%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC070-1 : 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 : n010.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 08:56:44 AM UTC 2026
% Result : Unsatisfiable 91.66s 13.37s
% Output : CNFRefutation 91.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 73 ( 21 unt; 0 def)
% Number of atoms : 177 ( 45 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 207 ( 103 ~; 104 |; 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 : 46 ( 4 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_12,axiom,
( frontsegP(sk4,sk3)
| nil = sk3 ),
file('theBenchmark.p',co1_12) ).
cnf(c_51,plain,
( frontsegP(sk4,sk3)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_52,plain,
( frontsegP(sk4,sk3)
| sk3 = nil ),
inference(copy,[status(thm)],[c_51]) ).
fof(co1_11,axiom,
( neq(sk3,nil)
| nil = sk3 ),
file('theBenchmark.p',co1_11) ).
cnf(c_53,plain,
( neq(sk3,nil)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_54,plain,
( neq(sk3,nil)
| sk3 = nil ),
inference(copy,[status(thm)],[c_53]) ).
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,
( nil != sk1
| nil != sk2 ),
file('theBenchmark.p',co1_8) ).
cnf(c_59,plain,
( nil != sk1
| nil != sk2 ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_14352,plain,
( nil != sk1
| sk2 != nil ),
inference(copy,[status(thm)],[c_59]) ).
cnf(c_60,plain,
( sk1 != nil
| sk2 != nil ),
inference(copy,[status(thm)],[c_14352]) ).
fof(co1_7,axiom,
! [VAR_0] :
( ~ segmentP(sk1,VAR_0)
| ~ segmentP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_7) ).
cnf(c_61,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_62,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_63,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_64,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_65,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_75,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
fof(clause154,axiom,
! [VAR_0,VAR_1,VAR_2] :
( frontsegP(VAR_0,VAR_2)
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_2)
| ~ frontsegP(VAR_1,VAR_2)
| ~ frontsegP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause154) ).
cnf(c_91,plain,
( frontsegP(A,C)
| ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ~ frontsegP(B,C)
| ~ frontsegP(A,B) ),
inference(clausify,[status(thm)],[clause154]) ).
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_112,plain,
( app(B,skaf45(A,B)) = A
| ~ ssList(A)
| ~ ssList(B)
| ~ frontsegP(A,B) ),
inference(clausify,[status(thm)],[clause132]) ).
fof(clause83,axiom,
! [VAR_0] :
( frontsegP(nil,VAR_0)
| ~ ssList(VAR_0)
| nil != VAR_0 ),
file('theBenchmark.p',clause83) ).
cnf(c_153,plain,
( frontsegP(nil,A)
| ~ ssList(A)
| nil != A ),
inference(clausify,[status(thm)],[clause83]) ).
fof(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_160,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
fof(clause60,axiom,
! [VAR_0] :
( frontsegP(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause60) ).
cnf(c_168,plain,
( frontsegP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause60]) ).
fof(clause57,axiom,
! [VAR_0] :
( segmentP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause57) ).
cnf(c_171,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_177,plain,
ssList(skaf45(A,B)),
inference(clausify,[status(thm)],[clause51]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_220,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_14353,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_63,c_61]) ).
cnf(c_324,plain,
( ~ segmentP(sk3,A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_62,c_14353]) ).
cnf(c_14354,plain,
( sk1 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_63,c_60]) ).
cnf(c_325,plain,
( sk3 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_62,c_14354]) ).
cnf(c_897,plain,
( segmentP(sk4,B)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != sk4 ),
inference(resolve,[status(thm)],[c_75,c_64]) ).
cnf(c_14355,plain,
( frontsegP(sk4,sk3)
| nil = sk3 ),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_14356,plain,
( frontsegP(sk4,sk3)
| frontsegP(nil,sk3)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_153,c_14355]) ).
cnf(c_1256,plain,
( frontsegP(sk4,sk3)
| frontsegP(nil,sk3) ),
inference(resolve,[status(thm)],[c_65,c_14356]) ).
cnf(c_1282,plain,
app(nil,sk3) = sk3,
inference(resolve,[status(thm)],[c_160,c_65]) ).
cnf(c_1289,plain,
frontsegP(sk4,nil),
inference(resolve,[status(thm)],[c_168,c_64]) ).
cnf(c_1294,plain,
segmentP(sk3,sk3),
inference(resolve,[status(thm)],[c_171,c_65]) ).
cnf(c_14357,plain,
( ~ segmentP(sk3,sk3)
| ~ segmentP(sk4,sk3)
| ~ neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_324,c_65]) ).
cnf(c_7992,plain,
( ~ segmentP(sk4,sk3)
| ~ neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1294,c_14357]) ).
cnf(c_8000,plain,
( neq(sk3,nil)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_325,c_58]) ).
cnf(c_14358,plain,
( frontsegP(A,sk3)
| ~ ssList(A)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ frontsegP(A,nil)
| frontsegP(sk4,sk3) ),
inference(resolve,[status(thm)],[c_1256,c_91]) ).
cnf(c_14359,plain,
( frontsegP(A,sk3)
| ~ ssList(A)
| ~ ssList(nil)
| ~ frontsegP(A,nil)
| frontsegP(sk4,sk3) ),
inference(resolve,[status(thm)],[c_65,c_14358]) ).
cnf(c_10305,plain,
( frontsegP(A,sk3)
| ~ ssList(A)
| ~ frontsegP(A,nil)
| frontsegP(sk4,sk3) ),
inference(resolve,[status(thm)],[c_220,c_14359]) ).
cnf(c_14360,plain,
( ~ ssList(sk4)
| ~ frontsegP(sk4,nil)
| frontsegP(sk4,sk3) ),
inference(factor,[status(thm)],[c_10305]) ).
cnf(c_14361,plain,
( ~ ssList(sk4)
| frontsegP(sk4,sk3) ),
inference(resolve,[status(thm)],[c_1289,c_14360]) ).
cnf(c_10316,plain,
frontsegP(sk4,sk3),
inference(resolve,[status(thm)],[c_64,c_14361]) ).
cnf(c_14362,plain,
( app(sk3,skaf45(sk4,sk3)) = sk4
| ~ ssList(sk4)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_10316,c_112]) ).
cnf(c_14363,plain,
( app(sk3,skaf45(sk4,sk3)) = sk4
| ~ ssList(sk4) ),
inference(resolve,[status(thm)],[c_65,c_14362]) ).
cnf(c_10327,plain,
app(sk3,skaf45(sk4,sk3)) = sk4,
inference(resolve,[status(thm)],[c_64,c_14363]) ).
cnf(c_14364,plain,
( neq(sk3,nil)
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_8000,c_54]) ).
cnf(c_12179,plain,
neq(sk3,nil),
inference(copy,[status(thm)],[c_14364]) ).
cnf(c_12180,plain,
~ segmentP(sk4,sk3),
inference(resolve,[status(thm)],[c_12179,c_7992]) ).
cnf(c_14365,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(paramod,[status(thm)],[c_1282,c_897]) ).
cnf(c_14366,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(resolve,[status(thm)],[c_220,c_14365]) ).
cnf(c_14367,plain,
( segmentP(sk4,sk3)
| ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(resolve,[status(thm)],[c_65,c_14366]) ).
cnf(c_13368,plain,
( ~ ssList(A)
| app(sk3,A) != sk4 ),
inference(resolve,[status(thm)],[c_12180,c_14367]) ).
cnf(c_14350,plain,
app(sk3,skaf45(A,B)) != sk4,
inference(resolve,[status(thm)],[c_13368,c_177]) ).
cnf(c_14351,plain,
$false,
inference(resolve,[status(thm)],[c_14350,c_10327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC070-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n010.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 12:11:30 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 3256222 was started by sandbox2 on n010,
% 0.11/0.38 % Sat Sep 26 12:11:30 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 91.66/13.37
% 91.66/13.37 % given #500 (I,wt=37): 563 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(300,e,f),merge(g)].
% 91.66/13.37
% 91.66/13.37 % given #1000 (F,wt=9): 9423 -neq(skaf61(A),skaf61(A)). [resolve(390,b,194,a)].
% 91.66/13.37
% 91.66/13.37 % SZS status Unsatisfiable for theBenchmark
% 91.66/13.37
% 91.66/13.37 % Proof 1 at 3.69 (+ 1.18) seconds.
% 91.66/13.37 % Length of proof is 39.
% 91.66/13.37 % Level of proof is 8.
% 91.66/13.37 % Maximum clause weight is 26.000.
% 91.66/13.37 % Given clauses 1272.
% 91.66/13.37
% 91.66/13.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------