%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC060-1 : 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 : n016.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 08:56:42 AM UTC 2026
% Result : Unsatisfiable 36.73s 5.71s
% Output : CNFRefutation 36.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 18
% Syntax : Number of formulae : 85 ( 28 unt; 0 def)
% Number of atoms : 205 ( 68 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 217 ( 97 ~; 120 |; 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 : 29 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_14,axiom,
( segmentP(sk4,sk3)
| nil = sk3 ),
file('theBenchmark.p',co1_14) ).
cnf(c_51,plain,
( segmentP(sk4,sk3)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_52,plain,
( segmentP(sk4,sk3)
| sk3 = nil ),
inference(copy,[status(thm)],[c_51]) ).
fof(co1_13,axiom,
( neq(sk3,nil)
| nil = sk3 ),
file('theBenchmark.p',co1_13) ).
cnf(c_53,plain,
( neq(sk3,nil)
| nil = sk3 ),
inference(clausify,[status(thm)],[co1_13]) ).
cnf(c_54,plain,
( neq(sk3,nil)
| sk3 = nil ),
inference(copy,[status(thm)],[c_53]) ).
fof(co1_11,axiom,
( neq(sk3,nil)
| nil = sk4 ),
file('theBenchmark.p',co1_11) ).
cnf(c_57,plain,
( neq(sk3,nil)
| nil = sk4 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_58,plain,
( neq(sk3,nil)
| sk4 = nil ),
inference(copy,[status(thm)],[c_57]) ).
fof(co1_9,axiom,
( neq(sk2,nil)
| nil != sk1 ),
file('theBenchmark.p',co1_9) ).
cnf(c_61,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_62,plain,
( neq(sk2,nil)
| sk1 != nil ),
inference(copy,[status(thm)],[c_61]) ).
fof(co1_8,axiom,
! [VAR_0] :
( ~ segmentP(sk1,VAR_0)
| ~ segmentP(sk2,VAR_0)
| ~ neq(VAR_0,nil)
| ~ ssList(VAR_0)
| nil = sk2 ),
file('theBenchmark.p',co1_8) ).
cnf(c_63,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_64,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A)
| sk2 = nil ),
inference(copy,[status(thm)],[c_63]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_67,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_68,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_69,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_68]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_70,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_71,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_72,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_1,axiom,
ssList(sk1),
file('theBenchmark.p',co1_1) ).
cnf(c_73,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_99,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_123,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_134,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
fof(clause79,axiom,
! [VAR_0] :
( segmentP(nil,VAR_0)
| ~ ssList(VAR_0)
| nil != VAR_0 ),
file('theBenchmark.p',clause79) ).
cnf(c_163,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_177,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_178,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause56]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_226,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_22183,plain,
( sk3 = nil
| ~ segmentP(sk1,sk3)
| ~ segmentP(sk2,sk3)
| ~ ssList(sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_64,c_54]) ).
cnf(c_840,plain,
( sk3 = nil
| ~ segmentP(sk1,sk3)
| ~ segmentP(sk2,sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_71,c_22183]) ).
cnf(c_22184,plain,
( sk3 = nil
| segmentP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ segmentP(A,sk4) ),
inference(resolve,[status(thm)],[c_99,c_52]) ).
cnf(c_22185,plain,
( sk3 = nil
| segmentP(A,sk3)
| ~ ssList(A)
| ~ ssList(sk4)
| ~ segmentP(A,sk4) ),
inference(resolve,[status(thm)],[c_71,c_22184]) ).
cnf(c_927,plain,
( sk3 = nil
| segmentP(A,sk3)
| ~ ssList(A)
| ~ segmentP(A,sk4) ),
inference(resolve,[status(thm)],[c_70,c_22185]) ).
cnf(c_22186,plain,
( sk4 = nil
| ~ ssList(sk3)
| ~ ssList(nil)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_134,c_58]) ).
cnf(c_22187,plain,
( sk4 = nil
| ~ ssList(sk3)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_226,c_22186]) ).
cnf(c_1059,plain,
( sk4 = nil
| sk3 != nil ),
inference(resolve,[status(thm)],[c_71,c_22187]) ).
cnf(c_22188,plain,
( segmentP(nil,sk2)
| nil != sk2 ),
inference(resolve,[status(thm)],[c_163,c_72]) ).
cnf(c_1093,plain,
( segmentP(nil,sk2)
| sk2 != nil ),
inference(copy,[status(thm)],[c_22188]) ).
cnf(c_1128,plain,
segmentP(sk1,sk1),
inference(resolve,[status(thm)],[c_177,c_73]) ).
cnf(c_1131,plain,
segmentP(sk4,sk4),
inference(resolve,[status(thm)],[c_177,c_70]) ).
cnf(c_1135,plain,
segmentP(sk3,nil),
inference(resolve,[status(thm)],[c_178,c_71]) ).
cnf(c_5033,plain,
segmentP(sk1,sk3),
inference(paramod,[status(thm)],[c_67,c_1128]) ).
cnf(c_5034,plain,
( sk3 = nil
| ~ segmentP(sk2,sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_5033,c_840]) ).
cnf(c_5131,plain,
segmentP(sk2,sk4),
inference(paramod,[status(thm)],[c_69,c_1131]) ).
cnf(c_22189,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ ssList(nil)
| ~ segmentP(nil,sk3) ),
inference(resolve,[status(thm)],[c_1135,c_123]) ).
cnf(c_22190,plain,
( sk3 = nil
| ~ ssList(sk3)
| ~ segmentP(nil,sk3) ),
inference(resolve,[status(thm)],[c_226,c_22189]) ).
cnf(c_5168,plain,
( sk3 = nil
| ~ segmentP(nil,sk3) ),
inference(resolve,[status(thm)],[c_71,c_22190]) ).
cnf(c_22191,plain,
( segmentP(A,sk4)
| ~ ssList(A)
| ~ ssList(sk2)
| ~ ssList(sk4)
| ~ segmentP(A,sk2) ),
inference(resolve,[status(thm)],[c_5131,c_99]) ).
cnf(c_22192,plain,
( segmentP(A,sk4)
| ~ ssList(A)
| ~ ssList(sk2)
| ~ segmentP(A,sk2) ),
inference(resolve,[status(thm)],[c_70,c_22191]) ).
cnf(c_6305,plain,
( segmentP(A,sk4)
| ~ ssList(A)
| ~ segmentP(A,sk2) ),
inference(resolve,[status(thm)],[c_72,c_22192]) ).
cnf(c_22193,plain,
( sk3 = nil
| segmentP(sk2,sk3)
| ~ ssList(sk2) ),
inference(resolve,[status(thm)],[c_927,c_5131]) ).
cnf(c_11296,plain,
( sk3 = nil
| segmentP(sk2,sk3) ),
inference(resolve,[status(thm)],[c_72,c_22193]) ).
cnf(c_22194,plain,
( sk3 = nil
| sk3 = nil
| sk2 = nil ),
inference(resolve,[status(thm)],[c_5034,c_11296]) ).
cnf(c_21720,plain,
( sk3 = nil
| sk2 = nil ),
inference(copy,[status(thm)],[c_22194]) ).
cnf(c_21721,plain,
( segmentP(nil,sk2)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_21720,c_1093]) ).
cnf(c_22195,plain,
( segmentP(nil,sk4)
| ~ ssList(nil)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_21721,c_6305]) ).
cnf(c_21724,plain,
( segmentP(nil,sk4)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_226,c_22195]) ).
cnf(c_22196,plain,
( sk3 = nil
| segmentP(nil,sk3)
| ~ ssList(nil)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_21724,c_927]) ).
cnf(c_22197,plain,
( segmentP(nil,sk3)
| ~ ssList(nil)
| sk3 = nil ),
inference(copy,[status(thm)],[c_22196]) ).
cnf(c_21768,plain,
( segmentP(nil,sk3)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_226,c_22197]) ).
cnf(c_22198,plain,
( sk3 = nil
| sk3 = nil ),
inference(resolve,[status(thm)],[c_21768,c_5168]) ).
cnf(c_21822,plain,
sk3 = nil,
inference(copy,[status(thm)],[c_22198]) ).
cnf(c_21837,plain,
sk4 = nil,
inference(resolve,[status(thm)],[c_21822,c_1059]) ).
cnf(c_21887,plain,
sk1 = nil,
inference(paramod,[status(thm)],[c_21822,c_67]) ).
cnf(c_21974,plain,
neq(sk2,nil),
inference(resolve,[status(thm)],[c_21887,c_62]) ).
cnf(c_22199,plain,
nil = sk2,
inference(paramod,[status(thm)],[c_21837,c_69]) ).
cnf(c_22030,plain,
sk2 = nil,
inference(copy,[status(thm)],[c_22199]) ).
cnf(c_22200,plain,
( ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_21974,c_134]) ).
cnf(c_22201,plain,
( ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_22030,c_22200]) ).
cnf(c_22202,plain,
~ ssList(sk2),
inference(resolve,[status(thm)],[c_226,c_22201]) ).
cnf(c_22182,plain,
$false,
inference(resolve,[status(thm)],[c_72,c_22202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC060-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 12:14:01 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 833759 was started by sandbox2 on n016,
% 0.09/0.37 % Sat Sep 26 12:14:01 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 36.73/5.71
% 36.73/5.71 % given #500 (I,wt=38): 564 app(app(A,cons(B,A)),cons(C,D)) != A | -ssList(D) | -ssList(A) | -ssItem(C) | -ssItem(B) | lt(B,C) | lt(C,B) | -lt(skaf59(A),skaf60(A)). [factor(304,c,f)].
% 36.73/5.71
% 36.73/5.71 % given #1000 (A,wt=20): 876 app(app(sk4,A),A) != B | -ssList(A) | -ssList(B) | segmentP(B,A). [factor(853,b,c)].
% 36.73/5.71
% 36.73/5.71 % given #1500 (T,wt=8): 12941 neq(sk3,sk4) | sk4 = sk3. [resolve(1071,a,71,a)].
% 36.73/5.71
% 36.73/5.71 % given #2000 (F,wt=13): 19179 cons(skaf59(A),skaf81(B)) != nil. [resolve(2088,b,220,a)].
% 36.73/5.71
% 36.73/5.71 % SZS status Unsatisfiable for theBenchmark
% 36.73/5.71
% 36.73/5.71 % Proof 1 at 3.87 (+ 1.38) seconds.
% 36.73/5.71 % Length of proof is 47.
% 36.73/5.71 % Level of proof is 11.
% 36.73/5.71 % Maximum clause weight is 17.000.
% 36.73/5.71 % Given clauses 2280.
% 36.73/5.71
% 36.73/5.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------