%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT093-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 08:28:29 AM UTC 2026
% Result : Unsatisfiable 166.43s 22.53s
% Output : CNFRefutation 166.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-5 aty)
% Number of variables : 93 ( 39 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_COMBS__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(c_COMBS(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),VAR_5) = hAPP(hAPP(VAR_0,VAR_5),hAPP(VAR_1,VAR_5)),
file('theBenchmark.p',cls_COMBS__def_0) ).
cnf(c_314,plain,
hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(A,F),hAPP(B,F)),
inference(clausify,[status(thm)],[cls_COMBS__def_0]) ).
fof(cls_COMBC__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(c_COMBC(VAR_0,VAR_1,VAR_2,VAR_3),VAR_4),VAR_5) = hAPP(hAPP(VAR_0,VAR_5),VAR_4),
file('theBenchmark.p',cls_COMBC__def_0) ).
cnf(c_315,plain,
hAPP(hAPP(c_COMBC(A,B,C,D),E),F) = hAPP(hAPP(A,F),E),
inference(clausify,[status(thm)],[cls_COMBC__def_0]) ).
fof(cls_COMBB__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(c_COMBB(VAR_0,VAR_1,VAR_2,VAR_3,VAR_4),VAR_5) = hAPP(VAR_0,hAPP(VAR_1,VAR_5)),
file('theBenchmark.p',cls_COMBB__def_0) ).
cnf(c_316,plain,
hAPP(c_COMBB(A,B,C,D,E),F) = hAPP(A,hAPP(B,F)),
inference(clausify,[status(thm)],[cls_COMBB__def_0]) ).
fof(cls_Suc__eq__plus1__left_0,axiom,
! [VAR_0] : c_Suc(VAR_0) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),VAR_0),
file('theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
cnf(c_442,plain,
c_Suc(A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),
inference(clausify,[status(thm)],[cls_Suc__eq__plus1__left_0]) ).
fof(cls_diff__add__inverse_0,axiom,
! [VAR_0,VAR_1] : hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_0),VAR_1)),VAR_0) = VAR_1,
file('theBenchmark.p',cls_diff__add__inverse_0) ).
cnf(c_510,plain,
hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),A) = B,
inference(clausify,[status(thm)],[cls_diff__add__inverse_0]) ).
fof(cls_n__not__Suc__n_0,axiom,
! [VAR_0] : VAR_0 != c_Suc(VAR_0),
file('theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(c_570,plain,
A != c_Suc(A),
inference(clausify,[status(thm)],[cls_n__not__Suc__n_0]) ).
cnf(c_10259,plain,
A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),
inference(paramod,[status(thm)],[c_442,c_570]) ).
cnf(c_571,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) != A,
inference(copy,[status(thm)],[c_10259]) ).
cnf(c_1135,plain,
hAPP(hAPP(c_COMBC(hAPP(c_COMBC(A,B,C,D),E),F,V6,V7),V8),V9) = hAPP(hAPP(hAPP(A,V9),E),V8),
inference(paramod,[status(thm)],[c_315,c_315]) ).
cnf(c_1145,plain,
hAPP(c_COMBB(A,c_COMBS(B,C,D,E,F),V6,V7,V8),V9) = hAPP(A,hAPP(hAPP(B,V9),hAPP(C,V9))),
inference(paramod,[status(thm)],[c_314,c_316]) ).
cnf(c_7620,plain,
hAPP(hAPP(c_COMBC(hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),A,B,C),D),E,F,V6),V7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),V8)) = hAPP(V8,V7),
inference(paramod,[status(thm)],[c_510,c_1135]) ).
cnf(c_10257,plain,
hAPP(c_COMBB(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_COMBS(A,B,C,D,E),F,V6,V7),V8) != hAPP(hAPP(A,V8),hAPP(B,V8)),
inference(paramod,[status(thm)],[c_1145,c_571]) ).
cnf(c_10260,plain,
hAPP(V8,V7) = hAPP(hAPP(c_COMBC(hAPP(c_COMBC(c_HOL_Ominus__class_Ominus(tc_nat),A,B,C),D),E,F,V6),V7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),V8)),
inference(copy,[status(thm)],[c_7620]) ).
cnf(c_10258,plain,
$false,
inference(resolve,[status(thm)],[c_10257,c_10260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT093-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n011.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 06:26:59 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.39 % Process 3975235 was started by sandbox2 on n011,
% 0.11/0.39 % Sat Sep 26 06:26:59 2026
% 0.11/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.46
% 0.11/0.46 % From the command line: assign(max_seconds, 300).
% 166.43/22.53
% 166.43/22.53 % given #500 (I,wt=76): 978 hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(212,a,214,a)].
% 166.43/22.53
% 166.43/22.53 % SZS status Unsatisfiable for theBenchmark
% 166.43/22.53
% 166.43/22.53 % Proof 1 at 5.19 (+ 0.67) seconds.
% 166.43/22.53 % Length of proof is 12.
% 166.43/22.53 % Level of proof is 3.
% 166.43/22.53 % Maximum clause weight is 66.000.
% 166.43/22.53 % Given clauses 752.
% 166.43/22.53
% 166.43/22.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------