TSTP Solution File: ITP317_1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n013.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 : Fri May 3 02:30:38 EDT 2024
% Result : Theorem 23.65s 3.68s
% Output : CNFRefutation 23.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 2 21:47:34 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.21/0.46 Running TFA theorem proving
% 0.21/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 23.65/3.68 % SZS status Started for theBenchmark.p
% 23.65/3.68 % SZS status Theorem for theBenchmark.p
% 23.65/3.68
% 23.65/3.68 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 23.65/3.68
% 23.65/3.68 ------ iProver source info
% 23.65/3.68
% 23.65/3.68 git: date: 2024-05-02 19:28:25 +0000
% 23.65/3.68 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 23.65/3.68 git: non_committed_changes: false
% 23.65/3.68
% 23.65/3.68 ------ Parsing...
% 23.65/3.68 ------ Clausification by vclausify_rel & Parsing by iProver...
% 23.65/3.68
% 23.65/3.68 ------ Preprocessing... sup_sim: 86 sf_s rm: 13 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 23.65/3.68
% 23.65/3.68 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 23.65/3.68
% 23.65/3.68 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 23.65/3.68 ------ Proving...
% 23.65/3.68 ------ Problem Properties
% 23.65/3.68
% 23.65/3.68
% 23.65/3.68 clauses 385
% 23.65/3.68 conjectures 2
% 23.65/3.68 EPR 21
% 23.65/3.68 Horn 234
% 23.65/3.68 unary 81
% 23.65/3.68 binary 121
% 23.65/3.68 lits 992
% 23.65/3.68 lits eq 110
% 23.65/3.68 fd_pure 1
% 23.65/3.68 fd_pseudo 0
% 23.65/3.68 fd_cond 8
% 23.65/3.68 fd_pseudo_cond 16
% 23.65/3.68 AC symbols 2
% 23.65/3.68
% 23.65/3.68 ------ Input Options Time Limit: Unbounded
% 23.65/3.68
% 23.65/3.68
% 23.65/3.68 ------
% 23.65/3.68 Current options:
% 23.65/3.68 ------
% 23.65/3.68
% 23.65/3.68
% 23.65/3.68
% 23.65/3.68
% 23.65/3.68 ------ Proving...
% 23.65/3.68
% 23.65/3.68
% 23.65/3.68 % SZS status Theorem for theBenchmark.p
% 23.65/3.68
% 23.65/3.68 % SZS output start CNFRefutation for theBenchmark.p
% 23.65/3.68
% 23.65/3.68 tff(f2,axiom,(
% 23.65/3.68 ! [X0 : $int,X1 : $int] : ('fun_app$b'('fun_app$c'('uub$',X0),X1) <=> $lesseq(X0,X1))),
% 23.65/3.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1)).
% 23.65/3.68
% 23.65/3.68 tff(f4,axiom,(
% 23.65/3.68 ! [X0 : $int,X1 : $int] : ('fun_app$b'('fun_app$c'('uud$',X0),X1) <=> $less(X0,X1))),
% 23.65/3.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3)).
% 23.65/3.68
% 23.65/3.68 tff(f6,conjecture,(
% 23.65/3.68 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$') <=> 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')),
% 23.65/3.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture5)).
% 23.65/3.68
% 23.65/3.68 tff(f7,negated_conjecture,(
% 23.65/3.68 ~('fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$') <=> 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a'))),
% 23.65/3.68 inference(negated_conjecture,[],[f6])).
% 23.65/3.68
% 23.65/3.68 tff(f8,axiom,(
% 23.65/3.68 'a$' = 'a$a'),
% 23.65/3.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6)).
% 23.65/3.68
% 23.65/3.68 tff(f9,axiom,(
% 23.65/3.68 'of_nat$'('n$') = 'of_nat$'('n$a')),
% 23.65/3.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7)).
% 23.65/3.68
% 23.65/3.68 tff(f10,axiom,(
% 23.65/3.68 ! [X0 : $real] : ($lesseq('fun_app$d'('of_int$','a$'),X0) => 'fun_app$e'('f$',X0) = 'fun_app$e'('g$',X0))),
% 23.65/3.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8)).
% 23.65/3.68
% 23.65/3.68 tff(f11,axiom,(
% 23.65/3.68 ! [X0 : $int,X1 : 'Real_a_fun$',X2 : 'Real_a_fun$',X3 : 'Nat$',X4 : 'Nat$',X5 : $int] : ((X0 = X5 & 'of_nat$'(X3) = 'of_nat$'(X4) & ! [X6 : $real] : ($lesseq('fun_app$d'('of_int$',X0),X6) => 'fun_app$e'(X1,X6) = 'fun_app$e'(X2,X6))) => ('fun_app$b'('eM_remainder_converges$'(X3,X1),X0) <=> 'fun_app$b'('eM_remainder_converges$'(X4,X2),X5)))),
% 23.65/3.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9)).
% 23.65/3.68
% 23.65/3.68 tff(f84,axiom,(
% 23.65/3.68 ! [X0 : 'Int_bool_fun$',X1 : $int] : ((! [X2 : $int] : ('fun_app$b'(X0,X2) => $lesseq(X2,X1)) & 'fun_app$b'(X0,X1)) => 'greatest$a'(X0) = X1)),
% 23.65/3.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom82)).
% 23.65/3.68
% 23.65/3.68 tff(f598,axiom,(
% 23.65/3.68 ! [X0 : $int,X1 : $int,X2 : 'Int_bool_fun$'] : ((! [X3 : $int] : (('fun_app$b'(X2,X3) & $less(X0,X3)) => 'fun_app$b'(X2,$sum(X3,1))) & 'fun_app$b'(X2,$sum(X0,1)) & $less(X0,X1)) => 'fun_app$b'(X2,X1))),
% 23.65/3.68 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom596)).
% 23.65/3.68
% 23.65/3.68 tff(f627,plain,(
% 23.65/3.68 ! [X0 : $int,X1 : $int] : ('fun_app$b'('fun_app$c'('uub$',X0),X1) <=> ~$less(X1,X0))),
% 23.65/3.68 inference(theory_normalization,[],[f2])).
% 23.65/3.68
% 23.65/3.68 tff(f628,plain,(
% 23.65/3.68 ! [X0 : $real] : (~$less(X0,'fun_app$d'('of_int$','a$')) => 'fun_app$e'('f$',X0) = 'fun_app$e'('g$',X0))),
% 23.65/3.68 inference(theory_normalization,[],[f10])).
% 23.65/3.68
% 23.65/3.68 tff(f629,plain,(
% 23.65/3.68 ! [X0 : $int,X1 : 'Real_a_fun$',X2 : 'Real_a_fun$',X3 : 'Nat$',X4 : 'Nat$',X5 : $int] : ((X0 = X5 & 'of_nat$'(X3) = 'of_nat$'(X4) & ! [X6 : $real] : (~$less(X6,'fun_app$d'('of_int$',X0)) => 'fun_app$e'(X1,X6) = 'fun_app$e'(X2,X6))) => ('fun_app$b'('eM_remainder_converges$'(X3,X1),X0) <=> 'fun_app$b'('eM_remainder_converges$'(X4,X2),X5)))),
% 23.65/3.68 inference(theory_normalization,[],[f11])).
% 23.65/3.68
% 23.65/3.68 tff(f701,plain,(
% 23.65/3.68 ! [X0 : 'Int_bool_fun$',X1 : $int] : ((! [X2 : $int] : ('fun_app$b'(X0,X2) => ~$less(X1,X2)) & 'fun_app$b'(X0,X1)) => 'greatest$a'(X0) = X1)),
% 23.65/3.68 inference(theory_normalization,[],[f84])).
% 23.65/3.68
% 23.65/3.68 tff(f1003,plain,(
% 23.65/3.68 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$') <~> 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')),
% 23.65/3.68 inference(ennf_transformation,[],[f7])).
% 23.65/3.68
% 23.65/3.68 tff(f1004,plain,(
% 23.65/3.68 ! [X0 : $real] : ('fun_app$e'('f$',X0) = 'fun_app$e'('g$',X0) | $less(X0,'fun_app$d'('of_int$','a$')))),
% 23.65/3.68 inference(ennf_transformation,[],[f628])).
% 23.65/3.68
% 23.65/3.68 tff(f1005,plain,(
% 23.65/3.68 ! [X0 : $int,X1 : 'Real_a_fun$',X2 : 'Real_a_fun$',X3 : 'Nat$',X4 : 'Nat$',X5 : $int] : (('fun_app$b'('eM_remainder_converges$'(X3,X1),X0) <=> 'fun_app$b'('eM_remainder_converges$'(X4,X2),X5)) | (X0 != X5 | 'of_nat$'(X3) != 'of_nat$'(X4) | ? [X6 : $real] : ('fun_app$e'(X1,X6) != 'fun_app$e'(X2,X6) & ~$less(X6,'fun_app$d'('of_int$',X0)))))),
% 23.65/3.68 inference(ennf_transformation,[],[f629])).
% 23.65/3.68
% 23.65/3.68 tff(f1006,plain,(
% 23.65/3.68 ! [X0 : $int,X1 : 'Real_a_fun$',X2 : 'Real_a_fun$',X3 : 'Nat$',X4 : 'Nat$',X5 : $int] : (('fun_app$b'('eM_remainder_converges$'(X3,X1),X0) <=> 'fun_app$b'('eM_remainder_converges$'(X4,X2),X5)) | X0 != X5 | 'of_nat$'(X3) != 'of_nat$'(X4) | ? [X6 : $real] : ('fun_app$e'(X1,X6) != 'fun_app$e'(X2,X6) & ~$less(X6,'fun_app$d'('of_int$',X0))))),
% 23.65/3.68 inference(flattening,[],[f1005])).
% 23.65/3.68
% 23.65/3.68 tff(f1093,plain,(
% 23.65/3.68 ! [X0 : 'Int_bool_fun$',X1 : $int] : ('greatest$a'(X0) = X1 | (? [X2 : $int] : ($less(X1,X2) & 'fun_app$b'(X0,X2)) | ~'fun_app$b'(X0,X1)))),
% 23.65/3.68 inference(ennf_transformation,[],[f701])).
% 23.65/3.68
% 23.65/3.68 tff(f1094,plain,(
% 23.65/3.68 ! [X0 : 'Int_bool_fun$',X1 : $int] : ('greatest$a'(X0) = X1 | ? [X2 : $int] : ($less(X1,X2) & 'fun_app$b'(X0,X2)) | ~'fun_app$b'(X0,X1))),
% 23.65/3.68 inference(flattening,[],[f1093])).
% 23.65/3.68
% 23.65/3.68 tff(f1376,plain,(
% 23.65/3.68 ! [X0 : $int,X1 : $int,X2 : 'Int_bool_fun$'] : ('fun_app$b'(X2,X1) | (? [X3 : $int] : (~'fun_app$b'(X2,$sum(X3,1)) & ('fun_app$b'(X2,X3) & $less(X0,X3))) | ~'fun_app$b'(X2,$sum(X0,1)) | ~$less(X0,X1)))),
% 23.65/3.68 inference(ennf_transformation,[],[f598])).
% 23.65/3.68
% 23.65/3.68 tff(f1377,plain,(
% 23.65/3.68 ! [X0 : $int,X1 : $int,X2 : 'Int_bool_fun$'] : ('fun_app$b'(X2,X1) | ? [X3 : $int] : (~'fun_app$b'(X2,$sum(X3,1)) & 'fun_app$b'(X2,X3) & $less(X0,X3)) | ~'fun_app$b'(X2,$sum(X0,1)) | ~$less(X0,X1))),
% 23.65/3.68 inference(flattening,[],[f1376])).
% 23.65/3.68
% 23.65/3.68 tff(f1400,plain,(
% 23.65/3.68 ! [X0 : $int,X1 : $int] : (('fun_app$b'('fun_app$c'('uub$',X0),X1) | $less(X1,X0)) & (~$less(X1,X0) | ~'fun_app$b'('fun_app$c'('uub$',X0),X1)))),
% 23.65/3.68 inference(nnf_transformation,[],[f627])).
% 23.65/3.68
% 23.65/3.68 tff(f1402,plain,(
% 23.65/3.68 ! [X0 : $int,X1 : $int] : (('fun_app$b'('fun_app$c'('uud$',X0),X1) | ~$less(X0,X1)) & ($less(X0,X1) | ~'fun_app$b'('fun_app$c'('uud$',X0),X1)))),
% 23.65/3.68 inference(nnf_transformation,[],[f4])).
% 23.65/3.68
% 23.65/3.68 tff(f1404,plain,(
% 23.65/3.68 (~'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a') | ~'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$')) & ('fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a') | 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$'))),
% 23.65/3.68 inference(nnf_transformation,[],[f1003])).
% 23.65/3.68
% 23.65/3.68 tff(f1405,plain,(
% 23.65/3.68 ! [X0 : $int,X1 : 'Real_a_fun$',X2 : 'Real_a_fun$',X3 : 'Nat$',X4 : 'Nat$',X5 : $int] : ((('fun_app$b'('eM_remainder_converges$'(X3,X1),X0) | ~'fun_app$b'('eM_remainder_converges$'(X4,X2),X5)) & ('fun_app$b'('eM_remainder_converges$'(X4,X2),X5) | ~'fun_app$b'('eM_remainder_converges$'(X3,X1),X0))) | X0 != X5 | 'of_nat$'(X3) != 'of_nat$'(X4) | ? [X6 : $real] : ('fun_app$e'(X1,X6) != 'fun_app$e'(X2,X6) & ~$less(X6,'fun_app$d'('of_int$',X0))))),
% 23.65/3.68 inference(nnf_transformation,[],[f1006])).
% 23.65/3.68
% 23.65/3.68 tff(f1406,plain,(
% 23.65/3.68 ! [X0 : $int,X1 : 'Real_a_fun$',X2 : 'Real_a_fun$'] : (? [X6 : $real] : ('fun_app$e'(X1,X6) != 'fun_app$e'(X2,X6) & ~$less(X6,'fun_app$d'('of_int$',X0))) => ('fun_app$e'(X1,sK7(X0,X1,X2)) != 'fun_app$e'(X2,sK7(X0,X1,X2)) & ~$less(sK7(X0,X1,X2),'fun_app$d'('of_int$',X0))))),
% 23.65/3.68 introduced(choice_axiom,[])).
% 23.65/3.68
% 23.65/3.68 tff(f1407,plain,(
% 23.65/3.68 ! [X0 : $int,X1 : 'Real_a_fun$',X2 : 'Real_a_fun$',X3 : 'Nat$',X4 : 'Nat$',X5 : $int] : ((('fun_app$b'('eM_remainder_converges$'(X3,X1),X0) | ~'fun_app$b'('eM_remainder_converges$'(X4,X2),X5)) & ('fun_app$b'('eM_remainder_converges$'(X4,X2),X5) | ~'fun_app$b'('eM_remainder_converges$'(X3,X1),X0))) | X0 != X5 | 'of_nat$'(X3) != 'of_nat$'(X4) | ('fun_app$e'(X1,sK7(X0,X1,X2)) != 'fun_app$e'(X2,sK7(X0,X1,X2)) & ~$less(sK7(X0,X1,X2),'fun_app$d'('of_int$',X0))))),
% 23.65/3.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f1405,f1406])).
% 23.65/3.68
% 23.65/3.68 tff(f1488,plain,(
% 23.65/3.68 ! [X0 : 'Int_bool_fun$',X1 : $int] : (? [X2 : $int] : ($less(X1,X2) & 'fun_app$b'(X0,X2)) => ($less(X1,sK53(X0,X1)) & 'fun_app$b'(X0,sK53(X0,X1))))),
% 23.65/3.68 introduced(choice_axiom,[])).
% 23.65/3.68
% 23.65/3.68 tff(f1489,plain,(
% 23.65/3.68 ! [X0 : 'Int_bool_fun$',X1 : $int] : ('greatest$a'(X0) = X1 | ($less(X1,sK53(X0,X1)) & 'fun_app$b'(X0,sK53(X0,X1))) | ~'fun_app$b'(X0,X1))),
% 23.65/3.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f1094,f1488])).
% 23.65/3.68
% 23.65/3.68 tff(f1842,plain,(
% 23.65/3.68 ! [X0 : $int,X2 : 'Int_bool_fun$'] : (? [X3 : $int] : (~'fun_app$b'(X2,$sum(X3,1)) & 'fun_app$b'(X2,X3) & $less(X0,X3)) => (~'fun_app$b'(X2,$sum(sK163(X0,X2),1)) & 'fun_app$b'(X2,sK163(X0,X2)) & $less(X0,sK163(X0,X2))))),
% 23.65/3.68 introduced(choice_axiom,[])).
% 23.65/3.68
% 23.65/3.68 tff(f1843,plain,(
% 23.65/3.68 ! [X0 : $int,X1 : $int,X2 : 'Int_bool_fun$'] : ('fun_app$b'(X2,X1) | (~'fun_app$b'(X2,$sum(sK163(X0,X2),1)) & 'fun_app$b'(X2,sK163(X0,X2)) & $less(X0,sK163(X0,X2))) | ~'fun_app$b'(X2,$sum(X0,1)) | ~$less(X0,X1))),
% 23.65/3.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK163])],[f1377,f1842])).
% 23.65/3.68
% 23.65/3.68 tff(f1871,plain,(
% 23.65/3.68 ( ! [X0 : $int,X1 : $int] : (~$less(X1,X0) | ~'fun_app$b'('fun_app$c'('uub$',X0),X1)) )),
% 23.65/3.68 inference(cnf_transformation,[],[f1400])).
% 23.65/3.68
% 23.65/3.68 tff(f1875,plain,(
% 23.65/3.68 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | ~'fun_app$b'('fun_app$c'('uud$',X0),X1)) )),
% 23.65/3.68 inference(cnf_transformation,[],[f1402])).
% 23.65/3.68
% 23.65/3.68 tff(f1879,plain,(
% 23.65/3.68 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a') | 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$')),
% 23.65/3.68 inference(cnf_transformation,[],[f1404])).
% 23.65/3.68
% 23.65/3.68 tff(f1880,plain,(
% 23.65/3.68 ~'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a') | ~'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$')),
% 23.65/3.68 inference(cnf_transformation,[],[f1404])).
% 23.65/3.68
% 23.65/3.68 tff(f1881,plain,(
% 23.65/3.68 'a$' = 'a$a'),
% 23.65/3.68 inference(cnf_transformation,[],[f8])).
% 23.65/3.68
% 23.65/3.68 tff(f1882,plain,(
% 23.65/3.68 'of_nat$'('n$') = 'of_nat$'('n$a')),
% 23.65/3.68 inference(cnf_transformation,[],[f9])).
% 23.65/3.68
% 23.65/3.68 tff(f1883,plain,(
% 23.65/3.68 ( ! [X0 : $real] : ('fun_app$e'('f$',X0) = 'fun_app$e'('g$',X0) | $less(X0,'fun_app$d'('of_int$','a$'))) )),
% 23.65/3.68 inference(cnf_transformation,[],[f1004])).
% 23.65/3.68
% 23.65/3.68 tff(f1884,plain,(
% 23.65/3.68 ( ! [X2 : 'Real_a_fun$',X3 : 'Nat$',X0 : $int,X1 : 'Real_a_fun$',X4 : 'Nat$',X5 : $int] : ('fun_app$b'('eM_remainder_converges$'(X4,X2),X5) | ~'fun_app$b'('eM_remainder_converges$'(X3,X1),X0) | X0 != X5 | 'of_nat$'(X3) != 'of_nat$'(X4) | ~$less(sK7(X0,X1,X2),'fun_app$d'('of_int$',X0))) )),
% 23.65/3.68 inference(cnf_transformation,[],[f1407])).
% 23.65/3.68
% 23.65/3.68 tff(f1885,plain,(
% 23.65/3.68 ( ! [X2 : 'Real_a_fun$',X3 : 'Nat$',X0 : $int,X1 : 'Real_a_fun$',X4 : 'Nat$',X5 : $int] : ('fun_app$b'('eM_remainder_converges$'(X4,X2),X5) | ~'fun_app$b'('eM_remainder_converges$'(X3,X1),X0) | X0 != X5 | 'of_nat$'(X3) != 'of_nat$'(X4) | 'fun_app$e'(X1,sK7(X0,X1,X2)) != 'fun_app$e'(X2,sK7(X0,X1,X2))) )),
% 23.65/3.68 inference(cnf_transformation,[],[f1407])).
% 23.65/3.68
% 23.65/3.68 tff(f1886,plain,(
% 23.65/3.68 ( ! [X2 : 'Real_a_fun$',X3 : 'Nat$',X0 : $int,X1 : 'Real_a_fun$',X4 : 'Nat$',X5 : $int] : ('fun_app$b'('eM_remainder_converges$'(X3,X1),X0) | ~'fun_app$b'('eM_remainder_converges$'(X4,X2),X5) | X0 != X5 | 'of_nat$'(X3) != 'of_nat$'(X4) | ~$less(sK7(X0,X1,X2),'fun_app$d'('of_int$',X0))) )),
% 23.65/3.68 inference(cnf_transformation,[],[f1407])).
% 23.65/3.68
% 23.65/3.68 tff(f1887,plain,(
% 23.65/3.68 ( ! [X2 : 'Real_a_fun$',X3 : 'Nat$',X0 : $int,X1 : 'Real_a_fun$',X4 : 'Nat$',X5 : $int] : ('fun_app$b'('eM_remainder_converges$'(X3,X1),X0) | ~'fun_app$b'('eM_remainder_converges$'(X4,X2),X5) | X0 != X5 | 'of_nat$'(X3) != 'of_nat$'(X4) | 'fun_app$e'(X1,sK7(X0,X1,X2)) != 'fun_app$e'(X2,sK7(X0,X1,X2))) )),
% 23.65/3.68 inference(cnf_transformation,[],[f1407])).
% 23.65/3.68
% 23.65/3.68 tff(f2036,plain,(
% 23.65/3.68 ( ! [X0 : 'Int_bool_fun$',X1 : $int] : ('greatest$a'(X0) = X1 | $less(X1,sK53(X0,X1)) | ~'fun_app$b'(X0,X1)) )),
% 23.65/3.68 inference(cnf_transformation,[],[f1489])).
% 23.65/3.68
% 23.65/3.68 tff(f2841,plain,(
% 23.65/3.68 ( ! [X2 : 'Int_bool_fun$',X0 : $int,X1 : $int] : ('fun_app$b'(X2,X1) | 'fun_app$b'(X2,sK163(X0,X2)) | ~'fun_app$b'(X2,$sum(X0,1)) | ~$less(X0,X1)) )),
% 23.65/3.68 inference(cnf_transformation,[],[f1843])).
% 23.65/3.68
% 23.65/3.68 tff(f2897,plain,(
% 23.65/3.68 ~'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a') | ~'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$a')),
% 23.65/3.68 inference(definition_unfolding,[],[f1880,f1881])).
% 23.65/3.68
% 23.65/3.68 tff(f2898,plain,(
% 23.65/3.68 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a') | 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$a')),
% 23.65/3.68 inference(definition_unfolding,[],[f1879,f1881])).
% 23.65/3.68
% 23.65/3.68 tff(f2899,plain,(
% 23.65/3.68 ( ! [X0 : $real] : ('fun_app$e'('f$',X0) = 'fun_app$e'('g$',X0) | $less(X0,'fun_app$d'('of_int$','a$a'))) )),
% 23.65/3.68 inference(definition_unfolding,[],[f1883,f1881])).
% 23.65/3.68
% 23.65/3.68 tff(f2900,plain,(
% 23.65/3.68 ( ! [X2 : 'Real_a_fun$',X3 : 'Nat$',X1 : 'Real_a_fun$',X4 : 'Nat$',X5 : $int] : ('fun_app$b'('eM_remainder_converges$'(X3,X1),X5) | ~'fun_app$b'('eM_remainder_converges$'(X4,X2),X5) | 'of_nat$'(X3) != 'of_nat$'(X4) | 'fun_app$e'(X1,sK7(X5,X1,X2)) != 'fun_app$e'(X2,sK7(X5,X1,X2))) )),
% 23.65/3.68 inference(equality_resolution,[],[f1887])).
% 23.65/3.68
% 23.65/3.68 tff(f2901,plain,(
% 23.65/3.68 ( ! [X2 : 'Real_a_fun$',X3 : 'Nat$',X1 : 'Real_a_fun$',X4 : 'Nat$',X5 : $int] : ('fun_app$b'('eM_remainder_converges$'(X3,X1),X5) | ~'fun_app$b'('eM_remainder_converges$'(X4,X2),X5) | 'of_nat$'(X3) != 'of_nat$'(X4) | ~$less(sK7(X5,X1,X2),'fun_app$d'('of_int$',X5))) )),
% 23.65/3.68 inference(equality_resolution,[],[f1886])).
% 23.65/3.68
% 23.65/3.68 tff(f2902,plain,(
% 23.65/3.68 ( ! [X2 : 'Real_a_fun$',X3 : 'Nat$',X1 : 'Real_a_fun$',X4 : 'Nat$',X5 : $int] : ('fun_app$b'('eM_remainder_converges$'(X4,X2),X5) | ~'fun_app$b'('eM_remainder_converges$'(X3,X1),X5) | 'of_nat$'(X3) != 'of_nat$'(X4) | 'fun_app$e'(X1,sK7(X5,X1,X2)) != 'fun_app$e'(X2,sK7(X5,X1,X2))) )),
% 23.65/3.68 inference(equality_resolution,[],[f1885])).
% 23.65/3.68
% 23.65/3.68 tff(f2903,plain,(
% 23.65/3.68 ( ! [X2 : 'Real_a_fun$',X3 : 'Nat$',X1 : 'Real_a_fun$',X4 : 'Nat$',X5 : $int] : ('fun_app$b'('eM_remainder_converges$'(X4,X2),X5) | ~'fun_app$b'('eM_remainder_converges$'(X3,X1),X5) | 'of_nat$'(X3) != 'of_nat$'(X4) | ~$less(sK7(X5,X1,X2),'fun_app$d'('of_int$',X5))) )),
% 23.65/3.68 inference(equality_resolution,[],[f1884])).
% 23.65/3.68
% 23.65/3.68 cnf(c_75,plain,
% 23.65/3.68 (~'fun_app$b'('fun_app$c'('uub$',X0_3),X1_3)|~$less_int(X1_3,X0_3)),
% 23.65/3.68 inference(cnf_transformation,[],[f1871])).
% 23.65/3.68
% 23.65/3.68 cnf(c_79,plain,
% 23.65/3.68 (~'fun_app$b'('fun_app$c'('uud$',X0_3),X1_3)|$less_int(X0_3,X1_3)),
% 23.65/3.68 inference(cnf_transformation,[],[f1875])).
% 23.65/3.68
% 23.65/3.68 cnf(c_82,negated_conjecture,
% 23.65/3.68 (~'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')|~'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$a')),
% 23.65/3.68 inference(cnf_transformation,[],[f2897])).
% 23.65/3.68
% 23.65/3.68 cnf(c_83,negated_conjecture,
% 23.65/3.68 ('fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')|'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$a')),
% 23.65/3.68 inference(cnf_transformation,[],[f2898])).
% 23.65/3.68
% 23.65/3.68 cnf(c_84,plain,
% 23.65/3.68 ('of_nat$'('n$a') = 'of_nat$'('n$')),
% 23.65/3.68 inference(cnf_transformation,[],[f1882])).
% 23.65/3.68
% 23.65/3.68 cnf(c_85,plain,
% 23.65/3.68 ('fun_app$e'('g$',X0_2) = 'fun_app$e'('f$',X0_2)|$less_real(X0_2,'fun_app$d'('of_int$','a$a'))),
% 23.65/3.68 inference(cnf_transformation,[],[f2899])).
% 23.65/3.68
% 23.65/3.68 cnf(c_86,plain,
% 23.65/3.68 ('fun_app$e'(X0_15,sK7(X0_3,X0_15,X1_15)) != 'fun_app$e'(X1_15,sK7(X0_3,X0_15,X1_15))|
% 23.65/3.68 'of_nat$'(X0_22) != 'of_nat$'(X1_22)|~'fun_app$b'('eM_remainder_converges$'(X1_22,X1_15),X0_3)|
% 23.65/3.68 'fun_app$b'('eM_remainder_converges$'(X0_22,X0_15),X0_3)),
% 23.65/3.68 inference(cnf_transformation,[],[f2900])).
% 23.65/3.68
% 23.65/3.68 cnf(c_87,plain,
% 23.65/3.68 ('of_nat$'(X0_22) != 'of_nat$'(X1_22)|~$less_real(sK7(X0_3,X0_15,X1_15),'fun_app$d'('of_int$',X0_3))|
% 23.65/3.68 ~'fun_app$b'('eM_remainder_converges$'(X1_22,X1_15),X0_3)|'fun_app$b'('eM_remainder_converges$'(X0_22,X0_15),X0_3)),
% 23.65/3.68 inference(cnf_transformation,[],[f2901])).
% 23.65/3.68
% 23.65/3.68 cnf(c_88,plain,
% 23.65/3.68 ('fun_app$e'(X0_15,sK7(X0_3,X0_15,X1_15)) != 'fun_app$e'(X1_15,sK7(X0_3,X0_15,X1_15))|
% 23.65/3.68 'of_nat$'(X0_22) != 'of_nat$'(X1_22)|~'fun_app$b'('eM_remainder_converges$'(X0_22,X0_15),X0_3)|
% 23.79/3.68 'fun_app$b'('eM_remainder_converges$'(X1_22,X1_15),X0_3)),
% 23.79/3.68 inference(cnf_transformation,[],[f2902])).
% 23.79/3.68
% 23.79/3.68 cnf(c_89,plain,
% 23.79/3.68 ('of_nat$'(X0_22) != 'of_nat$'(X1_22)|~$less_real(sK7(X0_3,X0_15,X1_15),'fun_app$d'('of_int$',X0_3))|
% 23.79/3.68 ~'fun_app$b'('eM_remainder_converges$'(X0_22,X0_15),X0_3)|'fun_app$b'('eM_remainder_converges$'(X1_22,X1_15),X0_3)),
% 23.79/3.68 inference(cnf_transformation,[],[f2903])).
% 23.79/3.68
% 23.79/3.68 cnf(c_230,plain,
% 23.79/3.68 (~'fun_app$b'(X0_14,X0_3)|'greatest$a'(X0_14) = X0_3|$less_int(X0_3,sK53(X0_14,X0_3))),
% 23.79/3.68 inference(cnf_transformation,[],[f2036])).
% 23.79/3.68
% 23.79/3.68 cnf(c_967,plain,
% 23.79/3.68 (~'fun_app$b'(X0_14,$sum_int(X0_3,1))|~$less_int(X0_3,X1_3)|'fun_app$b'(X0_14,sK163(X0_3,X0_14))|
% 23.79/3.68 'fun_app$b'(X0_14,X1_3)),
% 23.79/3.68 inference(cnf_transformation,[],[f2841])).
% 23.79/3.68
% 23.79/3.68 cnf(c_12498,plain,(X0_14 = X0_14),theory(equality)).
% 23.79/3.68
% 23.79/3.68 cnf(c_12534,plain,
% 23.79/3.68 (X0_3 != X1_3|X0_14 != X1_14|~'fun_app$b'(X1_14,X1_3)|'fun_app$b'(X0_14,X0_3)),
% 23.79/3.68 theory(equality)).
% 23.79/3.68
% 23.79/3.68 cnf(c_21270,plain,
% 23.79/3.68 (X0_3 != X1_3|~'fun_app$b'(X0_14,X1_3)|'fun_app$b'(X0_14,X0_3)),
% 23.79/3.68 inference(resolution,[status(thm)],[c_12534,c_12498])).
% 23.79/3.68
% 23.79/3.68 cnf(c_21279,plain,
% 23.79/3.68 (~'fun_app$b'(X0_14,X0_3)|~'fun_app$b'(X1_14,X0_3)|$less_int(X0_3,sK53(X1_14,X0_3))|
% 23.79/3.68 'fun_app$b'(X0_14,'greatest$a'(X1_14))),
% 23.79/3.68 inference(resolution,[status(thm)],[c_21270,c_230])).
% 23.79/3.68
% 23.79/3.68 cnf(c_21447,plain,
% 23.79/3.68 (~'fun_app$b'(X0_14,'a$a')|'fun_app$b'('eM_remainder_converges$'('n$','f$'),'greatest$a'(X0_14))|
% 23.79/3.68 $less_int('a$a',sK53(X0_14,'a$a'))|'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')),
% 23.79/3.68 inference(resolution,[status(thm)],[c_21279,c_83])).
% 23.79/3.68
% 23.79/3.68 cnf(c_21577,plain,
% 23.79/3.68 (~'fun_app$b'(X0_14,'greatest$a'(X1_14))|~'fun_app$b'(X1_14,'a$a')|
% 23.79/3.68 $less_int('greatest$a'(X1_14),sK53(X0_14,'greatest$a'(X1_14)))|'fun_app$b'('eM_remainder_converges$'('n$','f$'),'greatest$a'(X0_14))|
% 23.79/3.68 $less_int('a$a',sK53(X1_14,'a$a'))|'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')),
% 23.79/3.68 inference(resolution,[status(thm)],[c_21447,c_21279])).
% 23.79/3.68
% 23.79/3.68 cnf(c_21591,plain,
% 23.79/3.68 (~'fun_app$b'(X0_14,$sum_int('greatest$a'(X1_14),1))|~'fun_app$b'(X2_14,'greatest$a'(X1_14))|
% 23.79/3.68 ~'fun_app$b'(X1_14,'a$a')|'fun_app$b'(X0_14,sK53(X2_14,'greatest$a'(X1_14)))|
% 23.79/3.68 'fun_app$b'(X0_14,sK163('greatest$a'(X1_14),X0_14))|'fun_app$b'('eM_remainder_converges$'('n$','f$'),'greatest$a'(X2_14))|
% 23.79/3.68 $less_int('a$a',sK53(X1_14,'a$a'))|'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')),
% 23.79/3.68 inference(resolution,[status(thm)],[c_21577,c_967])).
% 23.79/3.68
% 23.79/3.68 cnf(c_21919,plain,
% 23.79/3.68 (~'fun_app$b'('fun_app$c'('uub$',X0_3),$sum_int('greatest$a'(X0_14),1))|
% 23.79/3.68 ~$less_int(sK53(X1_14,'greatest$a'(X0_14)),X0_3)|~'fun_app$b'(X1_14,'greatest$a'(X0_14))|
% 23.79/3.68 ~'fun_app$b'(X0_14,'a$a')|'fun_app$b'('fun_app$c'('uub$',X0_3),sK163('greatest$a'(X0_14),'fun_app$c'('uub$',X0_3)))|
% 23.79/3.68 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'greatest$a'(X1_14))|
% 23.79/3.68 $less_int('a$a',sK53(X0_14,'a$a'))|'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')),
% 23.79/3.68 inference(resolution,[status(thm)],[c_21591,c_75])).
% 23.79/3.68
% 23.79/3.68 cnf(c_21923,plain,
% 23.79/3.68 (~'fun_app$b'(X0_14,sK53(X1_14,'greatest$a'(X2_14)))|~'fun_app$b'(X3_14,$sum_int('greatest$a'(X2_14),1))|
% 23.79/3.68 ~'fun_app$b'(X1_14,'greatest$a'(X2_14))|~'fun_app$b'(X2_14,'a$a')|
% 23.79/3.68 $less_int(sK53(X1_14,'greatest$a'(X2_14)),sK53(X0_14,sK53(X1_14,'greatest$a'(X2_14))))|
% 23.79/3.68 'fun_app$b'(X3_14,sK163('greatest$a'(X2_14),X3_14))|'fun_app$b'('eM_remainder_converges$'('n$','f$'),'greatest$a'(X1_14))|
% 23.79/3.68 $less_int('a$a',sK53(X2_14,'a$a'))|'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')|
% 23.79/3.68 'fun_app$b'(X3_14,'greatest$a'(X0_14))),
% 23.79/3.68 inference(resolution,[status(thm)],[c_21591,c_21279])).
% 23.79/3.68
% 23.79/3.68 cnf(c_23922,plain,
% 23.79/3.68 (~'fun_app$b'('fun_app$c'('uud$',X0_3),$sum_int('greatest$a'(X0_14),1))|
% 23.79/3.68 ~'fun_app$b'(X1_14,sK53(X2_14,'greatest$a'(X0_14)))|~'fun_app$b'(X2_14,'greatest$a'(X0_14))|
% 23.79/3.68 ~'fun_app$b'(X0_14,'a$a')|$less_int(sK53(X2_14,'greatest$a'(X0_14)),sK53(X1_14,sK53(X2_14,'greatest$a'(X0_14))))|
% 23.79/3.68 'fun_app$b'('fun_app$c'('uud$',X0_3),sK163('greatest$a'(X0_14),'fun_app$c'('uud$',X0_3)))|
% 23.79/3.68 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'greatest$a'(X2_14))|
% 23.79/3.68 $less_int('a$a',sK53(X0_14,'a$a'))|'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')|
% 23.79/3.68 $less_int(X0_3,'greatest$a'(X1_14))),
% 23.79/3.68 inference(resolution,[status(thm)],[c_21923,c_79])).
% 23.79/3.68
% 23.79/3.68 cnf(c_30787,plain,
% 23.79/3.68 (~'fun_app$b'('fun_app$c'('uub$',sK53(X0_14,sK53(X1_14,'greatest$a'(X2_14)))),$sum_int('greatest$a'(X2_14),1))|
% 23.79/3.68 ~'fun_app$b'('fun_app$c'('uud$',X0_3),$sum_int('greatest$a'(X2_14),1))|
% 23.79/3.68 ~'fun_app$b'(X0_14,sK53(X1_14,'greatest$a'(X2_14)))|~'fun_app$b'(X1_14,'greatest$a'(X2_14))|
% 23.79/3.68 ~'fun_app$b'(X2_14,'a$a')|'fun_app$b'('fun_app$c'('uub$',sK53(X0_14,sK53(X1_14,'greatest$a'(X2_14)))),sK163('greatest$a'(X2_14),'fun_app$c'('uub$',sK53(X0_14,sK53(X1_14,'greatest$a'(X2_14))))))|
% 23.79/3.68 'fun_app$b'('fun_app$c'('uud$',X0_3),sK163('greatest$a'(X2_14),'fun_app$c'('uud$',X0_3)))|
% 23.79/3.68 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'greatest$a'(X1_14))|
% 23.79/3.68 $less_int('a$a',sK53(X2_14,'a$a'))|'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')|
% 23.79/3.68 $less_int(X0_3,'greatest$a'(X0_14))),
% 23.79/3.68 inference(resolution,[status(thm)],[c_23922,c_21919])).
% 23.79/3.68
% 23.79/3.68 cnf(c_31567,plain,
% 23.79/3.68 ('fun_app$e'('g$',sK7('a$a','g$','f$')) = 'fun_app$e'('f$',sK7('a$a','g$','f$'))|
% 23.79/3.68 $less_real(sK7('a$a','g$','f$'),'fun_app$d'('of_int$','a$a'))),
% 23.79/3.68 inference(instantiation,[status(thm)],[c_85])).
% 23.79/3.68
% 23.79/3.68 cnf(c_35151,plain,
% 23.79/3.68 ('fun_app$e'(X0_15,sK7('a$a',X0_15,'f$')) != 'fun_app$e'('f$',sK7('a$a',X0_15,'f$'))|
% 23.79/3.68 'of_nat$'(X0_22) != 'of_nat$'('n$')|~'fun_app$b'('eM_remainder_converges$'(X0_22,X0_15),'a$a')|
% 23.79/3.68 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$a')),
% 23.79/3.68 inference(instantiation,[status(thm)],[c_88])).
% 23.79/3.68
% 23.79/3.68 cnf(c_35317,plain,
% 23.79/3.68 ('fun_app$e'('g$',sK7('a$a','g$','f$')) != 'fun_app$e'('f$',sK7('a$a','g$','f$'))|
% 23.79/3.68 'of_nat$'('n$a') != 'of_nat$'('n$')|~'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')|
% 23.79/3.68 'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$a')),
% 23.79/3.68 inference(instantiation,[status(thm)],[c_35151])).
% 23.79/3.68
% 23.79/3.68 cnf(c_35320,plain,
% 23.79/3.68 ('fun_app$e'(X0_15,sK7('a$a',X0_15,X1_15)) != 'fun_app$e'(X1_15,sK7('a$a',X0_15,X1_15))|
% 23.79/3.68 'of_nat$'(X0_22) != 'of_nat$'(X1_22)|~'fun_app$b'('eM_remainder_converges$'(X1_22,X1_15),'a$a')|
% 23.79/3.68 'fun_app$b'('eM_remainder_converges$'(X0_22,X0_15),'a$a')),
% 23.79/3.68 inference(instantiation,[status(thm)],[c_86])).
% 23.79/3.68
% 23.79/3.68 cnf(c_40930,plain,
% 23.79/3.68 ('fun_app$e'('g$',sK7('a$a','g$',X0_15)) != 'fun_app$e'(X0_15,sK7('a$a','g$',X0_15))|
% 23.79/3.68 'of_nat$'('n$a') != 'of_nat$'(X0_22)|~'fun_app$b'('eM_remainder_converges$'(X0_22,X0_15),'a$a')|
% 23.79/3.68 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')),
% 23.79/3.68 inference(instantiation,[status(thm)],[c_35320])).
% 23.79/3.68
% 23.79/3.68 cnf(c_40931,plain,
% 23.79/3.68 ('fun_app$e'('g$',sK7('a$a','g$','f$')) != 'fun_app$e'('f$',sK7('a$a','g$','f$'))|
% 23.79/3.68 'of_nat$'('n$a') != 'of_nat$'('n$')|~'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$a')|
% 23.79/3.68 'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')),
% 23.79/3.68 inference(instantiation,[status(thm)],[c_40930])).
% 23.79/3.68
% 23.79/3.68 cnf(c_52802,plain,
% 23.79/3.68 ('of_nat$'('n$a') != 'of_nat$'(X0_22)|~$less_real(sK7('a$a','g$',X0_15),'fun_app$d'('of_int$','a$a'))|
% 23.79/3.68 ~'fun_app$b'('eM_remainder_converges$'(X0_22,X0_15),'a$a')|'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')),
% 23.79/3.68 inference(instantiation,[status(thm)],[c_87])).
% 23.79/3.68
% 23.79/3.68 cnf(c_52803,plain,
% 23.79/3.68 ('of_nat$'('n$a') != 'of_nat$'('n$')|~$less_real(sK7('a$a','g$','f$'),'fun_app$d'('of_int$','a$a'))|
% 23.79/3.68 ~'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$a')|'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')),
% 23.79/3.68 inference(instantiation,[status(thm)],[c_52802])).
% 23.79/3.68
% 23.79/3.68 cnf(c_52900,plain,
% 23.79/3.68 ('fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')),
% 23.79/3.68 inference(global_subsumption_just,
% 23.79/3.68 [status(thm)],
% 23.79/3.68 [c_30787,c_84,c_83,c_31567,c_40931,c_52803])).
% 23.79/3.68
% 23.79/3.68 cnf(c_53134,plain,
% 23.79/3.68 ('of_nat$'(X0_22) != 'of_nat$'(X1_22)|~$less_real(sK7('a$a',X0_15,X1_15),'fun_app$d'('of_int$','a$a'))|
% 23.79/3.68 ~'fun_app$b'('eM_remainder_converges$'(X0_22,X0_15),'a$a')|'fun_app$b'('eM_remainder_converges$'(X1_22,X1_15),'a$a')),
% 23.79/3.68 inference(instantiation,[status(thm)],[c_89])).
% 23.79/3.68
% 23.79/3.68 cnf(c_56780,plain,
% 23.79/3.68 ('of_nat$'('n$a') != 'of_nat$'(X0_22)|~$less_real(sK7('a$a','g$',X0_15),'fun_app$d'('of_int$','a$a'))|
% 23.79/3.68 ~'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')|'fun_app$b'('eM_remainder_converges$'(X0_22,X0_15),'a$a')),
% 23.79/3.68 inference(instantiation,[status(thm)],[c_53134])).
% 23.79/3.68
% 23.79/3.68 cnf(c_56781,plain,
% 23.79/3.68 ('of_nat$'('n$a') != 'of_nat$'('n$')|~$less_real(sK7('a$a','g$','f$'),'fun_app$d'('of_int$','a$a'))|
% 23.79/3.68 ~'fun_app$b'('eM_remainder_converges$'('n$a','g$'),'a$a')|'fun_app$b'('eM_remainder_converges$'('n$','f$'),'a$a')),
% 23.79/3.68 inference(instantiation,[status(thm)],[c_56780])).
% 23.79/3.68
% 23.79/3.68 cnf(c_56782,plain,
% 23.79/3.68 ($false),
% 23.79/3.68 inference(prop_impl_just,
% 23.79/3.68 [status(thm)],
% 23.79/3.68 [c_56781,c_52900,c_35317,c_31567,c_82,c_84])).
% 23.79/3.68
% 23.79/3.68
% 23.79/3.68 % SZS output end CNFRefutation for theBenchmark.p
% 23.79/3.68
% 23.79/3.68
%------------------------------------------------------------------------------