%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC085-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 08:56:46 AM UTC 2026
% Result : Unsatisfiable 89.77s 13.49s
% Output : CNFRefutation 89.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 23 unt; 0 def)
% Number of atoms : 134 ( 35 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 157 ( 81 ~; 76 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 4 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_10,axiom,
( frontsegP(sk4,sk3)
| nil = sk4 ),
file('theBenchmark.p',co1_10) ).
cnf(c_55,plain,
( frontsegP(sk4,sk3)
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_56,plain,
( frontsegP(sk4,sk3)
| sk4 = nil ),
inference(copy,[status(thm)],[c_55]) ).
fof(co1_9,axiom,
( neq(sk3,nil)
| nil = sk4 ),
file('theBenchmark.p',co1_9) ).
cnf(c_57,plain,
( neq(sk3,nil)
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_58,plain,
( neq(sk3,nil)
| sk4 = nil ),
inference(copy,[status(thm)],[c_57]) ).
fof(co1_8,axiom,
! [VAR_0] :
( ~ segmentP(sk1,VAR_0)
| ~ segmentP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_8) ).
cnf(c_59,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
neq(sk2,nil),
file('theBenchmark.p',co1_7) ).
cnf(c_60,plain,
neq(sk2,nil),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_61,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_62,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_63,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_64,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(clause173,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( segmentP(VAR_3,VAR_1)
| ~ ssList(VAR_3)
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ ssList(VAR_2)
| app(app(VAR_0,VAR_1),VAR_2) != VAR_3 ),
file('theBenchmark.p',clause173) ).
cnf(c_74,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
fof(clause132,axiom,
! [VAR_0,VAR_1] :
( app(VAR_1,skaf45(VAR_0,VAR_1)) = VAR_0
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ frontsegP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause132) ).
cnf(c_111,plain,
( app(B,skaf45(A,B)) = A
| ~ ssList(A)
| ~ ssList(B)
| ~ frontsegP(A,B) ),
inference(clausify,[status(thm)],[clause132]) ).
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_127,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
fof(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_159,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
fof(clause57,axiom,
! [VAR_0] :
( segmentP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause57) ).
cnf(c_170,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause57]) ).
fof(clause51,axiom,
! [VAR_0,VAR_1] : ssList(skaf45(VAR_0,VAR_1)),
file('theBenchmark.p',clause51) ).
cnf(c_176,plain,
ssList(skaf45(A,B)),
inference(clausify,[status(thm)],[clause51]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_219,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_14900,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_62,c_59]) ).
cnf(c_323,plain,
( ~ segmentP(sk3,A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_61,c_14900]) ).
cnf(c_324,plain,
neq(sk4,nil),
inference(paramod,[status(thm)],[c_62,c_60]) ).
cnf(c_896,plain,
( segmentP(sk4,B)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != sk4 ),
inference(resolve,[status(thm)],[c_74,c_63]) ).
cnf(c_14901,plain,
( sk4 = nil
| app(sk3,skaf45(sk4,sk3)) = sk4
| ~ ssList(sk4)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_111,c_56]) ).
cnf(c_14902,plain,
( sk4 = nil
| app(sk3,skaf45(sk4,sk3)) = sk4
| ~ ssList(sk4) ),
inference(resolve,[status(thm)],[c_64,c_14901]) ).
cnf(c_1141,plain,
( sk4 = nil
| app(sk3,skaf45(sk4,sk3)) = sk4 ),
inference(resolve,[status(thm)],[c_63,c_14902]) ).
cnf(c_14903,plain,
( neq(sk3,nil)
| ~ ssList(sk4)
| ~ ssList(nil)
| ~ neq(sk4,nil) ),
inference(resolve,[status(thm)],[c_127,c_58]) ).
cnf(c_14904,plain,
( neq(sk3,nil)
| ~ ssList(sk4)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_324,c_14903]) ).
cnf(c_14905,plain,
( neq(sk3,nil)
| ~ ssList(sk4) ),
inference(resolve,[status(thm)],[c_219,c_14904]) ).
cnf(c_1188,plain,
neq(sk3,nil),
inference(resolve,[status(thm)],[c_63,c_14905]) ).
cnf(c_1246,plain,
app(nil,sk3) = sk3,
inference(resolve,[status(thm)],[c_159,c_64]) ).
cnf(c_1258,plain,
segmentP(sk3,sk3),
inference(resolve,[status(thm)],[c_170,c_64]) ).
cnf(c_14906,plain,
( ~ segmentP(sk3,sk3)
| ~ segmentP(sk4,sk3)
| ~ neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_323,c_64]) ).
cnf(c_14907,plain,
( ~ segmentP(sk3,sk3)
| ~ segmentP(sk4,sk3) ),
inference(resolve,[status(thm)],[c_1188,c_14906]) ).
cnf(c_7956,plain,
~ segmentP(sk4,sk3),
inference(resolve,[status(thm)],[c_1258,c_14907]) ).
cnf(c_14908,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_324,c_127]) ).
cnf(c_14909,plain,
( ~ ssList(sk4)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_219,c_14908]) ).
cnf(c_7958,plain,
sk4 != nil,
inference(resolve,[status(thm)],[c_63,c_14909]) ).
cnf(c_7973,plain,
app(sk3,skaf45(sk4,sk3)) = sk4,
inference(resolve,[status(thm)],[c_7958,c_1141]) ).
cnf(c_14910,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(paramod,[status(thm)],[c_1246,c_896]) ).
cnf(c_14911,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(resolve,[status(thm)],[c_219,c_14910]) ).
cnf(c_14912,plain,
( segmentP(sk4,sk3)
| ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(resolve,[status(thm)],[c_64,c_14911]) ).
cnf(c_13038,plain,
( ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(resolve,[status(thm)],[c_7956,c_14912]) ).
cnf(c_14898,plain,
app(sk3,skaf45(A,B)) != sk4,
inference(resolve,[status(thm)],[c_13038,c_176]) ).
cnf(c_14899,plain,
$false,
inference(resolve,[status(thm)],[c_14898,c_7973]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC085-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 12:18:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1764765 was started by sandbox on n001,
% 0.09/0.36 % Sat Sep 26 12:18:43 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 89.77/13.49
% 89.77/13.49 % given #500 (I,wt=37): 562 app(app(A,cons(B,C)),cons(B,D)) != A | -ssList(D) | -ssList(C) | -ssList(A) | -ssItem(B) | lt(B,B) | -lt(skaf59(A),skaf60(A)). [factor(299,e,f),merge(g)].
% 89.77/13.49
% 89.77/13.49 % given #1000 (F,wt=9): 9479 -neq(skaf77(A),skaf77(A)). [resolve(389,b,209,a)].
% 89.77/13.49
% 89.77/13.49 % SZS status Unsatisfiable for theBenchmark
% 89.77/13.49
% 89.77/13.49 % Proof 1 at 3.77 (+ 1.24) seconds.
% 89.77/13.49 % Length of proof is 30.
% 89.77/13.49 % Level of proof is 6.
% 89.77/13.49 % Maximum clause weight is 26.000.
% 89.77/13.49 % Given clauses 1283.
% 89.77/13.49
% 89.77/13.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------