97/3.41 tff(282,plain,
% 4.97/3.41 (![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(X0, X1)) = ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1)))),
% 4.97/3.41 inference(modus_ponens,[status(thm)],[281, 280])).
% 4.97/3.41 tff(283,plain,(
% 4.97/3.41 ![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(X0, X1)) = ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1)))),
% 4.97/3.41 inference(skolemize,[status(sab)],[282])).
% 4.97/3.41 tff(284,plain,
% 4.97/3.41 (![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(X0, X1)) = ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1)))),
% 4.97/3.41 inference(modus_ponens,[status(thm)],[283, 279])).
% 4.97/3.41 tff(285,plain,
% 4.97/3.41 ((~![X0: tp__ty_2Enum_2Enum, X1: tp__ty_2Enum_2Enum] : (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(X0, X1)) = ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(X0)), inj__ty_2Enum_2Enum(X1)))) | (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(V0a!3, V1b!2)) = ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))),
% 4.97/3.41 inference(quant_inst,[status(thm)],[])).
% 4.97/3.41 tff(286,plain,
% 4.97/3.41 (inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(V0a!3, V1b!2)) = ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))),
% 4.97/3.41 inference(unit_resolution,[status(thm)],[285, 284])).
% 4.97/3.41 tff(287,plain,
% 4.97/3.41 (ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)) = inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(V0a!3, V1b!2))),
% 4.97/3.41 inference(symmetry,[status(thm)],[286])).
% 4.97/3.41 tff(288,plain,
% 4.97/3.41 (mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)), ty_2Enum_2Enum) <=> mem(inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(V0a!3, V1b!2)), ty_2Enum_2Enum)),
% 4.97/3.41 inference(monotonicity,[status(thm)],[287])).
% 4.97/3.41 tff(289,plain,
% 4.97/3.41 (mem(inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(V0a!3, V1b!2)), ty_2Enum_2Enum) <=> mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)), ty_2Enum_2Enum)),
% 4.97/3.41 inference(symmetry,[status(thm)],[288])).
% 4.97/3.41 tff(290,plain,
% 4.97/3.41 ((~![X: tp__ty_2Enum_2Enum] : mem(inj__ty_2Enum_2Enum(X), ty_2Enum_2Enum)) | mem(inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(V0a!3, V1b!2)), ty_2Enum_2Enum)),
% 4.97/3.41 inference(quant_inst,[status(thm)],[])).
% 4.97/3.41 tff(291,plain,
% 4.97/3.41 (mem(inj__ty_2Enum_2Enum(fo__c_2Earithmetic_2E_2D(V0a!3, V1b!2)), ty_2Enum_2Enum)),
% 4.97/3.41 inference(unit_resolution,[status(thm)],[290, 33])).
% 4.97/3.41 tff(292,plain,
% 4.97/3.41 (mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)), ty_2Enum_2Enum)),
% 4.97/3.41 inference(modus_ponens,[status(thm)],[291, 289])).
% 4.97/3.41 tff(293,plain,
% 4.97/3.41 (((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | ((~mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))), ty_2Efcp_2Ecart(bool, A_27a!4)))) <=> ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | (~mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.97/3.41 inference(rewrite,[status(thm)],[])).
% 4.97/3.41 tff(294,plain,
% 4.97/3.41 ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | ((~mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))), ty_2Efcp_2Ecart(bool, A_27a!4)))),
% 4.97/3.41 inference(quant_inst,[status(thm)],[])).
% 4.97/3.41 tff(295,plain,
% 4.97/3.41 ((~![X: $i] : ((~mem(X, ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), X), ty_2Efcp_2Ecart(bool, A_27a!4)))) | (~mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))), ty_2Efcp_2Ecart(bool, A_27a!4))),
% 4.97/3.41 inference(modus_ponens,[status(thm)],[294, 293])).
% 4.97/3.41 tff(296,plain,
% 4.97/3.41 ((~mem(ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)), ty_2Enum_2Enum)) | mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))), ty_2Efcp_2Ecart(bool, A_27a!4))),
% 4.97/3.41 inference(unit_resolution,[status(thm)],[295, 26])).
% 4.97/3.41 tff(297,plain,
% 4.97/3.41 (mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))), ty_2Efcp_2Ecart(bool, A_27a!4))),
% 4.97/3.41 inference(unit_resolution,[status(thm)],[296, 292])).
% 4.97/3.41 tff(298,plain,
% 4.97/3.41 (((~![V0t1: $i] : ((~mem(V0t1, ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | ((~mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))), ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), V1t2) = ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))))))) <=> ((~![V0t1: $i] : ((~mem(V0t1, ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))), ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), V1t2) = ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))))))),
% 4.97/3.41 inference(rewrite,[status(thm)],[])).
% 4.97/3.41 tff(299,plain,
% 4.97/3.41 ((~![V0t1: $i] : ((~mem(V0t1, ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | ((~mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))), ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), V1t2) = ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))))))),
% 4.97/3.41 inference(quant_inst,[status(thm)],[])).
% 4.97/3.41 tff(300,plain,
% 4.97/3.41 ((~![V0t1: $i] : ((~mem(V0t1, ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), V0t1), V1t2) = V0t1)))) | (~mem(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))), ty_2Efcp_2Ecart(bool, A_27a!4))) | ![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), V1t2) = ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))))),
% 4.97/3.41 inference(modus_ponens,[status(thm)],[299, 298])).
% 4.97/3.41 tff(301,plain,
% 4.97/3.41 (![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), V1t2) = ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))))),
% 4.97/3.41 inference(unit_resolution,[status(thm)],[300, 297, 277])).
% 4.97/3.41 tff(302,plain,
% 4.97/3.41 (((~![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), V1t2) = ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))))) | ((~mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))), ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))))) = ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))))) <=> ((~![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), V1t2) = ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))))) | (~mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))), ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))))) = ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))))),
% 4.97/3.41 inference(rewrite,[status(thm)],[])).
% 4.97/3.41 tff(303,plain,
% 4.97/3.41 ((~![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), V1t2) = ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))))) | ((~mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))), ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))))) = ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))))),
% 4.97/3.41 inference(quant_inst,[status(thm)],[])).
% 4.97/3.41 tff(304,plain,
% 4.97/3.41 ((~![V1t2: $i] : ((~mem(V1t2, ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), V1t2) = ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))))) | (~mem(ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))), ty_2Efcp_2Ecart(bool, A_27a!4))) | (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))))) = ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))))),
% 4.97/3.42 inference(modus_ponens,[status(thm)],[303, 302])).
% 4.97/3.42 tff(305,plain,
% 4.97/3.42 (ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3))))) = ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))),
% 4.97/3.42 inference(unit_resolution,[status(thm)],[304, 301, 257])).
% 4.97/3.42 tff(306,plain,
% 4.97/3.42 (ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Efcp_2Ecart(bool, A_27a!4)), inj__o(fo__c_2Ebool_2ET)), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2)))), ap(c_2Ewords_2Eword__2comp(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V1b!2)), inj__ty_2Enum_2Enum(V0a!3)))))),
% 4.97/3.42 inference(symmetry,[status(thm)],[305])).
% 4.97/3.42 tff(307,plain,
% 4.97/3.42 (ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))) = ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2)))),
% 4.97/3.42 inference(transitivity,[status(thm)],[306, 217, 88, 68])).
% 4.97/3.42 tff(308,plain,
% 4.97/3.42 (~(ap(c_2Ewords_2En2w(A_27a!4), ap(ap(c_2Earithmetic_2E_2D, inj__ty_2Enum_2Enum(V0a!3)), inj__ty_2Enum_2Enum(V1b!2))) = ap(ap(c_2Ewords_2Eword__sub(A_27a!4), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V0a!3))), ap(c_2Ewords_2En2w(A_27a!4), inj__ty_2Enum_2Enum(V1b!2))))),
% 4.97/3.42 inference(or_elim,[status(thm)],[175])).
% 4.97/3.42 tff(309,plain,
% 4.97/3.42 ($false),
% 4.97/3.42 inference(unit_resolution,[status(thm)],[308, 307])).
% 4.97/3.42 % SZS output end Proof
%------------------------------------------------------------------------------