%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV823-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 09:09:10 AM UTC 2026
% Result : Unsatisfiable 44.29s 6.85s
% Output : CNFRefutation 44.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 19 unt; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 12 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 92 ( 33 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_nat__add__commute_0,axiom,
! [VAR_0,VAR_1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_0),VAR_1) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_1),VAR_0),
file('theBenchmark.p',cls_nat__add__commute_0) ).
cnf(c_258,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),
inference(clausify,[status(thm)],[cls_nat__add__commute_0]) ).
fof(cls_add__eq__self__zero_0,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_0),VAR_1) != VAR_0 ),
file('theBenchmark.p',cls_add__eq__self__zero_0) ).
cnf(c_311,plain,
( B = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != A ),
inference(clausify,[status(thm)],[cls_add__eq__self__zero_0]) ).
cnf(c_312,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = B
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != A ),
inference(copy,[status(thm)],[c_311]) ).
fof(cls_Suc__neq__Zero_0,axiom,
! [VAR_0] : hAPP(c_Suc,VAR_0) != c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_Suc__neq__Zero_0) ).
cnf(c_640,plain,
hAPP(c_Suc,A) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(clausify,[status(thm)],[cls_Suc__neq__Zero_0]) ).
fof(cls_add__Suc__right_0,axiom,
! [VAR_0,VAR_1] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_0),hAPP(c_Suc,VAR_1)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),VAR_0),VAR_1)),
file('theBenchmark.p',cls_add__Suc__right_0) ).
cnf(c_700,plain,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,B)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),
inference(clausify,[status(thm)],[cls_add__Suc__right_0]) ).
fof(cls_COMBB__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(hAPP(c_COMBB(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),VAR_5) = hAPP(VAR_3,hAPP(VAR_4,VAR_5)),
file('theBenchmark.p',cls_COMBB__def_0) ).
cnf(c_804,plain,
hAPP(hAPP(hAPP(c_COMBB(A,B,C),D),E),F) = hAPP(D,hAPP(E,F)),
inference(clausify,[status(thm)],[cls_COMBB__def_0]) ).
fof(cls_COMBC__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(hAPP(c_COMBC(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),VAR_5) = hAPP(hAPP(VAR_3,VAR_5),VAR_4),
file('theBenchmark.p',cls_COMBC__def_0) ).
cnf(c_805,plain,
hAPP(hAPP(hAPP(c_COMBC(A,B,C),D),E),F) = hAPP(hAPP(D,F),E),
inference(clausify,[status(thm)],[cls_COMBC__def_0]) ).
fof(cls_COMBS__def_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] : hAPP(hAPP(hAPP(c_COMBS(VAR_0,VAR_1,VAR_2),VAR_3),VAR_4),VAR_5) = hAPP(hAPP(VAR_3,VAR_5),hAPP(VAR_4,VAR_5)),
file('theBenchmark.p',cls_COMBS__def_0) ).
cnf(c_806,plain,
hAPP(hAPP(hAPP(c_COMBS(A,B,C),D),E),F) = hAPP(hAPP(D,F),hAPP(E,F)),
inference(clausify,[status(thm)],[cls_COMBS__def_0]) ).
cnf(c_10658,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(c_Suc,B)
| hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) != A ),
inference(paramod,[status(thm)],[c_700,c_312]) ).
cnf(c_10659,plain,
( hAPP(c_Suc,B) = c_HOL_Ozero__class_Ozero(tc_nat)
| hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) != A ),
inference(copy,[status(thm)],[c_10658]) ).
cnf(c_3079,plain,
hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) != A,
inference(resolve,[status(thm)],[c_640,c_10659]) ).
cnf(c_5869,plain,
hAPP(hAPP(hAPP(c_COMBC(A,B,C),hAPP(c_COMBB(D,E,F),V6)),V7),V8) = hAPP(V6,hAPP(V8,V7)),
inference(paramod,[status(thm)],[c_805,c_804]) ).
cnf(c_8655,plain,
hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) != B,
inference(paramod,[status(thm)],[c_258,c_3079]) ).
cnf(c_8672,plain,
hAPP(c_Suc,hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_HOL_Oplus__class_Oplus(tc_nat)),D),E)) != hAPP(D,E),
inference(paramod,[status(thm)],[c_806,c_8655]) ).
cnf(c_10660,plain,
hAPP(c_Suc,hAPP(hAPP(hAPP(c_COMBS(A,B,C),c_HOL_Oplus__class_Oplus(tc_nat)),hAPP(hAPP(c_COMBS(D,E,F),V6),V7)),V8)) != hAPP(hAPP(V6,V8),hAPP(V7,V8)),
inference(paramod,[status(thm)],[c_806,c_8672]) ).
cnf(c_10656,plain,
hAPP(hAPP(A,B),hAPP(C,B)) != hAPP(c_Suc,hAPP(hAPP(hAPP(c_COMBS(D,E,F),c_HOL_Oplus__class_Oplus(tc_nat)),hAPP(hAPP(c_COMBS(V6,V7,V8),A),C)),B)),
inference(copy,[status(thm)],[c_10660]) ).
cnf(c_10657,plain,
$false,
inference(resolve,[status(thm)],[c_10656,c_5869]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV823-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n014.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 15:01:03 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 3453953 was started by sandbox on n014,
% 0.08/0.37 % Sat Sep 26 15:01:03 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.42
% 0.08/0.42 % From the command line: assign(max_seconds, 300).
% 44.29/6.85
% 44.29/6.85 % given #500 (I,wt=6): 815 class_Orderings_Opreorder(tc_fun(A,B)) | -class_Orderings_Opreorder(B) # tptp_name(clsarity_fun__Orderings_Opreorder) # clausal_fof(1). [assumption].
% 44.29/6.85
% 44.29/6.85 % SZS status Unsatisfiable for theBenchmark
% 44.29/6.85
% 44.29/6.85 % Proof 1 at 5.72 (+ 0.62) seconds.
% 44.29/6.85 % Length of proof is 14.
% 44.29/6.85 % Level of proof is 6.
% 44.29/6.85 % Maximum clause weight is 28.000.
% 44.29/6.85 % Given clauses 811.
% 44.29/6.85
% 44.29/6.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------