%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC127-1 : 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 08:56:55 AM UTC 2026
% Result : Unsatisfiable 36.65s 5.85s
% Output : CNFRefutation 36.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 21 unt; 0 def)
% Number of atoms : 74 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 72 ( 39 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 13 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_10,axiom,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('theBenchmark.p',co1_10) ).
cnf(c_51,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_9,axiom,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
file('theBenchmark.p',co1_9) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| singletonP(sk3) ),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
segmentP(sk4,sk3),
file('theBenchmark.p',co1_8) ).
cnf(c_53,plain,
segmentP(sk4,sk3),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
neq(sk2,nil),
file('theBenchmark.p',co1_7) ).
cnf(c_54,plain,
neq(sk2,nil),
inference(clausify,[status(thm)],[co1_7]) ).
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_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_56,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_58,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_121,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_136,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause11,axiom,
~ singletonP(nil),
file('theBenchmark.p',clause11) ).
cnf(c_210,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[clause11]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_213,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_15130,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk3,nil) ),
inference(paramod,[status(thm)],[c_55,c_51]) ).
cnf(c_15131,plain,
( ~ segmentP(sk4,sk1)
| ~ neq(sk3,nil) ),
inference(paramod,[status(thm)],[c_56,c_15130]) ).
cnf(c_15132,plain,
( ~ segmentP(sk4,sk3)
| ~ neq(sk3,nil) ),
inference(paramod,[status(thm)],[c_55,c_15131]) ).
cnf(c_317,plain,
~ neq(sk3,nil),
inference(resolve,[status(thm)],[c_53,c_15132]) ).
cnf(c_318,plain,
neq(sk4,nil),
inference(paramod,[status(thm)],[c_56,c_54]) ).
cnf(c_582,plain,
singletonP(sk3),
inference(resolve,[status(thm)],[c_318,c_52]) ).
cnf(c_15133,plain,
( ~ ssList(A)
| ~ neq(A,sk3)
| A != sk3 ),
inference(resolve,[status(thm)],[c_121,c_58]) ).
cnf(c_1136,plain,
( ~ ssList(A)
| ~ neq(A,sk3)
| sk3 != A ),
inference(copy,[status(thm)],[c_15133]) ).
cnf(c_15134,plain,
( A = sk3
| neq(A,sk3)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_136,c_58]) ).
cnf(c_1150,plain,
( sk3 = A
| neq(A,sk3)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_15134]) ).
cnf(c_1152,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_136,c_58]) ).
cnf(c_12823,plain,
( ~ neq(nil,sk3)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_1136,c_213]) ).
cnf(c_14582,plain,
( sk3 = nil
| neq(nil,sk3) ),
inference(resolve,[status(thm)],[c_1150,c_213]) ).
cnf(c_15135,plain,
( singletonP(nil)
| neq(nil,sk3) ),
inference(paramod,[status(thm)],[c_14582,c_582]) ).
cnf(c_14623,plain,
neq(nil,sk3),
inference(resolve,[status(thm)],[c_210,c_15135]) ).
cnf(c_14624,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_14623,c_12823]) ).
cnf(c_15136,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1152,c_213]) ).
cnf(c_15137,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_317,c_15136]) ).
cnf(c_15129,plain,
$false,
inference(resolve,[status(thm)],[c_14624,c_15137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC127-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 12:18:36 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.15/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.38 % Process 1678928 was started by sandbox2 on n004,
% 0.15/0.38 % Sat Sep 26 12:18:36 2026
% 0.15/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.39
% 0.15/0.39 % From the command line: assign(max_seconds, 300).
% 36.65/5.85
% 36.65/5.85 % given #500 (I,wt=55): 559 app(app(A,cons(B,C)),cons(D,C)) != A | -ssList(C) | -ssList(A) | -ssItem(D) | -ssItem(B) | lt(B,D) | lt(D,B) | app(app(skaf61(A),cons(skaf59(A),skaf62(A))),cons(skaf60(A),skaf63(A))) = A. [factor(295,c,f)].
% 36.65/5.85
% 36.65/5.85 % given #1000 (T,wt=9): 1211 frontsegP(skaf42(A,B),nil). [resolve(168,a,161,a)].
% 36.65/5.85
% 36.65/5.85 % SZS status Unsatisfiable for theBenchmark
% 36.65/5.85
% 36.65/5.85 % Proof 1 at 4.06 (+ 1.25) seconds.
% 36.65/5.85 % Length of proof is 22.
% 36.65/5.85 % Level of proof is 5.
% 36.65/5.85 % Maximum clause weight is 12.000.
% 36.65/5.85 % Given clauses 1364.
% 36.65/5.85
% 36.65/5.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------