%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC024-1 : 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 : n003.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 08:56:34 AM UTC 2026
% Result : Unsatisfiable 59.89s 13.01s
% Output : CNFRefutation 59.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 54 ( 31 unt; 0 def)
% Number of atoms : 101 ( 32 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 105 ( 58 ~; 47 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_13,axiom,
( nil != sk3
| nil = sk4 ),
file('theBenchmark.p',co1_13) ).
cnf(c_53,plain,
( nil != sk3
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_22688,plain,
( nil != sk3
| sk4 = nil ),
inference(copy,[status(thm)],[c_53]) ).
cnf(c_54,plain,
( sk3 != nil
| sk4 = nil ),
inference(copy,[status(thm)],[c_22688]) ).
fof(co1_10,axiom,
app(sk3,sk5) = sk4,
file('theBenchmark.p',co1_10) ).
cnf(c_56,plain,
app(sk3,sk5) = sk4,
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_9,axiom,
ssList(sk5),
file('theBenchmark.p',co1_9) ).
cnf(c_57,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
! [VAR_0] :
( ~ frontsegP(sk1,VAR_0)
| ~ frontsegP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',co1_8) ).
cnf(c_58,plain,
( ~ frontsegP(sk1,A)
| ~ frontsegP(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_59,plain,
neq(sk2,nil),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_60,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_61,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_62,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_63,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_64,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_65,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
fof(clause144,axiom,
! [VAR_0,VAR_1,VAR_2] :
( frontsegP(VAR_2,VAR_0)
| ~ ssList(VAR_2)
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| app(VAR_0,VAR_1) != VAR_2 ),
file('theBenchmark.p',clause144) ).
cnf(c_99,plain,
( frontsegP(C,A)
| ~ ssList(C)
| ~ ssList(A)
| ~ ssList(B)
| app(A,B) != C ),
inference(clausify,[status(thm)],[clause144]) ).
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_126,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_141,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause61,axiom,
! [VAR_0] :
( frontsegP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause61) ).
cnf(c_165,plain,
( frontsegP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause61]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_218,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_835,plain,
neq(sk4,nil),
inference(paramod,[status(thm)],[c_61,c_59]) ).
cnf(c_1009,plain,
( frontsegP(B,sk3)
| ~ ssList(B)
| ~ ssList(A)
| app(sk3,A) != B ),
inference(resolve,[status(thm)],[c_99,c_63]) ).
cnf(c_1116,plain,
( sk3 = A
| neq(sk3,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_141,c_63]) ).
cnf(c_1161,plain,
frontsegP(sk1,sk1),
inference(resolve,[status(thm)],[c_165,c_65]) ).
cnf(c_22689,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_835,c_126]) ).
cnf(c_22690,plain,
( ~ ssList(sk4)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_218,c_22689]) ).
cnf(c_11426,plain,
sk4 != nil,
inference(resolve,[status(thm)],[c_62,c_22690]) ).
cnf(c_11440,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_11426,c_54]) ).
cnf(c_11521,plain,
frontsegP(sk1,sk3),
inference(paramod,[status(thm)],[c_60,c_1161]) ).
cnf(c_22691,plain,
( sk3 = nil
| neq(sk3,nil) ),
inference(resolve,[status(thm)],[c_1116,c_218]) ).
cnf(c_16429,plain,
neq(sk3,nil),
inference(resolve,[status(thm)],[c_11440,c_22691]) ).
cnf(c_22692,plain,
( ~ frontsegP(sk1,sk3)
| ~ frontsegP(sk2,sk3)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_16429,c_58]) ).
cnf(c_22693,plain,
( ~ frontsegP(sk1,sk3)
| ~ frontsegP(sk2,sk3) ),
inference(resolve,[status(thm)],[c_63,c_22692]) ).
cnf(c_16457,plain,
~ frontsegP(sk2,sk3),
inference(resolve,[status(thm)],[c_11521,c_22693]) ).
cnf(c_22694,plain,
( frontsegP(sk2,sk3)
| ~ ssList(A)
| app(sk3,A) != sk2 ),
inference(resolve,[status(thm)],[c_1009,c_64]) ).
cnf(c_21129,plain,
( ~ ssList(A)
| app(sk3,A) != sk2 ),
inference(resolve,[status(thm)],[c_16457,c_22694]) ).
cnf(c_22455,plain,
app(sk3,sk5) != sk2,
inference(resolve,[status(thm)],[c_21129,c_57]) ).
cnf(c_22695,plain,
sk4 != sk2,
inference(paramod,[status(thm)],[c_56,c_22455]) ).
cnf(c_22696,plain,
sk2 != sk4,
inference(copy,[status(thm)],[c_22695]) ).
cnf(c_22687,plain,
$false,
inference(resolve,[status(thm)],[c_61,c_22696]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC024-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n003.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sat Sep 26 12:07:01 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.37 % Process 2821994 was started by sandbox2 on n003,
% 0.08/5.37 % Sat Sep 26 12:07:01 2026
% 0.08/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/5.37
% 0.08/5.37 % From the command line: assign(max_seconds, 300).
% 59.89/13.01
% 59.89/13.01 % given #500 (I,wt=49): 563 app(app(A,cons(B,C)),cons(B,D)) != C | -ssList(D) | -ssList(C) | -ssList(A) | -ssItem(B) | lt(B,B) | -lt(skaf59(C),skaf60(C)). [factor(297,e,f),merge(g)].
% 59.89/13.01
% 59.89/13.01 % given #1000 (T,wt=11): 16093 neq(sk2,sk5) | sk5 = sk2. [resolve(1113,a,64,a)].
% 59.89/13.01
% 59.89/13.01 % given #1500 (A,wt=22): 1014 app(A,B) != sk3 | -ssList(B) | -ssList(A) | frontsegP(sk3,A). [resolve(99,d,63,a)].
% 59.89/13.01
% 59.89/13.01 % SZS status Unsatisfiable for theBenchmark
% 59.89/13.01
% 59.89/13.01 % Proof 1 at 7.08 (+ 0.49) seconds.
% 59.89/13.01 % Length of proof is 29.
% 59.89/13.01 % Level of proof is 8.
% 59.89/13.01 % Maximum clause weight is 24.000.
% 59.89/13.01 % Given clauses 1581.
% 59.89/13.01
% 59.89/13.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------