%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW297+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:09:51 AM UTC 2026
% Result : Theorem 12.99s 4.94s
% Output : Refutation 13.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 44
% Syntax : Number of formulae : 90 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 179 ( 115 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 1009 ( 18 ~; 0 |; 19 &; 902 @)
% ( 7 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 41 usr; 6 con; 0-6 aty)
% Number of variables : 373 ( 0 ^; 370 !; 3 ?; 373 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_fun1_decl,type,
v_fun1: $i > $i > $o ).
thf(c_Natural_Oevaln_decl,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(v_com_decl,type,
v_com: $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Nat_OSuc_decl,type,
c_Nat_OSuc: $i ).
thf(v_n_decl,type,
v_n: $i ).
thf(v_fun2_decl,type,
v_fun2: $i > $i > $o ).
thf(c_Product__Type_OPair_decl,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_Com_Ocom_OSemi_decl,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_List_Orotate1_decl,type,
c_List_Orotate1: $i > $i ).
thf(c_List_Orotate_decl,type,
c_List_Orotate: $i > $i > $i ).
thf(c_Com_Ocom_OSKIP_decl,type,
c_Com_Ocom_OSKIP: $i ).
thf(c_Nitpick_Opair__box_OPairBox_decl,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__empty_decl,type,
c_New__Random__Sequence_Opos__empty: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__empty_decl,type,
c_New__DSequence_Opos__empty: $i > $i ).
thf(c_Typedef_Otype__definition_decl,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(c_Nitpick_Opair__box_Opair__box__rec_decl,type,
c_Nitpick_Opair__box_Opair__box__rec: $i > $i > $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Oneg__single_decl,type,
c_New__Random__Sequence_Oneg__single: $i > $i ).
thf(c_New__DSequence_Oneg__single_decl,type,
c_New__DSequence_Oneg__single: $i > $i > $i ).
thf(c_FunDef_Oreduction__pair_decl,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(c_FunDef_Orp__inv__image_decl,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(c_Lazy__Sequence_Ohb__single_decl,type,
c_Lazy__Sequence_Ohb__single: $i > $i > $i ).
thf(c_Nitpick_Opair__box_Opair__box__case_decl,type,
c_Nitpick_Opair__box_Opair__box__case: $i > $i > $i > $i > $i > $i ).
thf(c_Nat_Onat_Onat__rec_decl,type,
c_Nat_Onat_Onat__rec: $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__single_decl,type,
c_New__Random__Sequence_Opos__single: $i > $i ).
thf(c_New__DSequence_Opos__single_decl,type,
c_New__DSequence_Opos__single: $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__not__random__dseq_decl,type,
c_New__Random__Sequence_Opos__not__random__dseq: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__not__seq_decl,type,
c_New__DSequence_Opos__not__seq: $i > $i ).
thf(c_Product__Type_Oprod_Oprod__rec_decl,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Nat_Onat_Onat__case_decl,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofolding__one__idem_decl,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(class_Rings_Osemiring__1_decl,type,
class_Rings_Osemiring__1: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat__aux_decl,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Osingle_decl,type,
c_Lazy__Sequence_Osingle: $i > $i ).
thf(c_New__Random__Sequence_Opos__union_decl,type,
c_New__Random__Sequence_Opos__union: $i > $i > $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__union_decl,type,
c_New__DSequence_Opos__union: $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Oempty_decl,type,
c_Lazy__Sequence_Oempty: $i > $i ).
thf(c_Int_ORep__Integ_decl,type,
c_Int_ORep__Integ: $i ).
thf(c_Lazy__Sequence_Oappend_decl,type,
c_Lazy__Sequence_Oappend: $i > $i > $i > $i ).
thf(c_Power_Opower_Opower_decl,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofolding__image__simple__idem_decl,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_Com_Ocom_OSemi ) )
= ( A @ ( B @ c_Com_Ocom_OSemi ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I3_J) ).
thf(69,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ c_Com_Ocom_OSemi ) )
= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ) )
& ( ( ( C @ ( D @ c_Com_Ocom_OSemi ) )
= ( A @ ( B @ c_Com_Ocom_OSemi ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_New__DSequence_Opos__single ) @ hAPP ) )
= ( B @ ( C @ c_Lazy__Sequence_Osingle @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
thf(179,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_New__DSequence_Opos__single ) @ hAPP ) )
= ( B @ ( C @ c_Lazy__Sequence_Osingle @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(41,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I1_J) ).
thf(221,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( A @ ( A @ ( E @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(229,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( A @ ( A @ ( E @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(166,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I12_J) ).
thf(86,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( A @ ( A @ ( C @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(172,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( A @ ( A @ ( C @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_FunDef_Oreduction__pair ) )
=> ( A @ ( C @ ( B @ ( D @ c_FunDef_Orp__inv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_FunDef_Oreduction__pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
thf(123,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_FunDef_Oreduction__pair ) )
=> ( A @ ( C @ ( B @ ( D @ c_FunDef_Orp__inv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_FunDef_Oreduction__pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) )
=> ~ ! [F: $i] :
( ( F @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) )
=> ~ ( A @ ( B @ ( F @ ( D @ c_Natural_Oevaln ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I4_J) ).
thf(182,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) )
=> ~ ! [F: $i] :
( ( F @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) )
=> ~ ( A @ ( B @ ( F @ ( D @ c_Natural_Oevaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__Random__Sequence_Opos__empty ) ) ) )
= ( D @ c_New__DSequence_Opos__empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__empty__def) ).
thf(104,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__Random__Sequence_Opos__empty ) ) ) )
= ( D @ c_New__DSequence_Opos__empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_New__Random__Sequence_Opos__union ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ ( E @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ c_New__DSequence_Opos__union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__union__def) ).
thf(186,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_New__Random__Sequence_Opos__union ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ ( E @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ c_New__DSequence_Opos__union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Orotate1 @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__Suc) ).
thf(207,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Orotate1 @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__Random__Sequence_Opos__not__random__dseq ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ c_New__DSequence_Opos__not__seq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__not__random__dseq__def) ).
thf(151,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__Random__Sequence_Opos__not__random__dseq ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ c_New__DSequence_Opos__not__seq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) ) )
= ( A @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(163,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) ) )
= ( A @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Natural_Oevaln ) ) ) )
=> ( ( A @ ( D @ ( C @ ( B @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OSemi) ).
thf(170,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Natural_Oevaln ) ) ) )
=> ( ( A @ ( D @ ( C @ ( B @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(12,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OSkip) ).
thf(115,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_New__Random__Sequence_Oneg__single @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( E @ c_New__DSequence_Oneg__single ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__single__def) ).
thf(120,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_New__Random__Sequence_Oneg__single @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( E @ c_New__DSequence_Oneg__single ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(52,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_New__DSequence_Oneg__single ) @ hAPP ) )
= ( B @ ( C @ c_Lazy__Sequence_Ohb__single ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
thf(125,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_New__DSequence_Oneg__single ) @ hAPP ) )
= ( B @ ( C @ c_Lazy__Sequence_Ohb__single ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(196,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I1_J) ).
thf(157,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) )
<=> ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ c_Natural_Oevaln ) ) ) )
& ( F @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I4_J) ).
thf(189,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ c_Natural_Oevaln ) ) ) )
& ( F @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) )
=> ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ c_Natural_Oevaln ) ) ) )
& ( F @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(1,conjecture,
( ! [A: $i,B: $i] :
( ( B @ ( A @ v_fun1 ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( v_com @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_fun2 ) ) ) )
=> ! [A: $i,B: $i] :
( ( B @ ( A @ v_fun1 ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( B @ ( v_com @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_fun2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $i] :
( ( B @ ( A @ v_fun1 ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( v_com @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_fun2 ) ) ) )
=> ! [A: $i,B: $i] :
( ( B @ ( A @ v_fun1 ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( B @ ( v_com @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_fun2 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(46,plain,
~ ( ! [A: $i,B: $i] :
( ( B @ ( A @ v_fun1 ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( v_com @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_fun2 ) ) ) )
=> ! [A: $i,B: $i] :
( ( B @ ( A @ v_fun1 ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( B @ ( v_com @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_fun2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(233,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).
thf(117,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(160,plain,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( F @ ( E @ hAPP ) )
= ( F @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) @ ( A @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_def__nat__rec__Suc) ).
thf(137,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( F @ ( E @ hAPP ) )
= ( F @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) @ ( A @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__case ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
thf(134,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__case ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__Suc) ).
thf(128,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).
thf(176,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(59,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) @ ( A @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__rec__Suc) ).
thf(204,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) @ ( A @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_New__Random__Sequence_Opos__single @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( E @ c_New__DSequence_Opos__single ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__single__def) ).
thf(140,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_New__Random__Sequence_Opos__single @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( E @ c_New__DSequence_Opos__single ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Int_ORep__Integ @ hAPP ) )
= ( A @ ( c_Int_ORep__Integ @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(213,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( c_Int_ORep__Integ @ hAPP ) )
= ( A @ ( c_Int_ORep__Integ @ hAPP ) ) ) )
& ( ( ( B @ ( c_Int_ORep__Integ @ hAPP ) )
= ( A @ ( c_Int_ORep__Integ @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(18,axiom,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(130,plain,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__DSequence_Opos__union ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( D @ c_Lazy__Sequence_Oappend ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__union__def) ).
thf(223,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__DSequence_Opos__union ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( D @ c_Lazy__Sequence_Oappend ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
thf(226,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(154,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( ( B @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(143,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) ) ) )
& ( ( ( B @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_New__DSequence_Opos__empty @ hAPP ) )
= ( B @ c_Lazy__Sequence_Oempty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
thf(210,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_New__DSequence_Opos__empty @ hAPP ) )
= ( B @ c_Lazy__Sequence_Oempty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I13_J) ).
thf(107,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Orotate1 @ hAPP ) )
= ( A @ ( C @ c_List_Orotate1 @ hAPP ) @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__rotate__swap) ).
thf(83,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Orotate1 @ hAPP ) )
= ( A @ ( C @ c_List_Orotate1 @ hAPP ) @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) )
= ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).
thf(90,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) )
= ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) )
= ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( A @ ( D @ hAPP ) @ ( C @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(111,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( A @ ( D @ hAPP ) @ ( C @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(236,plain,
$false,
inference(e,[status(thm)],[69,179,221,229,166,86,172,123,182,104,186,207,151,163,170,115,120,52,125,196,157,189,46,233,117,160,137,134,128,176,59,204,140,213,130,223,226,154,143,210,107,83,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW297+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.42 % Computer : n002.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 15:39:20 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/1.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 4.25/2.00 % [INFO] Parsing done (985ms).
% 4.25/2.01 % [INFO] Running in sequential loop mode.
% 5.39/2.40 % [INFO] eprover registered as external prover.
% 5.39/2.41 % [INFO] Scanning for conjecture ...
% 8.25/3.19 % [INFO] Found a conjecture (or negated_conjecture) and 5224 axioms. Running axiom selection ...
% 9.91/3.85 % [INFO] Axiom selection finished. Selected 43 axioms (removed 5181 axioms).
% 10.17/3.94 % [INFO] Problem is first-order (TPTP FOF).
% 10.17/3.95 % [INFO] Type checking passed.
% 10.17/3.96 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 12.99/4.94 % External prover 'e' found a proof!
% 12.99/4.94 % [INFO] Killing All external provers ...
% 12.99/4.94 % Time passed: 4380ms (effective reasoning time: 2923ms)
% 12.99/4.94 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 12.99/4.94 % Axioms used in derivation (43): fact_pos__union__def, fact_nat__rec__Suc, fact_New__DSequence_Oneg__single__def, fact_pos__single__def, fact_Pair__inject, fact_n__not__Suc__n, fact_Pair__eq, fact_type__definition_ORep__inverse, fact_prod_Orecs, fact_pair__box_Oinject, fact_neg__single__def, fact_evaln__Suc, fact_nat_Oinject, fact_com_Osimps_I3_J, fact_com_Osimps_I13_J, fact_pos__empty__def, fact_Rep__Integ__inject, fact_evaln_OSkip, fact_evaln_OSemi, fact_com_Osimps_I12_J, fact_folding__one__idem_Oidem, fact_of__nat__aux_Osimps_I2_J, fact_rp__inv__image__rp, fact_pair__box_Orecs, fact_Suc__inject, fact_ext, fact_New__DSequence_Opos__empty__def, fact_evaln__elim__cases_I4_J, fact_nat__case__Suc, fact_rotate__Suc, fact_power_Opower_Opower__Suc, fact_evaln_Oequations_I4_J, fact_New__DSequence_Opos__single__def, fact_type__definition_ORep__inject, fact_New__DSequence_Opos__union__def, fact_pair__box_Osimps_I2_J, fact_Suc__n__not__n, fact_pos__not__random__dseq__def, fact_folding__image__simple__idem_Oidem, fact_def__nat__rec__Suc, fact_evaln_Oequations_I1_J, fact_rotate1__rotate__swap, fact_evaln__elim__cases_I1_J
% 12.99/4.94 % No. of inferences in proof: 90
% 12.99/4.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4380 ms resp. 2923 ms w/o parsing
% 13.50/5.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.50/5.03 % [INFO] Killing All external provers ...
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