TSTP Solution File: ITP376_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 : n015.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 02:30:45 EDT 2024
% Result : Theorem 23.89s 3.67s
% Output : CNFRefutation 23.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.04/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 22:18:51 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.49 Running TFA theorem proving
% 0.21/0.49 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
% 23.89/3.67 % SZS status Started for theBenchmark.p
% 23.89/3.67 % SZS status Theorem for theBenchmark.p
% 23.89/3.67
% 23.89/3.67 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 23.89/3.67
% 23.89/3.67 ------ iProver source info
% 23.89/3.67
% 23.89/3.67 git: date: 2024-05-02 19:28:25 +0000
% 23.89/3.67 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 23.89/3.67 git: non_committed_changes: false
% 23.89/3.67
% 23.89/3.67 ------ Parsing...
% 23.89/3.67 ------ Clausification by vclausify_rel & Parsing by iProver...
% 23.89/3.67
% 23.89/3.67 ------ Preprocessing... sup_sim: 66 sf_s rm: 8 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e
% 23.89/3.67
% 23.89/3.67 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 23.89/3.67
% 23.89/3.67 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 23.89/3.67 ------ Proving...
% 23.89/3.67 ------ Problem Properties
% 23.89/3.67
% 23.89/3.67
% 23.89/3.67 clauses 652
% 23.89/3.67 conjectures 1
% 23.89/3.67 EPR 18
% 23.89/3.67 Horn 405
% 23.89/3.67 unary 130
% 23.89/3.67 binary 191
% 23.89/3.67 lits 1653
% 23.89/3.67 lits eq 250
% 23.89/3.67 fd_pure 1
% 23.89/3.67 fd_pseudo 0
% 23.89/3.67 fd_cond 12
% 23.89/3.67 fd_pseudo_cond 18
% 23.89/3.67 AC symbols 4
% 23.89/3.67
% 23.89/3.67 ------ Input Options Time Limit: Unbounded
% 23.89/3.67
% 23.89/3.67
% 23.89/3.67 ------
% 23.89/3.67 Current options:
% 23.89/3.67 ------
% 23.89/3.67
% 23.89/3.67
% 23.89/3.67
% 23.89/3.67
% 23.89/3.67 ------ Proving...
% 23.89/3.67
% 23.89/3.67
% 23.89/3.67 % SZS status Theorem for theBenchmark.p
% 23.89/3.67
% 23.89/3.67 % SZS output start CNFRefutation for theBenchmark.p
% 23.89/3.67
% 23.89/3.67 tff(f2,conjecture,(
% 23.89/3.67 $lesseq('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$'))),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$')))),
% 23.89/3.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture1)).
% 23.89/3.67
% 23.89/3.67 tff(f3,negated_conjecture,(
% 23.89/3.67 ~$lesseq('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$'))),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$')))),
% 23.89/3.67 inference(negated_conjecture,[],[f2])).
% 23.89/3.67
% 23.89/3.67 tff(f4,axiom,(
% 23.89/3.67 $lesseq('fun_app$a'('of_nat$','size$'('ys$')),'fun_app$a'('of_nat$','n$'))),
% 23.89/3.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2)).
% 23.89/3.67
% 23.89/3.67 tff(f246,axiom,(
% 23.89/3.67 ! [X0 : $int,X1 : $int,X2 : $int] : (($lesseq(X2,X0) & $lesseq(X0,X1)) => $lesseq(X2,X1))),
% 23.89/3.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom244)).
% 23.89/3.67
% 23.89/3.67 tff(f327,axiom,(
% 23.89/3.67 'zero$' = 'fun_app$b'('power$'('zero$'),'nat$'(2))),
% 23.89/3.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom325)).
% 23.89/3.67
% 23.89/3.67 tff(f385,axiom,(
% 23.89/3.67 ! [X0 : 'Nat$',X1 : 'Nat$'] : ($less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) <=> ('fun_app$a'('of_nat$',X1) = 0 | $less(0,'fun_app$a'('of_nat$',X0))))),
% 23.89/3.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom383)).
% 23.89/3.67
% 23.89/3.67 tff(f387,axiom,(
% 23.89/3.67 ! [X0 : 'Nat$',X1 : 'Nat$'] : ('fun_app$b'('power$'(X0),X1) = 'zero$' <=> ($less(0,'fun_app$a'('of_nat$',X1)) & 'zero$' = X0))),
% 23.89/3.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom385)).
% 23.89/3.67
% 23.89/3.67 tff(f587,axiom,(
% 23.89/3.67 ! [X0 : 'Nat$',X1 : 'Nat$',X2 : 'Nat$'] : (($less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X2))) & $less(0,'fun_app$a'('of_nat$',X0))) => $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)))),
% 23.89/3.67 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom585)).
% 23.89/3.67
% 23.89/3.67 tff(f642,plain,(
% 23.89/3.67 ~~$less('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$'))))),
% 23.89/3.67 inference(theory_normalization,[],[f3])).
% 23.89/3.67
% 23.89/3.67 tff(f643,plain,(
% 23.89/3.67 ~$less('fun_app$a'('of_nat$','n$'),'fun_app$a'('of_nat$','size$'('ys$')))),
% 23.89/3.67 inference(theory_normalization,[],[f4])).
% 23.89/3.67
% 23.89/3.67 tff(f746,plain,(
% 23.89/3.67 ! [X0 : $int,X1 : $int,X2 : $int] : ((~$less(X0,X2) & ~$less(X1,X0)) => ~$less(X1,X2))),
% 23.89/3.67 inference(theory_normalization,[],[f246])).
% 23.89/3.67
% 23.89/3.67 tff(f848,plain,(
% 23.89/3.67 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 23.89/3.67 introduced(theory_axiom_138,[])).
% 23.89/3.67
% 23.89/3.67 tff(f849,plain,(
% 23.89/3.67 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 23.89/3.67 introduced(theory_axiom_139,[])).
% 23.89/3.67
% 23.89/3.67 tff(f859,plain,(
% 23.89/3.67 ( ! [X0 : $int,X1 : $int] : ($product(X0,X1) = $product(X1,X0)) )),
% 23.89/3.67 introduced(theory_axiom_138,[])).
% 23.89/3.67
% 23.89/3.67 tff(f860,plain,(
% 23.89/3.67 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($product(X0,$product(X1,X2)) = $product($product(X0,X1),X2)) )),
% 23.89/3.67 introduced(theory_axiom_139,[])).
% 23.89/3.67
% 23.89/3.67 tff(f865,plain,(
% 23.89/3.67 ( ! [X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X1,$sum(X0,1))) )),
% 23.89/3.67 introduced(theory_axiom_164,[])).
% 23.89/3.67
% 23.89/3.67 tff(f866,plain,(
% 23.89/3.67 ( ! [X0 : $real,X1 : $real] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 23.89/3.67 introduced(theory_axiom_138,[])).
% 23.89/3.67
% 23.89/3.67 tff(f867,plain,(
% 23.89/3.67 ( ! [X2 : $real,X0 : $real,X1 : $real] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 23.89/3.67 introduced(theory_axiom_139,[])).
% 23.89/3.67
% 23.89/3.67 tff(f877,plain,(
% 23.89/3.67 ( ! [X0 : $real,X1 : $real] : ($product(X0,X1) = $product(X1,X0)) )),
% 23.89/3.67 introduced(theory_axiom_138,[])).
% 23.89/3.67
% 23.89/3.67 tff(f878,plain,(
% 23.89/3.67 ( ! [X2 : $real,X0 : $real,X1 : $real] : ($product(X0,$product(X1,X2)) = $product($product(X0,X1),X2)) )),
% 23.89/3.67 introduced(theory_axiom_139,[])).
% 23.89/3.67
% 23.89/3.67 tff(f883,plain,(
% 23.89/3.67 $less('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$'))))),
% 23.89/3.67 inference(flattening,[],[f642])).
% 23.89/3.67
% 23.89/3.67 tff(f1124,plain,(
% 23.89/3.67 ! [X0 : $int,X1 : $int,X2 : $int] : (~$less(X1,X2) | ($less(X0,X2) | $less(X1,X0)))),
% 23.89/3.67 inference(ennf_transformation,[],[f746])).
% 23.89/3.67
% 23.89/3.67 tff(f1125,plain,(
% 23.89/3.67 ! [X0 : $int,X1 : $int,X2 : $int] : (~$less(X1,X2) | $less(X0,X2) | $less(X1,X0))),
% 23.89/3.67 inference(flattening,[],[f1124])).
% 23.89/3.67
% 23.89/3.67 tff(f1457,plain,(
% 23.89/3.67 ! [X0 : 'Nat$',X1 : 'Nat$',X2 : 'Nat$'] : ($less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) | (~$less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X2))) | ~$less(0,'fun_app$a'('of_nat$',X0))))),
% 23.89/3.67 inference(ennf_transformation,[],[f587])).
% 23.89/3.67
% 23.89/3.67 tff(f1458,plain,(
% 23.89/3.67 ! [X0 : 'Nat$',X1 : 'Nat$',X2 : 'Nat$'] : ($less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) | ~$less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X2))) | ~$less(0,'fun_app$a'('of_nat$',X0)))),
% 23.89/3.67 inference(flattening,[],[f1457])).
% 23.89/3.67
% 23.89/3.67 tff(f1813,plain,(
% 23.89/3.67 ! [X0 : 'Nat$',X1 : 'Nat$'] : (($less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) | ('fun_app$a'('of_nat$',X1) != 0 & ~$less(0,'fun_app$a'('of_nat$',X0)))) & (('fun_app$a'('of_nat$',X1) = 0 | $less(0,'fun_app$a'('of_nat$',X0))) | ~$less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))))),
% 23.89/3.67 inference(nnf_transformation,[],[f385])).
% 23.89/3.67
% 23.89/3.67 tff(f1814,plain,(
% 23.89/3.67 ! [X0 : 'Nat$',X1 : 'Nat$'] : (($less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) | ('fun_app$a'('of_nat$',X1) != 0 & ~$less(0,'fun_app$a'('of_nat$',X0)))) & ('fun_app$a'('of_nat$',X1) = 0 | $less(0,'fun_app$a'('of_nat$',X0)) | ~$less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))))),
% 23.89/3.67 inference(flattening,[],[f1813])).
% 23.89/3.67
% 23.89/3.67 tff(f1816,plain,(
% 23.89/3.67 ! [X0 : 'Nat$',X1 : 'Nat$'] : (('fun_app$b'('power$'(X0),X1) = 'zero$' | (~$less(0,'fun_app$a'('of_nat$',X1)) | 'zero$' != X0)) & (($less(0,'fun_app$a'('of_nat$',X1)) & 'zero$' = X0) | 'fun_app$b'('power$'(X0),X1) != 'zero$'))),
% 23.89/3.67 inference(nnf_transformation,[],[f387])).
% 23.89/3.67
% 23.89/3.67 tff(f1817,plain,(
% 23.89/3.67 ! [X0 : 'Nat$',X1 : 'Nat$'] : (('fun_app$b'('power$'(X0),X1) = 'zero$' | ~$less(0,'fun_app$a'('of_nat$',X1)) | 'zero$' != X0) & (($less(0,'fun_app$a'('of_nat$',X1)) & 'zero$' = X0) | 'fun_app$b'('power$'(X0),X1) != 'zero$'))),
% 23.89/3.67 inference(flattening,[],[f1816])).
% 23.89/3.67
% 23.89/3.67 tff(f2080,plain,(
% 23.89/3.67 $less('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$'))))),
% 23.89/3.67 inference(cnf_transformation,[],[f883])).
% 23.89/3.67
% 23.89/3.67 tff(f2081,plain,(
% 23.89/3.67 ~$less('fun_app$a'('of_nat$','n$'),'fun_app$a'('of_nat$','size$'('ys$')))),
% 23.89/3.67 inference(cnf_transformation,[],[f643])).
% 23.89/3.67
% 23.89/3.67 tff(f2495,plain,(
% 23.89/3.67 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | $less(X0,X2) | $less(X1,X0)) )),
% 23.89/3.67 inference(cnf_transformation,[],[f1125])).
% 23.89/3.67
% 23.89/3.67 tff(f2628,plain,(
% 23.89/3.67 'zero$' = 'fun_app$b'('power$'('zero$'),'nat$'(2))),
% 23.89/3.67 inference(cnf_transformation,[],[f327])).
% 23.89/3.67
% 23.89/3.67 tff(f2717,plain,(
% 23.89/3.67 ( ! [X0 : 'Nat$',X1 : 'Nat$'] : ($less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) | ~$less(0,'fun_app$a'('of_nat$',X0))) )),
% 23.89/3.67 inference(cnf_transformation,[],[f1814])).
% 23.89/3.67
% 23.89/3.67 tff(f2722,plain,(
% 23.89/3.67 ( ! [X0 : 'Nat$',X1 : 'Nat$'] : ($less(0,'fun_app$a'('of_nat$',X1)) | 'fun_app$b'('power$'(X0),X1) != 'zero$') )),
% 23.89/3.67 inference(cnf_transformation,[],[f1817])).
% 23.89/3.67
% 23.89/3.67 tff(f3085,plain,(
% 23.89/3.67 ( ! [X2 : 'Nat$',X0 : 'Nat$',X1 : 'Nat$'] : ($less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) | ~$less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X2))) | ~$less(0,'fun_app$a'('of_nat$',X0))) )),
% 23.89/3.67 inference(cnf_transformation,[],[f1458])).
% 23.89/3.67
% 23.89/3.67 cnf(c_53,plain,
% 23.89/3.67 ($product_real($product_real(X0_2,X1_2),X2_2) = $product_real(X0_2,$product_real(X1_2,X2_2))),
% 23.89/3.67 inference(cnf_transformation,[],[f878])).
% 23.89/3.67
% 23.89/3.67 cnf(c_54,plain,
% 23.89/3.67 ($product_real(X0_2,X1_2) = $product_real(X1_2,X0_2)),
% 23.89/3.67 inference(cnf_transformation,[],[f877])).
% 23.89/3.67
% 23.89/3.67 cnf(c_64,plain,
% 23.89/3.67 ($sum_real($sum_real(X0_2,X1_2),X2_2) = $sum_real(X0_2,$sum_real(X1_2,X2_2))),
% 23.89/3.67 inference(cnf_transformation,[],[f867])).
% 23.89/3.67
% 23.89/3.67 cnf(c_65,plain,
% 23.89/3.67 ($sum_real(X0_2,X1_2) = $sum_real(X1_2,X0_2)),
% 23.89/3.67 inference(cnf_transformation,[],[f866])).
% 23.89/3.67
% 23.89/3.67 cnf(c_66,plain,
% 23.89/3.67 (~$less_int(X0_3,$sum_int(X1_3,1))|~$less_int(X1_3,X0_3)),
% 23.89/3.67 inference(cnf_transformation,[],[f865])).
% 23.89/3.67
% 23.89/3.67 cnf(c_71,plain,
% 23.89/3.67 ($product_int($product_int(X0_3,X1_3),X2_3) = $product_int(X0_3,$product_int(X1_3,X2_3))),
% 23.89/3.67 inference(cnf_transformation,[],[f860])).
% 23.89/3.67
% 23.89/3.67 cnf(c_72,plain,
% 23.89/3.67 ($product_int(X0_3,X1_3) = $product_int(X1_3,X0_3)),
% 23.89/3.67 inference(cnf_transformation,[],[f859])).
% 23.89/3.67
% 23.89/3.67 cnf(c_82,plain,
% 23.89/3.67 ($sum_int($sum_int(X0_3,X1_3),X2_3) = $sum_int(X0_3,$sum_int(X1_3,X2_3))),
% 23.89/3.67 inference(cnf_transformation,[],[f849])).
% 23.89/3.67
% 23.89/3.67 cnf(c_83,plain,
% 23.89/3.67 ($sum_int(X0_3,X1_3) = $sum_int(X1_3,X0_3)),
% 23.89/3.67 inference(cnf_transformation,[],[f848])).
% 23.89/3.67
% 23.89/3.67 cnf(c_86,negated_conjecture,
% 23.89/3.67 ($less_int('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int('fun_app$a'('of_nat$','n$'),1))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$'))))),
% 23.89/3.67 inference(cnf_transformation,[],[f2080])).
% 23.89/3.67
% 23.89/3.67 cnf(c_87,plain,
% 23.89/3.67 (~$less_int('fun_app$a'('of_nat$','n$'),'fun_app$a'('of_nat$','size$'('ys$')))),
% 23.89/3.67 inference(cnf_transformation,[],[f2081])).
% 23.89/3.67
% 23.89/3.67 cnf(c_474,plain,
% 23.89/3.67 (~$less_int(X0_3,X1_3)|$less_int(X0_3,X2_3)|$less_int(X2_3,X1_3)),
% 23.89/3.67 inference(cnf_transformation,[],[f2495])).
% 23.89/3.67
% 23.89/3.67 cnf(c_603,plain,
% 23.89/3.67 ('fun_app$b'('power$'('zero$'),'nat$'(2)) = 'zero$'),
% 23.89/3.67 inference(cnf_transformation,[],[f2628])).
% 23.89/3.67
% 23.89/3.67 cnf(c_688,plain,
% 23.89/3.67 (~$less_int(0,'fun_app$a'('of_nat$',X0_28))|$less_int(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0_28),X1_28)))),
% 23.89/3.67 inference(cnf_transformation,[],[f2717])).
% 23.89/3.67
% 23.89/3.67 cnf(c_693,plain,
% 23.89/3.67 ('fun_app$b'('power$'(X0_28),X1_28) != 'zero$'|$less_int(0,'fun_app$a'('of_nat$',X1_28))),
% 23.89/3.67 inference(cnf_transformation,[],[f2722])).
% 23.89/3.67
% 23.89/3.67 cnf(c_1042,plain,
% 23.89/3.67 (~$less_int('fun_app$a'('of_nat$','fun_app$b'('power$'(X0_28),X1_28)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0_28),X2_28)))|
% 23.89/3.67 ~$less_int(0,'fun_app$a'('of_nat$',X0_28))|$less_int('fun_app$a'('of_nat$',X1_28),'fun_app$a'('of_nat$',X2_28))),
% 23.89/3.67 inference(cnf_transformation,[],[f3085])).
% 23.89/3.67
% 23.89/3.67 cnf(c_1606,negated_conjecture,
% 23.89/3.67 ($less_int('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int(1,'fun_app$a'('of_nat$','n$')))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int(1,'fun_app$a'('of_nat$','n$')))))),'size$'('ys$'))))),
% 23.89/3.67 inference(theory_normalisation,
% 23.89/3.67 [status(thm)],
% 23.89/3.67 [c_86,c_71,c_72,c_82,c_83,c_53,c_54,c_64,c_65])).
% 23.89/3.67
% 23.89/3.67 cnf(c_21840,plain,
% 23.89/3.67 (~$less_int('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int(1,'fun_app$a'('of_nat$','n$')))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int(1,'fun_app$a'('of_nat$','n$')))))),'size$'('ys$'))))|
% 23.89/3.67 ~$less_int(0,'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int(1,'fun_app$a'('of_nat$','n$')))))))|
% 23.89/3.67 $less_int('fun_app$a'('of_nat$','n$'),'fun_app$a'('of_nat$','size$'('ys$')))),
% 23.89/3.67 inference(instantiation,[status(thm)],[c_1042])).
% 23.89/3.67
% 23.89/3.67 cnf(c_23475,plain,
% 23.89/3.67 ($less_int(X0_3,'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int(1,'fun_app$a'('of_nat$','n$')))))),'size$'('ys$'))))|
% 23.89/3.67 $less_int('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int(1,'fun_app$a'('of_nat$','n$')))))),'n$')),X0_3)),
% 23.89/3.67 inference(resolution,[status(thm)],[c_474,c_1606])).
% 23.89/3.67
% 23.89/3.67 cnf(c_23487,plain,
% 23.89/3.67 ($less_int(X0_3,'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int(1,'fun_app$a'('of_nat$','n$')))))),'size$'('ys$'))))|
% 23.89/3.67 $less_int('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int(1,'fun_app$a'('of_nat$','n$')))))),'n$')),X1_3)|
% 23.89/3.67 $less_int(X1_3,X0_3)),
% 23.89/3.67 inference(resolution,[status(thm)],[c_23475,c_474])).
% 23.89/3.67
% 23.89/3.67 cnf(c_23569,plain,
% 23.89/3.67 (~$less_int(X0_3,'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int(1,'fun_app$a'('of_nat$','n$')))))),'n$')))|
% 23.89/3.67 $less_int(X1_3,'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int(1,'fun_app$a'('of_nat$','n$')))))),'size$'('ys$'))))|
% 23.89/3.67 $less_int($sum_int(X0_3,1),X1_3)),
% 23.89/3.67 inference(resolution,[status(thm)],[c_23487,c_66])).
% 23.89/3.67
% 23.89/3.67 cnf(c_46968,plain,
% 23.89/3.67 ($less_int(0,'fun_app$a'('of_nat$','nat$'(2)))),
% 23.89/3.67 inference(resolution,[status(thm)],[c_693,c_603])).
% 23.89/3.67
% 23.89/3.67 cnf(c_63471,plain,
% 23.89/3.67 (~$less_int(0,'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int(1,'fun_app$a'('of_nat$','n$')))))))|
% 23.89/3.67 $less_int(X0_3,'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int(1,'fun_app$a'('of_nat$','n$')))))),'size$'('ys$'))))|
% 23.89/3.67 $less_int($sum_int(0,1),X0_3)),
% 23.89/3.67 inference(resolution,[status(thm)],[c_688,c_23569])).
% 23.89/3.67
% 23.89/3.67 cnf(c_63729,plain,
% 23.89/3.67 (~$less_int(0,'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum_int(1,'fun_app$a'('of_nat$','n$')))))))),
% 23.89/3.67 inference(global_subsumption_just,
% 23.89/3.67 [status(thm)],
% 23.89/3.67 [c_63471,c_87,c_1606,c_21840])).
% 23.89/3.67
% 23.89/3.67 cnf(c_63777,plain,
% 23.89/3.67 (~$less_int(0,'fun_app$a'('of_nat$','nat$'(2)))),
% 23.89/3.67 inference(resolution,[status(thm)],[c_63729,c_688])).
% 23.89/3.67
% 23.89/3.67 cnf(c_63778,plain,
% 23.89/3.67 ($false),
% 23.89/3.67 inference(prop_impl_just,[status(thm)],[c_63777,c_46968])).
% 23.89/3.67
% 23.89/3.67
% 23.89/3.67 % SZS output end CNFRefutation for theBenchmark.p
% 23.89/3.67
% 23.89/3.67
%------------------------------------------------------------------------------