%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC386-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 08:57:40 AM UTC 2026
% Result : Unsatisfiable 54.42s 8.35s
% Output : CNFRefutation 54.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 20
% Syntax : Number of formulae : 98 ( 23 unt; 0 def)
% Number of atoms : 228 ( 105 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 241 ( 111 ~; 130 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_15,axiom,
( neq(sk2,nil)
| nil != sk1 ),
file('theBenchmark.p',co1_15) ).
cnf(c_31,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_15]) ).
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_32,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
cnf(c_35,plain,
( nil != sk1
| ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_32,c_31]) ).
cnf(c_36,plain,
( sk1 != nil
| ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(copy,[status(thm)],[c_35]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_57,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
fof(clause11,axiom,
~ singletonP(nil),
file('theBenchmark.p',clause11) ).
cnf(c_60,plain,
~ singletonP(nil),
inference(clausify,[status(thm)],[clause11]) ).
fof(clause71,axiom,
! [VAR_0] :
( ~ ssItem(VAR_0)
| ~ memberP(nil,VAR_0) ),
file('theBenchmark.p',clause71) ).
cnf(c_115,plain,
( ~ ssItem(A)
| ~ memberP(nil,A) ),
inference(clausify,[status(thm)],[clause71]) ).
fof(clause73,axiom,
! [VAR_0] :
( app(VAR_0,nil) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause73) ).
cnf(c_116,plain,
( app(A,nil) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause73]) ).
fof(clause116,axiom,
! [VAR_0,VAR_1] :
( singletonP(VAR_1)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0)
| cons(VAR_0,nil) != VAR_1 ),
file('theBenchmark.p',clause116) ).
cnf(c_147,plain,
( singletonP(B)
| ~ ssList(B)
| ~ ssItem(A)
| cons(A,nil) != B ),
inference(clausify,[status(thm)],[clause116]) ).
fof(clause140,axiom,
! [VAR_0,VAR_1,VAR_2] :
( memberP(app(VAR_0,VAR_2),VAR_1)
| ~ ssItem(VAR_1)
| ~ ssList(VAR_0)
| ~ ssList(VAR_2)
| ~ memberP(VAR_0,VAR_1) ),
file('theBenchmark.p',clause140) ).
cnf(c_169,plain,
( memberP(app(A,C),B)
| ~ ssItem(B)
| ~ ssList(A)
| ~ ssList(C)
| ~ memberP(A,B) ),
inference(clausify,[status(thm)],[clause140]) ).
fof(co1_2,axiom,
ssList(sk2),
file('theBenchmark.p',co1_2) ).
cnf(c_207,plain,
ssList(sk2),
inference(clausify,[status(thm)],[co1_2]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_208,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_210,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_211,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_210]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_212,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_7,axiom,
( nil = sk4
| ssItem(sk5) ),
file('theBenchmark.p',co1_7) ).
cnf(c_213,plain,
( nil = sk4
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_11072,plain,
( nil = sk2
| ssItem(sk5) ),
inference(paramod,[status(thm)],[c_211,c_213]) ).
cnf(c_214,plain,
( sk2 = nil
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_11072]) ).
fof(co1_8,axiom,
( nil = sk3
| ssItem(sk5) ),
file('theBenchmark.p',co1_8) ).
cnf(c_215,plain,
( nil = sk3
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_216,plain,
( sk3 = nil
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_215]) ).
fof(co1_9,axiom,
( nil = sk4
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_9) ).
cnf(c_217,plain,
( nil = sk4
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_11073,plain,
( nil = sk2
| cons(sk5,nil) = sk3 ),
inference(paramod,[status(thm)],[c_211,c_217]) ).
cnf(c_218,plain,
( sk2 = nil
| cons(sk5,nil) = sk3 ),
inference(copy,[status(thm)],[c_11073]) ).
fof(co1_10,axiom,
( nil = sk4
| memberP(sk4,sk5) ),
file('theBenchmark.p',co1_10) ).
cnf(c_219,plain,
( nil = sk4
| memberP(sk4,sk5) ),
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_11074,plain,
( nil = sk4
| memberP(sk2,sk5) ),
inference(paramod,[status(thm)],[c_211,c_219]) ).
cnf(c_11075,plain,
( nil = sk2
| memberP(sk2,sk5) ),
inference(paramod,[status(thm)],[c_211,c_11074]) ).
cnf(c_220,plain,
( sk2 = nil
| memberP(sk2,sk5) ),
inference(copy,[status(thm)],[c_11075]) ).
fof(co1_11,axiom,
( nil = sk3
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_11) ).
cnf(c_221,plain,
( nil = sk3
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_222,plain,
( sk3 = nil
| cons(sk5,nil) = sk3 ),
inference(copy,[status(thm)],[c_221]) ).
fof(co1_12,axiom,
( nil = sk3
| memberP(sk4,sk5) ),
file('theBenchmark.p',co1_12) ).
cnf(c_223,plain,
( nil = sk3
| memberP(sk4,sk5) ),
inference(clausify,[status(thm)],[co1_12]) ).
cnf(c_11076,plain,
( nil = sk3
| memberP(sk2,sk5) ),
inference(paramod,[status(thm)],[c_211,c_223]) ).
cnf(c_224,plain,
( sk3 = nil
| memberP(sk2,sk5) ),
inference(copy,[status(thm)],[c_11076]) ).
fof(co1_14,axiom,
! [VAR_0] :
( ~ memberP(sk2,VAR_0)
| cons(VAR_0,nil) != sk1
| ~ ssItem(VAR_0)
| nil = sk2 ),
file('theBenchmark.p',co1_14) ).
cnf(c_225,plain,
( ~ memberP(sk2,A)
| cons(A,nil) != sk1
| ~ ssItem(A)
| nil = sk2 ),
inference(clausify,[status(thm)],[co1_14]) ).
cnf(c_11077,plain,
( ~ memberP(sk2,A)
| cons(A,nil) != sk3
| ~ ssItem(A)
| nil = sk2 ),
inference(paramod,[status(thm)],[c_212,c_225]) ).
cnf(c_226,plain,
( ~ memberP(sk2,A)
| cons(A,nil) != sk3
| ~ ssItem(A)
| sk2 = nil ),
inference(copy,[status(thm)],[c_11077]) ).
fof(co1_16,axiom,
! [VAR_0] :
( ~ memberP(sk2,VAR_0)
| cons(VAR_0,nil) != sk1
| ~ ssItem(VAR_0)
| nil != sk1 ),
file('theBenchmark.p',co1_16) ).
cnf(c_227,plain,
( ~ memberP(sk2,A)
| cons(A,nil) != sk1
| ~ ssItem(A)
| nil != sk1 ),
inference(clausify,[status(thm)],[co1_16]) ).
cnf(c_11078,plain,
( ~ memberP(sk2,A)
| cons(A,nil) != sk1
| ~ ssItem(A)
| nil != sk3 ),
inference(paramod,[status(thm)],[c_212,c_227]) ).
cnf(c_11079,plain,
( ~ memberP(sk2,A)
| cons(A,nil) != sk3
| ~ ssItem(A)
| nil != sk3 ),
inference(paramod,[status(thm)],[c_212,c_11078]) ).
cnf(c_228,plain,
( ~ memberP(sk2,A)
| cons(A,nil) != sk3
| ~ ssItem(A)
| sk3 != nil ),
inference(copy,[status(thm)],[c_11079]) ).
cnf(c_11080,plain,
( sk3 != nil
| ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(paramod,[status(thm)],[c_212,c_36]) ).
cnf(c_11081,plain,
( sk3 != nil
| ~ ssList(sk2)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_57,c_11080]) ).
cnf(c_313,plain,
( sk3 != nil
| sk2 != nil ),
inference(resolve,[status(thm)],[c_207,c_11081]) ).
cnf(c_329,plain,
( memberP(app(A,A),B)
| ~ ssItem(B)
| ~ ssList(A)
| ~ memberP(A,B) ),
inference(factor,[status(thm)],[c_169]) ).
cnf(c_1129,plain,
app(nil,nil) = nil,
inference(resolve,[status(thm)],[c_116,c_57]) ).
cnf(c_11082,plain,
( singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_218,c_147]) ).
cnf(c_7530,plain,
( singletonP(sk3)
| ~ ssItem(sk5)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_208,c_11082]) ).
cnf(c_11083,plain,
( singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_222,c_147]) ).
cnf(c_7586,plain,
( singletonP(sk3)
| ~ ssItem(sk5)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_208,c_11083]) ).
cnf(c_11084,plain,
( sk2 = nil
| cons(sk5,nil) != sk3
| ~ ssItem(sk5)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_226,c_220]) ).
cnf(c_7662,plain,
( cons(sk5,nil) != sk3
| ~ ssItem(sk5)
| sk2 = nil ),
inference(copy,[status(thm)],[c_11084]) ).
cnf(c_8546,plain,
( ssItem(sk5)
| sk3 != nil ),
inference(resolve,[status(thm)],[c_313,c_214]) ).
cnf(c_11085,plain,
( sk3 = nil
| memberP(app(sk2,sk2),sk5)
| ~ ssItem(sk5)
| ~ ssList(sk2) ),
inference(resolve,[status(thm)],[c_329,c_224]) ).
cnf(c_8919,plain,
( sk3 = nil
| memberP(app(sk2,sk2),sk5)
| ~ ssItem(sk5) ),
inference(resolve,[status(thm)],[c_207,c_11085]) ).
cnf(c_11086,plain,
( ssItem(sk5)
| ssItem(sk5) ),
inference(resolve,[status(thm)],[c_8546,c_216]) ).
cnf(c_10776,plain,
ssItem(sk5),
inference(copy,[status(thm)],[c_11086]) ).
cnf(c_10815,plain,
( sk3 = nil
| memberP(app(sk2,sk2),sk5) ),
inference(resolve,[status(thm)],[c_10776,c_8919]) ).
cnf(c_10840,plain,
( cons(sk5,nil) != sk3
| sk2 = nil ),
inference(resolve,[status(thm)],[c_10776,c_7662]) ).
cnf(c_10858,plain,
( singletonP(sk3)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_10776,c_7586]) ).
cnf(c_10876,plain,
( singletonP(sk3)
| sk2 = nil ),
inference(resolve,[status(thm)],[c_10776,c_7530]) ).
cnf(c_10909,plain,
( ~ memberP(sk2,sk5)
| cons(sk5,nil) != sk3
| sk3 != nil ),
inference(resolve,[status(thm)],[c_10776,c_228]) ).
cnf(c_10978,plain,
~ memberP(nil,sk5),
inference(resolve,[status(thm)],[c_10776,c_115]) ).
cnf(c_10991,plain,
( sk2 != nil
| singletonP(sk3) ),
inference(resolve,[status(thm)],[c_10858,c_313]) ).
cnf(c_11087,plain,
( singletonP(sk3)
| singletonP(sk3) ),
inference(resolve,[status(thm)],[c_10991,c_10876]) ).
cnf(c_11022,plain,
singletonP(sk3),
inference(copy,[status(thm)],[c_11087]) ).
cnf(c_11088,plain,
( singletonP(nil)
| cons(sk5,nil) = sk3 ),
inference(paramod,[status(thm)],[c_222,c_11022]) ).
cnf(c_11024,plain,
cons(sk5,nil) = sk3,
inference(resolve,[status(thm)],[c_60,c_11088]) ).
cnf(c_11089,plain,
( singletonP(nil)
| memberP(sk2,sk5) ),
inference(paramod,[status(thm)],[c_224,c_11022]) ).
cnf(c_11025,plain,
memberP(sk2,sk5),
inference(resolve,[status(thm)],[c_60,c_11089]) ).
cnf(c_11090,plain,
( ~ memberP(sk2,sk5)
| sk3 != sk3
| sk3 != nil ),
inference(paramod,[status(thm)],[c_11024,c_10909]) ).
cnf(c_11091,plain,
( ~ memberP(sk2,sk5)
| sk3 != nil ),
inference(copy,[status(thm)],[c_11090]) ).
cnf(c_11032,plain,
sk3 != nil,
inference(resolve,[status(thm)],[c_11025,c_11091]) ).
cnf(c_11092,plain,
( sk3 != sk3
| sk2 = nil ),
inference(paramod,[status(thm)],[c_11024,c_10840]) ).
cnf(c_11038,plain,
sk2 = nil,
inference(copy,[status(thm)],[c_11092]) ).
cnf(c_11093,plain,
( sk3 = nil
| memberP(app(nil,sk2),sk5) ),
inference(paramod,[status(thm)],[c_11038,c_10815]) ).
cnf(c_11094,plain,
( sk3 = nil
| memberP(app(nil,nil),sk5) ),
inference(paramod,[status(thm)],[c_11038,c_11093]) ).
cnf(c_11095,plain,
( sk3 = nil
| memberP(nil,sk5) ),
inference(paramod,[status(thm)],[c_1129,c_11094]) ).
cnf(c_11096,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_10978,c_11095]) ).
cnf(c_11071,plain,
$false,
inference(resolve,[status(thm)],[c_11032,c_11096]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC386-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n026.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 12:59:25 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 1040663 was started by sandbox on n026,
% 0.17/0.44 % Sat Sep 26 12:59:25 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 54.42/8.35
% 54.42/8.35 % given #500 (I,wt=33): 571 app(A,cons(B,cons(C,A))) != A | -ssList(A) | -ssItem(C) | -ssItem(B) | B = C | skaf79(A) != skaf78(A). [factor(383,b,e)].
% 54.42/8.35
% 54.42/8.35 % SZS status Unsatisfiable for theBenchmark
% 54.42/8.35
% 54.42/8.35 % Proof 1 at 5.49 (+ 1.70) seconds.
% 54.42/8.35 % Length of proof is 53.
% 54.42/8.35 % Level of proof is 11.
% 54.42/8.35 % Maximum clause weight is 18.000.
% 54.42/8.35 % Given clauses 842.
% 54.42/8.35
% 54.42/8.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------