%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC090-1 : 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 : n005.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 08:56:47 AM UTC 2026
% Result : Unsatisfiable 31.91s 5.05s
% Output : CNFRefutation 31.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 92 ( 39 unt; 0 def)
% Number of atoms : 206 ( 59 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 238 ( 124 ~; 114 |; 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 : 54 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_12,axiom,
app(sk6,sk5) = sk3,
file('theBenchmark.p',co1_12) ).
cnf(c_51,plain,
app(sk6,sk5) = sk3,
inference(clausify,[status(thm)],[co1_12]) ).
fof(co1_11,axiom,
app(sk5,sk6) = sk4,
file('theBenchmark.p',co1_11) ).
cnf(c_52,plain,
app(sk5,sk6) = sk4,
inference(clausify,[status(thm)],[co1_11]) ).
fof(co1_10,axiom,
ssList(sk6),
file('theBenchmark.p',co1_10) ).
cnf(c_53,plain,
ssList(sk6),
inference(clausify,[status(thm)],[co1_10]) ).
fof(co1_9,axiom,
ssList(sk5),
file('theBenchmark.p',co1_9) ).
cnf(c_54,plain,
ssList(sk5),
inference(clausify,[status(thm)],[co1_9]) ).
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_55,plain,
( ~ segmentP(sk1,A)
| ~ segmentP(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_56,plain,
neq(sk2,nil),
inference(clausify,[status(thm)],[co1_7]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_57,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_58,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_59,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_58]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_60,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
cnf(c_61,plain,
ssList(sk2),
inference(paramod,[status(thm)],[c_59,c_60]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_62,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_71,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
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(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_156,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
fof(clause73,axiom,
! [VAR_0] :
( app(VAR_0,nil) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause73) ).
cnf(c_157,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_167,plain,
( segmentP(A,A)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause57]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_216,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
cnf(c_320,plain,
( ~ segmentP(sk3,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ ssList(A) ),
inference(paramod,[status(thm)],[c_57,c_55]) ).
cnf(c_321,plain,
app(sk5,sk6) = sk2,
inference(paramod,[status(thm)],[c_59,c_52]) ).
cnf(c_912,plain,
( segmentP(sk3,B)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != sk3 ),
inference(resolve,[status(thm)],[c_71,c_62]) ).
cnf(c_913,plain,
( segmentP(sk2,B)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != sk2 ),
inference(resolve,[status(thm)],[c_71,c_61]) ).
cnf(c_20057,plain,
( segmentP(B,sk5)
| ~ ssList(B)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(A)
| app(sk3,A) != B ),
inference(paramod,[status(thm)],[c_51,c_71]) ).
cnf(c_20058,plain,
( segmentP(B,sk5)
| ~ ssList(B)
| ~ ssList(sk5)
| ~ ssList(A)
| app(sk3,A) != B ),
inference(resolve,[status(thm)],[c_53,c_20057]) ).
cnf(c_916,plain,
( segmentP(B,sk5)
| ~ ssList(B)
| ~ ssList(A)
| app(sk3,A) != B ),
inference(resolve,[status(thm)],[c_54,c_20058]) ).
cnf(c_20059,plain,
( ~ ssList(A)
| ~ neq(A,sk2)
| A != sk2 ),
inference(resolve,[status(thm)],[c_124,c_61]) ).
cnf(c_1435,plain,
( ~ ssList(A)
| ~ neq(A,sk2)
| sk2 != A ),
inference(copy,[status(thm)],[c_20059]) ).
cnf(c_20060,plain,
( ~ ssList(A)
| ~ neq(A,sk5)
| A != sk5 ),
inference(resolve,[status(thm)],[c_124,c_54]) ).
cnf(c_1436,plain,
( ~ ssList(A)
| ~ neq(A,sk5)
| sk5 != A ),
inference(copy,[status(thm)],[c_20060]) ).
cnf(c_20061,plain,
( A = sk2
| neq(A,sk2)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_139,c_61]) ).
cnf(c_1472,plain,
( sk2 = A
| neq(A,sk2)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_20061]) ).
cnf(c_20062,plain,
( A = sk5
| neq(A,sk5)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_139,c_54]) ).
cnf(c_1473,plain,
( sk5 = A
| neq(A,sk5)
| ~ ssList(A) ),
inference(copy,[status(thm)],[c_20062]) ).
cnf(c_1477,plain,
( sk5 = A
| neq(sk5,A)
| ~ ssList(A) ),
inference(resolve,[status(thm)],[c_139,c_54]) ).
cnf(c_1548,plain,
app(nil,sk2) = sk2,
inference(resolve,[status(thm)],[c_156,c_61]) ).
cnf(c_1549,plain,
app(nil,sk5) = sk5,
inference(resolve,[status(thm)],[c_156,c_54]) ).
cnf(c_1550,plain,
app(nil,sk6) = sk6,
inference(resolve,[status(thm)],[c_156,c_53]) ).
cnf(c_1551,plain,
app(sk3,nil) = sk3,
inference(resolve,[status(thm)],[c_157,c_62]) ).
cnf(c_1572,plain,
segmentP(sk2,sk2),
inference(resolve,[status(thm)],[c_167,c_61]) ).
cnf(c_20063,plain,
( ~ segmentP(sk3,sk2)
| ~ segmentP(sk2,sk2)
| ~ neq(sk2,nil) ),
inference(resolve,[status(thm)],[c_320,c_61]) ).
cnf(c_20064,plain,
( ~ segmentP(sk3,sk2)
| ~ segmentP(sk2,sk2) ),
inference(resolve,[status(thm)],[c_56,c_20063]) ).
cnf(c_8266,plain,
~ segmentP(sk3,sk2),
inference(resolve,[status(thm)],[c_1572,c_20064]) ).
cnf(c_8267,plain,
( ~ segmentP(sk3,sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil) ),
inference(resolve,[status(thm)],[c_320,c_54]) ).
cnf(c_20065,plain,
( ~ neq(sk6,sk2)
| sk2 != sk6 ),
inference(resolve,[status(thm)],[c_1435,c_53]) ).
cnf(c_13059,plain,
( ~ neq(sk6,sk2)
| sk6 != sk2 ),
inference(copy,[status(thm)],[c_20065]) ).
cnf(c_13175,plain,
( ~ neq(nil,sk5)
| sk5 != nil ),
inference(resolve,[status(thm)],[c_1436,c_216]) ).
cnf(c_20066,plain,
( segmentP(sk3,sk2)
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ ssList(A)
| app(sk2,A) != sk3 ),
inference(paramod,[status(thm)],[c_1548,c_912]) ).
cnf(c_20067,plain,
( segmentP(sk3,sk2)
| ~ ssList(sk2)
| ~ ssList(A)
| app(sk2,A) != sk3 ),
inference(resolve,[status(thm)],[c_216,c_20066]) ).
cnf(c_20068,plain,
( segmentP(sk3,sk2)
| ~ ssList(A)
| app(sk2,A) != sk3 ),
inference(resolve,[status(thm)],[c_61,c_20067]) ).
cnf(c_14295,plain,
( ~ ssList(A)
| app(sk2,A) != sk3 ),
inference(resolve,[status(thm)],[c_8266,c_20068]) ).
cnf(c_20069,plain,
( segmentP(sk2,sk5)
| ~ ssList(sk5)
| ~ ssList(nil)
| ~ ssList(A)
| app(sk5,A) != sk2 ),
inference(paramod,[status(thm)],[c_1549,c_913]) ).
cnf(c_20070,plain,
( segmentP(sk2,sk5)
| ~ ssList(sk5)
| ~ ssList(A)
| app(sk5,A) != sk2 ),
inference(resolve,[status(thm)],[c_216,c_20069]) ).
cnf(c_14301,plain,
( segmentP(sk2,sk5)
| ~ ssList(A)
| app(sk5,A) != sk2 ),
inference(resolve,[status(thm)],[c_54,c_20070]) ).
cnf(c_20071,plain,
( segmentP(sk3,sk5)
| ~ ssList(sk3)
| ~ ssList(nil) ),
inference(resolve,[status(thm)],[c_916,c_1551]) ).
cnf(c_20072,plain,
( segmentP(sk3,sk5)
| ~ ssList(sk3) ),
inference(resolve,[status(thm)],[c_216,c_20071]) ).
cnf(c_14357,plain,
segmentP(sk3,sk5),
inference(resolve,[status(thm)],[c_62,c_20072]) ).
cnf(c_14424,plain,
( ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil) ),
inference(resolve,[status(thm)],[c_14357,c_8267]) ).
cnf(c_14811,plain,
app(sk2,sk5) != sk3,
inference(resolve,[status(thm)],[c_14295,c_54]) ).
cnf(c_20073,plain,
( sk2 = sk6
| neq(sk6,sk2) ),
inference(resolve,[status(thm)],[c_1472,c_53]) ).
cnf(c_17317,plain,
( sk6 = sk2
| neq(sk6,sk2) ),
inference(copy,[status(thm)],[c_20073]) ).
cnf(c_20074,plain,
( app(sk2,sk5) = sk3
| neq(sk6,sk2) ),
inference(paramod,[status(thm)],[c_17317,c_51]) ).
cnf(c_17370,plain,
neq(sk6,sk2),
inference(resolve,[status(thm)],[c_14811,c_20074]) ).
cnf(c_17371,plain,
sk6 != sk2,
inference(resolve,[status(thm)],[c_17370,c_13059]) ).
cnf(c_17415,plain,
( sk5 = nil
| neq(nil,sk5) ),
inference(resolve,[status(thm)],[c_1473,c_216]) ).
cnf(c_20075,plain,
( app(nil,sk6) = sk2
| neq(nil,sk5) ),
inference(paramod,[status(thm)],[c_17415,c_321]) ).
cnf(c_20076,plain,
( sk6 = sk2
| neq(nil,sk5) ),
inference(paramod,[status(thm)],[c_1550,c_20075]) ).
cnf(c_17461,plain,
neq(nil,sk5),
inference(resolve,[status(thm)],[c_17371,c_20076]) ).
cnf(c_17462,plain,
sk5 != nil,
inference(resolve,[status(thm)],[c_17461,c_13175]) ).
cnf(c_20077,plain,
( sk5 = nil
| neq(sk5,nil) ),
inference(resolve,[status(thm)],[c_1477,c_216]) ).
cnf(c_19972,plain,
neq(sk5,nil),
inference(resolve,[status(thm)],[c_17462,c_20077]) ).
cnf(c_20002,plain,
~ segmentP(sk2,sk5),
inference(resolve,[status(thm)],[c_19972,c_14424]) ).
cnf(c_20012,plain,
( ~ ssList(A)
| app(sk5,A) != sk2 ),
inference(resolve,[status(thm)],[c_20002,c_14301]) ).
cnf(c_20078,plain,
~ ssList(sk6),
inference(resolve,[status(thm)],[c_20012,c_321]) ).
cnf(c_20056,plain,
$false,
inference(resolve,[status(thm)],[c_53,c_20078]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC090-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n005.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 12:13:31 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.40 % Process 2098651 was started by sandbox2 on n005,
% 0.12/0.40 % Sat Sep 26 12:13:31 2026
% 0.12/0.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.40
% 0.12/0.40 % From the command line: assign(max_seconds, 300).
% 31.91/5.05
% 31.91/5.05 % given #500 (I,wt=37): 559 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)].
% 31.91/5.05
% 31.91/5.05 % given #1000 (F,wt=9): 9580 -neq(skaf72(A),skaf72(A)). [resolve(386,b,201,a)].
% 31.91/5.05
% 31.91/5.05 % given #1500 (W,wt=8): 15288 neq(nil,sk3) | segmentP(nil,sk5). [resolve(15250,b,15186,a)].
% 31.91/5.05
% 31.91/5.05 % given #2000 (F,wt=11): 18573 app(A,sk6) != nil | -ssList(A). [back_unit_del(1410),unit_del(c,18559)].
% 31.91/5.05
% 31.91/5.05 % SZS status Unsatisfiable for theBenchmark
% 31.91/5.05
% 31.91/5.05 % Proof 1 at 3.47 (+ 1.12) seconds.
% 31.91/5.05 % Length of proof is 53.
% 31.91/5.05 % Level of proof is 14.
% 31.91/5.05 % Maximum clause weight is 26.000.
% 31.91/5.05 % Given clauses 2196.
% 31.91/5.05
% 31.91/5.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------