%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC275-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 08:57:21 AM UTC 2026
% Result : Unsatisfiable 101.37s 13.85s
% Output : CNFRefutation 101.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 22 unt; 0 def)
% Number of atoms : 81 ( 27 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 75 ( 39 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_10,axiom,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_10) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_9,axiom,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
file('theBenchmark.p',co1_9) ).
cnf(c_53,plain,
( ~ neq(sk4,nil)
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
( nil != sk4
| nil = sk3 ),
file('theBenchmark.p',co1_8) ).
cnf(c_54,plain,
( nil != sk4
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_16265,plain,
( nil != sk4
| sk3 = nil ),
inference(copy,[status(thm)],[c_54]) ).
cnf(c_55,plain,
( sk4 != nil
| sk3 = nil ),
inference(copy,[status(thm)],[c_16265]) ).
fof(co1_7,axiom,
~ totalorderedP(sk1),
file('theBenchmark.p',co1_7) ).
cnf(c_56,plain,
~ totalorderedP(sk1),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_57,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_59,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_60,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(clause115,axiom,
! [VAR_0,VAR_1] :
( ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ neq(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',clause115) ).
cnf(c_123,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
fof(clause100,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| neq(VAR_1,VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause100) ).
cnf(c_138,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause67,axiom,
! [VAR_0] :
( totalorderedP(cons(VAR_0,nil))
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',clause67) ).
cnf(c_158,plain,
( totalorderedP(cons(A,nil))
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[clause67]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_215,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
fof(clause4,axiom,
totalorderedP(nil),
file('theBenchmark.p',clause4) ).
cnf(c_216,plain,
totalorderedP(nil),
inference(clausify,[status(thm)],[clause4]) ).
cnf(c_319,plain,
~ totalorderedP(sk3),
inference(paramod,[status(thm)],[c_57,c_56]) ).
cnf(c_16266,plain,
( ~ ssList(A)
| ~ neq(A,sk3)
| A != sk3 ),
inference(resolve,[status(thm)],[c_123,c_60]) ).
cnf(c_1130,plain,
( ~ ssList(A)
| ~ neq(A,sk3)
| sk3 != A ),
inference(copy,[status(thm)],[c_16266]) ).
cnf(c_16267,plain,
( A = sk3
| neq(A,sk3)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_138,c_60]) ).
cnf(c_1144,plain,
( sk3 = A
| neq(A,sk3)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_16267]) ).
cnf(c_1147,plain,
( sk4 = A
| neq(sk4,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_138,c_59]) ).
cnf(c_12386,plain,
( ~ neq(nil,sk3)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_1130,c_215]) ).
cnf(c_14086,plain,
( sk3 = nil
| neq(nil,sk3) ),
inference(resolve,[status(thm)],[c_1144,c_215]) ).
cnf(c_16268,plain,
( ~ totalorderedP(nil)
| neq(nil,sk3) ),
inference(paramod,[status(thm)],[c_14086,c_319]) ).
cnf(c_14135,plain,
neq(nil,sk3),
inference(resolve,[status(thm)],[c_216,c_16268]) ).
cnf(c_14136,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_14135,c_12386]) ).
cnf(c_14157,plain,
sk4 != nil,
inference(resolve,[status(thm)],[c_14136,c_55]) ).
cnf(c_16269,plain,
( sk4 = nil
| neq(sk4,nil) ),
inference(resolve,[status(thm)],[c_1147,c_215]) ).
cnf(c_16087,plain,
neq(sk4,nil),
inference(resolve,[status(thm)],[c_14157,c_16269]) ).
cnf(c_16115,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_16087,c_53]) ).
cnf(c_16116,plain,
cons(sk5,nil) = sk3,
inference(resolve,[status(thm)],[c_16087,c_52]) ).
cnf(c_16270,plain,
totalorderedP(cons(sk5,nil)),
inference(resolve,[status(thm)],[c_16115,c_158]) ).
cnf(c_16271,plain,
totalorderedP(sk3),
inference(paramod,[status(thm)],[c_16116,c_16270]) ).
cnf(c_16264,plain,
$false,
inference(resolve,[status(thm)],[c_319,c_16271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC275-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 12:40:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 1725666 was started by sandbox2 on n004,
% 0.13/0.36 % Sat Sep 26 12:40:21 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 101.37/13.85
% 101.37/13.85 % given #500 (I,wt=55): 558 app(app(A,cons(B,A)),cons(C,A)) != D | -ssList(A) | -ssItem(C) | -ssItem(B) | -ssList(D) | lt(B,C) | lt(C,B) | app(app(skaf61(D),cons(skaf59(D),skaf62(D))),cons(skaf60(D),skaf63(D))) = D. [factor(297,b,c)].
% 101.37/13.85
% 101.37/13.85 % given #1000 (T,wt=9): 1203 rearsegP(skaf42(A,B),nil). [resolve(170,a,165,a)].
% 101.37/13.85
% 101.37/13.85 % SZS status Unsatisfiable for theBenchmark
% 101.37/13.85
% 101.37/13.85 % Proof 1 at 4.10 (+ 1.29) seconds.
% 101.37/13.85 % Length of proof is 26.
% 101.37/13.85 % Level of proof is 8.
% 101.37/13.85 % Maximum clause weight is 12.000.
% 101.37/13.85 % Given clauses 1475.
% 101.37/13.85
% 101.37/13.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------