%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC068-1 : 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 : n006.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 60.37s 8.08s
% Output : CNFRefutation 60.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 72 ( 21 unt; 0 def)
% Number of atoms : 181 ( 71 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 229 ( 120 ~; 109 |; 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_9,axiom,
( nil != sk1
| nil != sk2 ),
file('theBenchmark.p',co1_9) ).
cnf(c_51,plain,
( nil != sk1
| nil != sk2 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_15456,plain,
( nil != sk1
| sk2 != nil ),
inference(copy,[status(thm)],[c_51]) ).
cnf(c_52,plain,
( sk1 != nil
| sk2 != nil ),
inference(copy,[status(thm)],[c_15456]) ).
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_53,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[co1_8]) ).
fof(co1_7,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_7) ).
cnf(c_54,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_6) ).
cnf(c_55,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
app(sk4,sk4) = sk3,
file('theBenchmark.p',co1_5) ).
cnf(c_56,plain,
app(sk4,sk4) = sk3,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_57,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_58,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_68,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
fof(clause145,axiom,
! [VAR_0,VAR_1] :
( app(VAR_0,VAR_1) = nil
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| nil != VAR_1
| nil != VAR_0 ),
file('theBenchmark.p',clause145) ).
cnf(c_93,plain,
( app(A,B) = nil
| ~ ssList(A)
| ~ ssList(B)
| nil != B
| nil != A ),
inference(clausify,[status(thm)],[clause145]) ).
fof(clause119,axiom,
! [VAR_0,VAR_1] :
( nil = VAR_1
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| app(VAR_0,VAR_1) != nil ),
file('theBenchmark.p',clause119) ).
cnf(c_117,plain,
( nil = B
| ~ ssList(A)
| ~ ssList(B)
| app(A,B) != nil ),
inference(clausify,[status(thm)],[clause119]) ).
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(clause73,axiom,
! [VAR_0] :
( app(VAR_0,nil) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause73) ).
cnf(c_154,plain,
( app(A,nil) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause73]) ).
fof(clause57,axiom,
! [VAR_0] :
( segmentP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause57) ).
cnf(c_164,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause57]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_213,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_15457,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_55,c_53]) ).
cnf(c_317,plain,
( ~ segmentP(sk3,A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_54,c_15457]) ).
cnf(c_15458,plain,
( sk1 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_55,c_52]) ).
cnf(c_318,plain,
( sk3 != nil
| sk4 != nil ),
inference(paramod,[status(thm)],[c_54,c_15458]) ).
cnf(c_15459,plain,
( app(A,A) = nil
| ~ ssList(A)
| ~ ssList(A)
| nil != A ),
inference(factor,[status(thm)],[c_93]) ).
cnf(c_363,plain,
( app(A,A) = nil
| ~ ssList(A)
| nil != A ),
inference(copy,[status(thm)],[c_15459]) ).
cnf(c_15460,plain,
( segmentP(B,sk4)
| ~ ssList(B)
| ~ ssList(sk4)
| ~ ssList(sk4)
| ~ ssList(A)
| app(sk3,A) != B ),
inference(paramod,[status(thm)],[c_56,c_68]) ).
cnf(c_15461,plain,
( segmentP(B,sk4)
| ~ ssList(B)
| ~ ssList(sk4)
| ~ ssList(A)
| app(sk3,A) != B ),
inference(copy,[status(thm)],[c_15460]) ).
cnf(c_871,plain,
( segmentP(B,sk4)
| ~ ssList(B)
| ~ ssList(A)
| app(sk3,A) != B ),
inference(resolve,[status(thm)],[c_57,c_15461]) ).
cnf(c_15462,plain,
( nil = sk4
| ~ ssList(sk4)
| ~ ssList(sk4)
| sk3 != nil ),
inference(paramod,[status(thm)],[c_56,c_117]) ).
cnf(c_15463,plain,
( sk4 = nil
| ~ ssList(sk4)
| ~ ssList(sk4)
| sk3 != nil ),
inference(copy,[status(thm)],[c_15462]) ).
cnf(c_15464,plain,
( sk4 = nil
| ~ ssList(sk4)
| sk3 != nil ),
inference(copy,[status(thm)],[c_15463]) ).
cnf(c_1129,plain,
( sk4 = nil
| sk3 != nil ),
inference(resolve,[status(thm)],[c_57,c_15464]) ).
cnf(c_15465,plain,
( ~ ssList(A)
| ~ neq(A,sk3)
| A != sk3 ),
inference(resolve,[status(thm)],[c_121,c_58]) ).
cnf(c_1139,plain,
( ~ ssList(A)
| ~ neq(A,sk3)
| sk3 != A ),
inference(copy,[status(thm)],[c_15465]) ).
cnf(c_15466,plain,
( A = sk3
| neq(A,sk3)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_136,c_58]) ).
cnf(c_1153,plain,
( sk3 = A
| neq(A,sk3)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_15466]) ).
cnf(c_1156,plain,
( sk4 = A
| neq(sk4,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_136,c_57]) ).
cnf(c_1196,plain,
app(sk3,nil) = sk3,
inference(resolve,[status(thm)],[c_154,c_58]) ).
cnf(c_1207,plain,
segmentP(sk4,sk4),
inference(resolve,[status(thm)],[c_164,c_57]) ).
cnf(c_15467,plain,
( ~ segmentP(sk3,sk4)
| ~ segmentP(sk4,sk4)
| ~ neq(sk4,nil) ),
inference(resolve,[status(thm)],[c_317,c_57]) ).
cnf(c_7905,plain,
( ~ segmentP(sk3,sk4)
| ~ neq(sk4,nil) ),
inference(resolve,[status(thm)],[c_1207,c_15467]) ).
cnf(c_15468,plain,
( app(sk4,sk4) = nil
| nil != sk4 ),
inference(resolve,[status(thm)],[c_363,c_57]) ).
cnf(c_15469,plain,
( sk3 = nil
| nil != sk4 ),
inference(paramod,[status(thm)],[c_56,c_15468]) ).
cnf(c_8873,plain,
( sk3 = nil
| sk4 != nil ),
inference(copy,[status(thm)],[c_15469]) ).
cnf(c_15470,plain,
( segmentP(sk3,sk4)
| ~ ssList(sk3)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_871,c_1196]) ).
cnf(c_15471,plain,
( segmentP(sk3,sk4)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_213,c_15470]) ).
cnf(c_12257,plain,
segmentP(sk3,sk4),
inference(resolve,[status(thm)],[c_58,c_15471]) ).
cnf(c_12315,plain,
~ neq(sk4,nil),
inference(resolve,[status(thm)],[c_12257,c_7905]) ).
cnf(c_12345,plain,
( ~ neq(nil,sk3)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_1139,c_213]) ).
cnf(c_14195,plain,
( sk3 = nil
| neq(nil,sk3) ),
inference(resolve,[status(thm)],[c_1153,c_213]) ).
cnf(c_14253,plain,
( sk4 = nil
| neq(nil,sk3) ),
inference(resolve,[status(thm)],[c_14195,c_1129]) ).
cnf(c_14254,plain,
( sk4 != nil
| neq(nil,sk3) ),
inference(resolve,[status(thm)],[c_14195,c_318]) ).
cnf(c_15472,plain,
( neq(nil,sk3)
| neq(nil,sk3) ),
inference(resolve,[status(thm)],[c_14254,c_14253]) ).
cnf(c_14636,plain,
neq(nil,sk3),
inference(copy,[status(thm)],[c_15472]) ).
cnf(c_14637,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_14636,c_12345]) ).
cnf(c_14647,plain,
sk4 != nil,
inference(resolve,[status(thm)],[c_14637,c_8873]) ).
cnf(c_15473,plain,
( sk4 = nil
| neq(sk4,nil) ),
inference(resolve,[status(thm)],[c_1156,c_213]) ).
cnf(c_15474,plain,
sk4 = nil,
inference(resolve,[status(thm)],[c_12315,c_15473]) ).
cnf(c_15455,plain,
$false,
inference(resolve,[status(thm)],[c_14647,c_15474]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC068-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n006.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 12:10:25 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.34 % Process 1216185 was started by sandbox2 on n006,
% 0.07/0.34 % Sat Sep 26 12:10:25 2026
% 0.07/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 60.37/8.08
% 60.37/8.08 % 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)].
% 60.37/8.08
% 60.37/8.08 % given #1000 (T,wt=8): 12245 sk3 != sk4 | sk4 = nil. [para(1195(a,1),355(a,1)),rewrite([56(4)]),flip(a),unit_del(b,57),unit_del(c,213)].
% 60.37/8.08
% 60.37/8.08 % SZS status Unsatisfiable for theBenchmark
% 60.37/8.08
% 60.37/8.08 % Proof 1 at 5.38 (+ 1.73) seconds.
% 60.37/8.08 % Length of proof is 38.
% 60.37/8.08 % Level of proof is 7.
% 60.37/8.08 % Maximum clause weight is 26.000.
% 60.37/8.08 % Given clauses 1428.
% 60.37/8.08
% 60.37/8.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------