%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC076-1 : 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 : n014.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 08:56:45 AM UTC 2026
% Result : Unsatisfiable 32.85s 5.26s
% Output : CNFRefutation 32.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 53 ( 23 unt; 0 def)
% Number of atoms : 111 ( 39 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 127 ( 69 ~; 58 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_15,axiom,
( nil != sk1
| nil != sk2 ),
file('theBenchmark.p',co1_15) ).
cnf(c_53,plain,
( nil != sk1
| nil != sk2 ),
inference(clausify,[status(thm)],[co1_15]) ).
cnf(c_6747,plain,
( nil != sk1
| sk2 != nil ),
inference(copy,[status(thm)],[c_53]) ).
cnf(c_54,plain,
( sk1 != nil
| sk2 != nil ),
inference(copy,[status(thm)],[c_6747]) ).
fof(co1_14,axiom,
( nil != sk3
| nil = sk4 ),
file('theBenchmark.p',co1_14) ).
cnf(c_55,plain,
( nil != sk3
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_6748,plain,
( nil != sk3
| sk4 = nil ),
inference(copy,[status(thm)],[c_55]) ).
cnf(c_56,plain,
( sk3 != nil
| sk4 = nil ),
inference(copy,[status(thm)],[c_6748]) ).
fof(co1_10,axiom,
app(app(sk5,sk3),sk6) = sk4,
file('theBenchmark.p',co1_10) ).
cnf(c_59,plain,
app(app(sk5,sk3),sk6) = sk4,
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_9,axiom,
ssList(sk6),
file('theBenchmark.p',co1_9) ).
cnf(c_60,plain,
ssList(sk6),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
ssList(sk5),
file('theBenchmark.p',co1_8) ).
cnf(c_61,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_8]) ).
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_62,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_63,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_64,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_65,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_66,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_76,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
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_144,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause57,axiom,
! [VAR_0] :
( segmentP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause57) ).
cnf(c_172,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause57]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_221,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_6749,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_64,c_62]) ).
cnf(c_330,plain,
( ~ segmentP(sk3,A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_63,c_6749]) ).
cnf(c_6750,plain,
( sk1 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_64,c_54]) ).
cnf(c_331,plain,
( sk3 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_63,c_6750]) ).
cnf(c_6751,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6) ),
inference(resolve,[status(thm)],[c_76,c_59]) ).
cnf(c_6752,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(sk5) ),
inference(resolve,[status(thm)],[c_60,c_6751]) ).
cnf(c_6753,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_61,c_6752]) ).
cnf(c_6754,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4) ),
inference(resolve,[status(thm)],[c_66,c_6753]) ).
cnf(c_880,plain,
segmentP(sk4,sk3),
inference(resolve,[status(thm)],[c_65,c_6754]) ).
cnf(c_1244,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_144,c_66]) ).
cnf(c_1343,plain,
segmentP(sk3,sk3),
inference(resolve,[status(thm)],[c_172,c_66]) ).
cnf(c_6755,plain,
( ~ segmentP(sk3,sk3)
| ~ segmentP(sk4,sk3)
| ~ neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_330,c_66]) ).
cnf(c_6756,plain,
( ~ segmentP(sk3,sk3)
| ~ neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_880,c_6755]) ).
cnf(c_4748,plain,
~ neq(sk3,nil),
inference(resolve,[status(thm)],[c_1343,c_6756]) ).
cnf(c_6757,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1244,c_221]) ).
cnf(c_6514,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_4748,c_6757]) ).
cnf(c_6758,plain,
( nil != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_6514,c_331]) ).
cnf(c_6742,plain,
sk4 != nil,
inference(copy,[status(thm)],[c_6758]) ).
cnf(c_6759,plain,
( nil != nil
| sk4 = nil ),
inference(paramod,[status(thm)],[c_6514,c_56]) ).
cnf(c_6760,plain,
sk4 = nil,
inference(copy,[status(thm)],[c_6759]) ).
cnf(c_6746,plain,
$false,
inference(resolve,[status(thm)],[c_6742,c_6760]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC076-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n014.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 12:11:31 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 3109192 was started by sandbox2 on n014,
% 0.16/0.43 % Sat Sep 26 12:11:31 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 32.85/5.26
% 32.85/5.26 % given #500 (I,wt=49): 556 app(app(A,cons(B,C)),cons(B,D)) != C | -ssList(D) | -ssList(C) | -ssList(A) | -ssItem(B) | lt(B,B) | -lt(skaf60(C),skaf59(C)). [factor(293,e,f),merge(g)].
% 32.85/5.26
% 32.85/5.26 % SZS status Unsatisfiable for theBenchmark
% 32.85/5.26
% 32.85/5.26 % Proof 1 at 3.32 (+ 1.42) seconds.
% 32.85/5.26 % Length of proof is 25.
% 32.85/5.26 % Level of proof is 5.
% 32.85/5.26 % Maximum clause weight is 35.000.
% 32.85/5.26 % Given clauses 926.
% 32.85/5.26
% 32.85/5.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------