%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC116-1 : 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 : n020.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 08:56:53 AM UTC 2026
% Result : Unsatisfiable 25.31s 4.11s
% Output : CNFRefutation 25.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 19
% Syntax : Number of formulae : 88 ( 26 unt; 0 def)
% Number of atoms : 203 ( 64 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 222 ( 107 ~; 115 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 35 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_11,axiom,
( segmentP(sk4,sk3)
| ~ neq(sk4,nil) ),
file('theBenchmark.p',co1_11) ).
cnf(c_51,plain,
( segmentP(sk4,sk3)
| ~ neq(sk4,nil) ),
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_10,axiom,
( neq(sk3,nil)
| ~ neq(sk4,nil) ),
file('theBenchmark.p',co1_10) ).
cnf(c_52,plain,
( neq(sk3,nil)
| ~ neq(sk4,nil) ),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_9,axiom,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('theBenchmark.p',co1_9) ).
cnf(c_53,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(clausify,[status(thm)],[co1_9]) ).
fof(co1_8,axiom,
( nil != sk1
| nil != sk2 ),
file('theBenchmark.p',co1_8) ).
cnf(c_54,plain,
( nil != sk1
| nil != sk2 ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_20565,plain,
( nil != sk1
| sk2 != nil ),
inference(copy,[status(thm)],[c_54]) ).
cnf(c_55,plain,
( sk1 != nil
| sk2 != nil ),
inference(copy,[status(thm)],[c_20565]) ).
fof(co1_7,axiom,
( nil != sk4
| nil = sk3 ),
file('theBenchmark.p',co1_7) ).
cnf(c_56,plain,
( nil != sk4
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_20566,plain,
( nil != sk4
| sk3 = nil ),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_57,plain,
( sk4 != nil
| sk3 = nil ),
inference(copy,[status(thm)],[c_20566]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_58,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_59,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_60,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_61,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_62,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_63,plain,
ssList(sk1),
inference(clausify,[status(thm)],[co1_1]) ).
fof(clause152,axiom,
! [VAR_0,VAR_1,VAR_2] :
( segmentP(VAR_0,VAR_2)
| ~ ssList(VAR_0)
| ~ ssList(VAR_1)
| ~ ssList(VAR_2)
| ~ segmentP(VAR_1,VAR_2)
| ~ segmentP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause152) ).
cnf(c_89,plain,
( segmentP(A,C)
| ~ ssList(A)
| ~ ssList(B)
| ~ ssList(C)
| ~ segmentP(B,C)
| ~ segmentP(A,B) ),
inference(clausify,[status(thm)],[clause152]) ).
fof(clause127,axiom,
! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ ssList(VAR_1)
| ~ ssList(VAR_0)
| ~ segmentP(VAR_1,VAR_0)
| ~ segmentP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause127) ).
cnf(c_113,plain,
( B = A
| ~ ssList(B)
| ~ ssList(A)
| ~ segmentP(B,A)
| ~ segmentP(A,B) ),
inference(clausify,[status(thm)],[clause127]) ).
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_124,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_139,plain,
( B = A
| neq(B,A)
| ~ ssList(B)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause100]) ).
fof(clause79,axiom,
! [VAR_0] :
( segmentP(nil,VAR_0)
| ~ ssList(VAR_0)
| nil != VAR_0 ),
file('theBenchmark.p',clause79) ).
cnf(c_153,plain,
( segmentP(nil,A)
| ~ ssList(A)
| nil != A ),
inference(clausify,[status(thm)],[clause79]) ).
fof(clause57,axiom,
! [VAR_0] :
( segmentP(VAR_0,VAR_0)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause57) ).
cnf(c_167,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause57]) ).
fof(clause56,axiom,
! [VAR_0] :
( segmentP(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause56) ).
cnf(c_168,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause56]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_216,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_1043,plain,
( sk1 = A
| neq(sk1,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_139,c_63]) ).
cnf(c_1046,plain,
( sk4 = A
| neq(sk4,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_139,c_60]) ).
cnf(c_20567,plain,
( segmentP(nil,sk1)
| nil != sk1 ),
inference(resolve,[status(thm)],[c_153,c_63]) ).
cnf(c_1063,plain,
( segmentP(nil,sk1)
| sk1 != nil ),
inference(copy,[status(thm)],[c_20567]) ).
cnf(c_1099,plain,
segmentP(sk1,sk1),
inference(resolve,[status(thm)],[c_167,c_63]) ).
cnf(c_1100,plain,
segmentP(sk2,sk2),
inference(resolve,[status(thm)],[c_167,c_62]) ).
cnf(c_1105,plain,
segmentP(sk3,nil),
inference(resolve,[status(thm)],[c_168,c_61]) ).
cnf(c_5335,plain,
segmentP(sk3,sk1),
inference(paramod,[status(thm)],[c_58,c_1099]) ).
cnf(c_5336,plain,
segmentP(sk1,sk3),
inference(paramod,[status(thm)],[c_58,c_1099]) ).
cnf(c_5344,plain,
segmentP(sk2,sk4),
inference(paramod,[status(thm)],[c_59,c_1100]) ).
cnf(c_20568,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ segmentP(nil,sk3) ),
inference(resolve,[status(thm)],[c_1105,c_113]) ).
cnf(c_20569,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ segmentP(nil,sk3) ),
inference(resolve,[status(thm)],[c_216,c_20568]) ).
cnf(c_5730,plain,
( sk3 = nil
| ~ segmentP(nil,sk3) ),
inference(resolve,[status(thm)],[c_61,c_20569]) ).
cnf(c_20570,plain,
( segmentP(A,sk1)
| ~ ssList(A)
| ~ ssList(sk3)
| ~ ssList(sk1)
| ~ segmentP(A,sk3) ),
inference(resolve,[status(thm)],[c_5335,c_89]) ).
cnf(c_20571,plain,
( segmentP(A,sk1)
| ~ ssList(A)
| ~ ssList(sk3)
| ~ segmentP(A,sk3) ),
inference(resolve,[status(thm)],[c_63,c_20570]) ).
cnf(c_6873,plain,
( segmentP(A,sk1)
| ~ ssList(A)
| ~ segmentP(A,sk3) ),
inference(resolve,[status(thm)],[c_61,c_20571]) ).
cnf(c_20572,plain,
( segmentP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk1)
| ~ ssList(sk3)
| ~ segmentP(A,sk1) ),
inference(resolve,[status(thm)],[c_5336,c_89]) ).
cnf(c_20573,plain,
( segmentP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk1)
| ~ segmentP(A,sk1) ),
inference(resolve,[status(thm)],[c_61,c_20572]) ).
cnf(c_6886,plain,
( segmentP(A,sk3)
| ~ ssList(A)
| ~ segmentP(A,sk1) ),
inference(resolve,[status(thm)],[c_63,c_20573]) ).
cnf(c_20574,plain,
( segmentP(sk2,A)
| ~ ssList(sk2)
| ~ ssList(sk4)
| ~ ssList(A)
| ~ segmentP(sk4,A) ),
inference(resolve,[status(thm)],[c_5344,c_89]) ).
cnf(c_20575,plain,
( segmentP(sk2,A)
| ~ ssList(sk2)
| ~ ssList(A)
| ~ segmentP(sk4,A) ),
inference(resolve,[status(thm)],[c_60,c_20574]) ).
cnf(c_7257,plain,
( segmentP(sk2,A)
| ~ ssList(A)
| ~ segmentP(sk4,A) ),
inference(resolve,[status(thm)],[c_62,c_20575]) ).
cnf(c_12771,plain,
( sk1 = nil
| neq(sk1,nil) ),
inference(resolve,[status(thm)],[c_1043,c_216]) ).
cnf(c_12799,plain,
( ~ segmentP(sk2,sk1)
| sk1 = nil ),
inference(resolve,[status(thm)],[c_12771,c_53]) ).
cnf(c_12931,plain,
( sk4 = nil
| neq(sk4,nil) ),
inference(resolve,[status(thm)],[c_1046,c_216]) ).
cnf(c_12959,plain,
( neq(sk3,nil)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_12931,c_52]) ).
cnf(c_12960,plain,
( segmentP(sk4,sk3)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_12931,c_51]) ).
cnf(c_20576,plain,
( ~ ssList(sk3)
| ~ ssList(nil)
| sk3 != nil
| sk4 = nil ),
inference(resolve,[status(thm)],[c_12959,c_124]) ).
cnf(c_20577,plain,
( ~ ssList(sk3)
| sk3 != nil
| sk4 = nil ),
inference(resolve,[status(thm)],[c_216,c_20576]) ).
cnf(c_12973,plain,
( sk3 != nil
| sk4 = nil ),
inference(resolve,[status(thm)],[c_61,c_20577]) ).
cnf(c_20578,plain,
( sk4 = nil
| segmentP(sk4,sk1)
| ~ ssList(sk4) ),
inference(resolve,[status(thm)],[c_6873,c_12960]) ).
cnf(c_19468,plain,
( sk4 = nil
| segmentP(sk4,sk1) ),
inference(resolve,[status(thm)],[c_60,c_20578]) ).
cnf(c_20579,plain,
( sk4 = nil
| segmentP(sk2,sk1)
| ~ ssList(sk1) ),
inference(resolve,[status(thm)],[c_7257,c_19468]) ).
cnf(c_19544,plain,
( sk4 = nil
| segmentP(sk2,sk1) ),
inference(resolve,[status(thm)],[c_63,c_20579]) ).
cnf(c_19614,plain,
( sk1 = nil
| sk4 = nil ),
inference(resolve,[status(thm)],[c_19544,c_12799]) ).
cnf(c_19629,plain,
( segmentP(nil,sk1)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_19614,c_1063]) ).
cnf(c_20580,plain,
( segmentP(nil,sk3)
| ~ ssList(nil)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_19629,c_6886]) ).
cnf(c_19632,plain,
( segmentP(nil,sk3)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_216,c_20580]) ).
cnf(c_19766,plain,
( sk3 = nil
| sk4 = nil ),
inference(resolve,[status(thm)],[c_19632,c_5730]) ).
cnf(c_20581,plain,
( sk4 = nil
| sk4 = nil ),
inference(resolve,[status(thm)],[c_19766,c_12973]) ).
cnf(c_19928,plain,
sk4 = nil,
inference(copy,[status(thm)],[c_20581]) ).
cnf(c_19987,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_19928,c_57]) ).
cnf(c_20087,plain,
sk2 = nil,
inference(paramod,[status(thm)],[c_19928,c_59]) ).
cnf(c_20189,plain,
sk1 != nil,
inference(resolve,[status(thm)],[c_20087,c_55]) ).
cnf(c_20582,plain,
sk3 != nil,
inference(paramod,[status(thm)],[c_58,c_20189]) ).
cnf(c_20564,plain,
$false,
inference(resolve,[status(thm)],[c_19987,c_20582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC116-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.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 12:18:33 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 1526282 was started by sandbox2 on n020,
% 0.09/0.36 % Sat Sep 26 12:18:33 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 25.31/4.11
% 25.31/4.11 % given #500 (I,wt=35): 557 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(296,e,f),merge(g)].
% 25.31/4.11
% 25.31/4.11 % given #1000 (F,wt=13): 4844 cons(skac2,skaf42(A,B)) != nil. [resolve(3343,b,171,a)].
% 25.31/4.11
% 25.31/4.11 % given #1500 (W,wt=8): 12931 neq(sk4,nil) | sk4 = nil. [resolve(1046,a,216,a)].
% 25.31/4.11
% 25.31/4.11 % SZS status Unsatisfiable for theBenchmark
% 25.31/4.11
% 25.31/4.11 % Proof 1 at 2.75 (+ 0.94) seconds.
% 25.31/4.11 % Length of proof is 51.
% 25.31/4.11 % Level of proof is 13.
% 25.31/4.11 % Maximum clause weight is 17.000.
% 25.31/4.11 % Given clauses 1995.
% 25.31/4.11
% 25.31/4.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------