%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC271-1 : 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 : n007.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 08:57:20 AM UTC 2026
% Result : Unsatisfiable 53.90s 13.21s
% Output : CNFRefutation 53.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 24 unt; 0 def)
% Number of atoms : 106 ( 8 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 127 ( 64 ~; 63 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 5 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_10,axiom,
~ totalorderedP(sk1),
file('theBenchmark.p',co1_10) ).
cnf(c_51,plain,
~ totalorderedP(sk1),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_8,axiom,
strictorderedP(sk3),
file('theBenchmark.p',co1_8) ).
cnf(c_53,plain,
strictorderedP(sk3),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_55,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_58,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(clause181,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( lt(VAR_1,VAR_3)
| ~ ssList(VAR_5)
| ~ strictorderedP(VAR_5)
| ~ ssItem(VAR_1)
| ~ ssItem(VAR_3)
| ~ ssList(VAR_0)
| ~ ssList(VAR_2)
| ~ ssList(VAR_4)
| app(app(VAR_0,cons(VAR_1,VAR_2)),cons(VAR_3,VAR_4)) != VAR_5 ),
file('theBenchmark.p',clause181) ).
cnf(c_62,plain,
( lt(B,D)
| ~ ssList(F)
| ~ strictorderedP(F)
| ~ ssItem(B)
| ~ ssItem(D)
| ~ ssList(A)
| ~ ssList(C)
| ~ ssList(E)
| app(app(A,cons(B,C)),cons(D,E)) != F ),
inference(clausify,[status(thm)],[clause181]) ).
fof(clause164,axiom,
! [VAR_0] :
( app(app(skaf66(VAR_0),cons(skaf64(VAR_0),skaf67(VAR_0))),cons(skaf65(VAR_0),skaf68(VAR_0))) = VAR_0
| totalorderedP(VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause164) ).
cnf(c_74,plain,
( app(app(skaf66(A),cons(skaf64(A),skaf67(A))),cons(skaf65(A),skaf68(A))) = A
| totalorderedP(A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause164]) ).
fof(clause103,axiom,
! [VAR_0,VAR_1] :
( leq(VAR_0,VAR_1)
| ~ ssItem(VAR_0)
| ~ ssItem(VAR_1)
| ~ lt(VAR_0,VAR_1) ),
file('theBenchmark.p',clause103) ).
cnf(c_133,plain,
( leq(A,B)
| ~ ssItem(A)
| ~ ssItem(B)
| ~ lt(A,B) ),
inference(clausify,[status(thm)],[clause103]) ).
fof(clause91,axiom,
! [VAR_0] :
( totalorderedP(VAR_0)
| ~ ssList(VAR_0)
| ~ leq(skaf64(VAR_0),skaf65(VAR_0)) ),
file('theBenchmark.p',clause91) ).
cnf(c_141,plain,
( totalorderedP(A)
| ~ ssList(A)
| ~ leq(skaf64(A),skaf65(A)) ),
inference(clausify,[status(thm)],[clause91]) ).
fof(clause31,axiom,
! [VAR_0] : ssItem(skaf64(VAR_0)),
file('theBenchmark.p',clause31) ).
cnf(c_190,plain,
ssItem(skaf64(A)),
inference(clausify,[status(thm)],[clause31]) ).
fof(clause30,axiom,
! [VAR_0] : ssItem(skaf65(VAR_0)),
file('theBenchmark.p',clause30) ).
cnf(c_191,plain,
ssItem(skaf65(A)),
inference(clausify,[status(thm)],[clause30]) ).
fof(clause29,axiom,
! [VAR_0] : ssList(skaf66(VAR_0)),
file('theBenchmark.p',clause29) ).
cnf(c_192,plain,
ssList(skaf66(A)),
inference(clausify,[status(thm)],[clause29]) ).
fof(clause28,axiom,
! [VAR_0] : ssList(skaf67(VAR_0)),
file('theBenchmark.p',clause28) ).
cnf(c_193,plain,
ssList(skaf67(A)),
inference(clausify,[status(thm)],[clause28]) ).
fof(clause27,axiom,
! [VAR_0] : ssList(skaf68(VAR_0)),
file('theBenchmark.p',clause27) ).
cnf(c_194,plain,
ssList(skaf68(A)),
inference(clausify,[status(thm)],[clause27]) ).
cnf(c_317,plain,
~ totalorderedP(sk3),
inference(paramod,[status(thm)],[c_55,c_51]) ).
cnf(c_16388,plain,
( app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3
| totalorderedP(sk3) ),
inference(resolve,[status(thm)],[c_74,c_58]) ).
cnf(c_956,plain,
app(app(skaf66(sk3),cons(skaf64(sk3),skaf67(sk3))),cons(skaf65(sk3),skaf68(sk3))) = sk3,
inference(resolve,[status(thm)],[c_317,c_16388]) ).
cnf(c_16389,plain,
( totalorderedP(sk3)
| ~ leq(skaf64(sk3),skaf65(sk3)) ),
inference(resolve,[status(thm)],[c_141,c_58]) ).
cnf(c_1161,plain,
~ leq(skaf64(sk3),skaf65(sk3)),
inference(resolve,[status(thm)],[c_317,c_16389]) ).
cnf(c_16390,plain,
( lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(sk3)
| ~ strictorderedP(sk3)
| ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(skaf67(sk3))
| ~ ssList(skaf68(sk3)) ),
inference(resolve,[status(thm)],[c_956,c_62]) ).
cnf(c_16391,plain,
( lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(sk3)
| ~ strictorderedP(sk3)
| ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf66(sk3))
| ~ ssList(skaf67(sk3)) ),
inference(resolve,[status(thm)],[c_194,c_16390]) ).
cnf(c_16392,plain,
( lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(sk3)
| ~ strictorderedP(sk3)
| ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3))
| ~ ssList(skaf66(sk3)) ),
inference(resolve,[status(thm)],[c_193,c_16391]) ).
cnf(c_16393,plain,
( lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(sk3)
| ~ strictorderedP(sk3)
| ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3)) ),
inference(resolve,[status(thm)],[c_192,c_16392]) ).
cnf(c_16394,plain,
( lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(sk3)
| ~ strictorderedP(sk3)
| ~ ssItem(skaf64(sk3)) ),
inference(resolve,[status(thm)],[c_191,c_16393]) ).
cnf(c_16395,plain,
( lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(sk3)
| ~ strictorderedP(sk3) ),
inference(resolve,[status(thm)],[c_190,c_16394]) ).
cnf(c_16396,plain,
( lt(skaf64(sk3),skaf65(sk3))
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_53,c_16395]) ).
cnf(c_16236,plain,
lt(skaf64(sk3),skaf65(sk3)),
inference(resolve,[status(thm)],[c_58,c_16396]) ).
cnf(c_16397,plain,
( leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf64(sk3))
| ~ ssItem(skaf65(sk3)) ),
inference(resolve,[status(thm)],[c_16236,c_133]) ).
cnf(c_16398,plain,
( leq(skaf64(sk3),skaf65(sk3))
| ~ ssItem(skaf64(sk3)) ),
inference(resolve,[status(thm)],[c_191,c_16397]) ).
cnf(c_16399,plain,
leq(skaf64(sk3),skaf65(sk3)),
inference(resolve,[status(thm)],[c_190,c_16398]) ).
cnf(c_16387,plain,
$false,
inference(resolve,[status(thm)],[c_1161,c_16399]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC271-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n007.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 12:37:44 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 3743464 was started by sandbox2 on n007,
% 0.11/5.39 % Sat Sep 26 12:37:44 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/5.40
% 0.14/5.40 % From the command line: assign(max_seconds, 300).
% 53.90/13.21
% 53.90/13.21 % given #500 (I,wt=55): 557 app(app(A,cons(B,C)),cons(D,C)) != C | -ssList(C) | -ssList(A) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B) | app(app(skaf61(C),cons(skaf59(C),skaf62(C))),cons(skaf60(C),skaf63(C))) = C. [factor(295,b,f)].
% 53.90/13.21
% 53.90/13.21 % given #1000 (T,wt=9): 1208 rearsegP(skaf42(A,B),nil). [resolve(168,a,163,a)].
% 53.90/13.21
% 53.90/13.21 % SZS status Unsatisfiable for theBenchmark
% 53.90/13.21
% 53.90/13.21 % Proof 1 at 5.69 (+ 1.94) seconds.
% 53.90/13.21 % Length of proof is 18.
% 53.90/13.21 % Level of proof is 4.
% 53.90/13.21 % Maximum clause weight is 38.000.
% 53.90/13.21 % Given clauses 1494.
% 53.90/13.21
% 53.90/13.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------