%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC389-1 : 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 : n008.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 08:57:41 AM UTC 2026
% Result : Unsatisfiable 113.38s 15.76s
% Output : CNFRefutation 113.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 24
% Syntax : Number of formulae : 119 ( 27 unt; 0 def)
% Number of atoms : 284 ( 99 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 311 ( 146 ~; 165 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(clause179,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ ssList(VAR_4)
| ~ duplicatefreeP(VAR_4)
| ~ ssItem(VAR_1)
| ~ ssList(VAR_0)
| ~ ssList(VAR_2)
| ~ ssList(VAR_3)
| app(app(VAR_0,cons(VAR_1,VAR_2)),cons(VAR_1,VAR_3)) != VAR_4 ),
file('theBenchmark.p',clause179) ).
cnf(c_7,plain,
( ~ ssList(E)
| ~ duplicatefreeP(E)
| ~ ssItem(B)
| ~ ssList(A)
| ~ ssList(C)
| ~ ssList(D)
| app(app(A,cons(B,C)),cons(B,D)) != E ),
inference(clausify,[status(thm)],[clause179]) ).
fof(clause2,axiom,
duplicatefreeP(nil),
file('theBenchmark.p',clause2) ).
cnf(c_10,plain,
duplicatefreeP(nil),
inference(clausify,[status(thm)],[clause2]) ).
fof(co1_21,axiom,
( neq(sk2,nil)
| ~ segmentP(sk2,sk1) ),
file('theBenchmark.p',co1_21) ).
cnf(c_30,plain,
( neq(sk2,nil)
| ~ segmentP(sk2,sk1) ),
inference(clausify,[status(thm)],[co1_21]) ).
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_31,plain,
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(A,B)
| A != B ),
inference(clausify,[status(thm)],[clause115]) ).
cnf(c_34,plain,
( ~ segmentP(sk2,sk1)
| ~ ssList(sk2)
| ~ ssList(nil)
| sk2 != nil ),
inference(resolve,[status(thm)],[c_31,c_30]) ).
cnf(c_44,plain,
( ~ ssList(nil)
| ~ ssItem(B)
| ~ ssList(A)
| ~ ssList(C)
| ~ ssList(D)
| app(app(A,cons(B,C)),cons(B,D)) != nil ),
inference(resolve,[status(thm)],[c_10,c_7]) ).
fof(clause8,axiom,
ssList(nil),
file('theBenchmark.p',clause8) ).
cnf(c_52,plain,
ssList(nil),
inference(clausify,[status(thm)],[clause8]) ).
fof(clause56,axiom,
! [VAR_0] :
( segmentP(VAR_0,nil)
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause56) ).
cnf(c_100,plain,
( segmentP(A,nil)
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause56]) ).
fof(clause73,axiom,
! [VAR_0] :
( app(VAR_0,nil) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause73) ).
cnf(c_111,plain,
( app(A,nil) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause73]) ).
fof(clause74,axiom,
! [VAR_0] :
( app(nil,VAR_0) = VAR_0
| ~ ssList(VAR_0) ),
file('theBenchmark.p',clause74) ).
cnf(c_112,plain,
( app(nil,A) = A
| ~ ssList(A) ),
inference(clausify,[status(thm)],[clause74]) ).
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_142,plain,
( singletonP(B)
| ~ ssList(B)
| ~ ssItem(A)
| cons(A,nil) != B ),
inference(clausify,[status(thm)],[clause116]) ).
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_193,plain,
( segmentP(D,B)
| ~ ssList(D)
| ~ ssList(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,B),C) != D ),
inference(clausify,[status(thm)],[clause173]) ).
fof(co1_3,axiom,
ssList(sk3),
file('theBenchmark.p',co1_3) ).
cnf(c_203,plain,
ssList(sk3),
inference(clausify,[status(thm)],[co1_3]) ).
fof(co1_4,axiom,
ssList(sk4),
file('theBenchmark.p',co1_4) ).
cnf(c_204,plain,
ssList(sk4),
inference(clausify,[status(thm)],[co1_4]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_205,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_206,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
fof(co1_7,axiom,
( nil = sk4
| ssItem(sk5) ),
file('theBenchmark.p',co1_7) ).
cnf(c_207,plain,
( nil = sk4
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_208,plain,
( sk4 = nil
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_207]) ).
fof(co1_8,axiom,
( nil = sk3
| ssItem(sk5) ),
file('theBenchmark.p',co1_8) ).
cnf(c_209,plain,
( nil = sk3
| ssItem(sk5) ),
inference(clausify,[status(thm)],[co1_8]) ).
cnf(c_210,plain,
( sk3 = nil
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_209]) ).
fof(co1_9,axiom,
( nil = sk4
| ssList(sk6) ),
file('theBenchmark.p',co1_9) ).
cnf(c_211,plain,
( nil = sk4
| ssList(sk6) ),
inference(clausify,[status(thm)],[co1_9]) ).
cnf(c_212,plain,
( sk4 = nil
| ssList(sk6) ),
inference(copy,[status(thm)],[c_211]) ).
fof(co1_10,axiom,
( nil = sk4
| ssList(sk7) ),
file('theBenchmark.p',co1_10) ).
cnf(c_213,plain,
( nil = sk4
| ssList(sk7) ),
inference(clausify,[status(thm)],[co1_10]) ).
cnf(c_214,plain,
( sk4 = nil
| ssList(sk7) ),
inference(copy,[status(thm)],[c_213]) ).
fof(co1_11,axiom,
( nil = sk4
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_11) ).
cnf(c_215,plain,
( nil = sk4
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_11]) ).
cnf(c_216,plain,
( sk4 = nil
| cons(sk5,nil) = sk3 ),
inference(copy,[status(thm)],[c_215]) ).
fof(co1_15,axiom,
( nil = sk3
| ssList(sk6) ),
file('theBenchmark.p',co1_15) ).
cnf(c_223,plain,
( nil = sk3
| ssList(sk6) ),
inference(clausify,[status(thm)],[co1_15]) ).
cnf(c_224,plain,
( sk3 = nil
| ssList(sk6) ),
inference(copy,[status(thm)],[c_223]) ).
fof(co1_16,axiom,
( nil = sk3
| ssList(sk7) ),
file('theBenchmark.p',co1_16) ).
cnf(c_225,plain,
( nil = sk3
| ssList(sk7) ),
inference(clausify,[status(thm)],[co1_16]) ).
cnf(c_226,plain,
( sk3 = nil
| ssList(sk7) ),
inference(copy,[status(thm)],[c_225]) ).
fof(co1_17,axiom,
( nil = sk3
| cons(sk5,nil) = sk3 ),
file('theBenchmark.p',co1_17) ).
cnf(c_227,plain,
( nil = sk3
| cons(sk5,nil) = sk3 ),
inference(clausify,[status(thm)],[co1_17]) ).
cnf(c_228,plain,
( sk3 = nil
| cons(sk5,nil) = sk3 ),
inference(copy,[status(thm)],[c_227]) ).
fof(co1_18,axiom,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
file('theBenchmark.p',co1_18) ).
cnf(c_229,plain,
( nil = sk3
| app(app(sk6,sk3),sk7) = sk4 ),
inference(clausify,[status(thm)],[co1_18]) ).
cnf(c_230,plain,
( sk3 = nil
| app(app(sk6,sk3),sk7) = sk4 ),
inference(copy,[status(thm)],[c_229]) ).
fof(co1_22,axiom,
( ~ singletonP(sk1)
| ~ segmentP(sk2,sk1) ),
file('theBenchmark.p',co1_22) ).
cnf(c_235,plain,
( ~ singletonP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(clausify,[status(thm)],[co1_22]) ).
cnf(c_13813,plain,
( ~ singletonP(sk1)
| ~ segmentP(sk4,sk1) ),
inference(paramod,[status(thm)],[c_205,c_235]) ).
cnf(c_13814,plain,
( ~ singletonP(sk1)
| ~ segmentP(sk4,sk3) ),
inference(paramod,[status(thm)],[c_206,c_13813]) ).
cnf(c_236,plain,
( ~ singletonP(sk3)
| ~ segmentP(sk4,sk3) ),
inference(paramod,[status(thm)],[c_206,c_13814]) ).
cnf(c_13815,plain,
( ~ ssList(nil)
| ~ ssItem(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,cons(B,C)),cons(B,C)) != nil ),
inference(factor,[status(thm)],[c_44]) ).
cnf(c_294,plain,
( ~ ssItem(B)
| ~ ssList(A)
| ~ ssList(C)
| app(app(A,cons(B,C)),cons(B,C)) != nil ),
inference(resolve,[status(thm)],[c_52,c_13815]) ).
cnf(c_13816,plain,
( ~ segmentP(sk2,sk1)
| ~ ssList(sk2)
| ~ ssList(nil)
| sk4 != nil ),
inference(paramod,[status(thm)],[c_205,c_34]) ).
cnf(c_13817,plain,
( ~ segmentP(sk2,sk1)
| ~ ssList(sk4)
| ~ ssList(nil)
| sk4 != nil ),
inference(paramod,[status(thm)],[c_205,c_13816]) ).
cnf(c_13818,plain,
( ~ segmentP(sk4,sk1)
| ~ ssList(sk4)
| ~ ssList(nil)
| sk4 != nil ),
inference(paramod,[status(thm)],[c_205,c_13817]) ).
cnf(c_13819,plain,
( ~ segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(nil)
| sk4 != nil ),
inference(paramod,[status(thm)],[c_206,c_13818]) ).
cnf(c_13820,plain,
( ~ segmentP(sk4,sk3)
| ~ ssList(sk4)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_52,c_13819]) ).
cnf(c_321,plain,
( ~ segmentP(sk4,sk3)
| sk4 != nil ),
inference(resolve,[status(thm)],[c_204,c_13820]) ).
cnf(c_508,plain,
( ~ ssItem(B)
| ~ ssList(A)
| app(app(A,cons(B,A)),cons(B,A)) != nil ),
inference(factor,[status(thm)],[c_294]) ).
cnf(c_887,plain,
segmentP(nil,nil),
inference(resolve,[status(thm)],[c_100,c_52]) ).
cnf(c_1137,plain,
app(nil,nil) = nil,
inference(resolve,[status(thm)],[c_111,c_52]) ).
cnf(c_7091,plain,
app(nil,sk3) = sk3,
inference(resolve,[status(thm)],[c_203,c_112]) ).
cnf(c_7272,plain,
segmentP(sk4,nil),
inference(resolve,[status(thm)],[c_204,c_100]) ).
cnf(c_13821,plain,
( singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_216,c_142]) ).
cnf(c_7924,plain,
( singletonP(sk3)
| ~ ssItem(sk5)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_203,c_13821]) ).
cnf(c_13822,plain,
( singletonP(sk3)
| ~ ssList(sk3)
| ~ ssItem(sk5)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_228,c_142]) ).
cnf(c_8350,plain,
( singletonP(sk3)
| ~ ssItem(sk5)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_203,c_13822]) ).
cnf(c_13823,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk7)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_230,c_193]) ).
cnf(c_13824,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(sk6)
| ~ ssList(sk7)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_203,c_13823]) ).
cnf(c_8375,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk6)
| ~ ssList(sk7)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_204,c_13824]) ).
cnf(c_13825,plain,
( ~ singletonP(sk3)
| ~ segmentP(sk4,nil)
| cons(sk5,nil) = sk3 ),
inference(paramod,[status(thm)],[c_228,c_236]) ).
cnf(c_8444,plain,
( ~ singletonP(sk3)
| cons(sk5,nil) = sk3 ),
inference(resolve,[status(thm)],[c_7272,c_13825]) ).
cnf(c_9052,plain,
( ssList(sk7)
| ~ segmentP(sk4,sk3) ),
inference(resolve,[status(thm)],[c_321,c_214]) ).
cnf(c_9053,plain,
( ssList(sk6)
| ~ segmentP(sk4,sk3) ),
inference(resolve,[status(thm)],[c_321,c_212]) ).
cnf(c_9054,plain,
( ssItem(sk5)
| ~ segmentP(sk4,sk3) ),
inference(resolve,[status(thm)],[c_321,c_208]) ).
cnf(c_13826,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| app(app(nil,sk3),cons(sk5,nil)) != nil
| sk4 = nil ),
inference(paramod,[status(thm)],[c_216,c_508]) ).
cnf(c_13827,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| app(sk3,cons(sk5,nil)) != nil
| sk4 = nil ),
inference(paramod,[status(thm)],[c_7091,c_13826]) ).
cnf(c_10153,plain,
( ~ ssItem(sk5)
| app(sk3,cons(sk5,nil)) != nil
| sk4 = nil ),
inference(resolve,[status(thm)],[c_52,c_13827]) ).
cnf(c_13828,plain,
( ssList(sk7)
| ~ segmentP(sk4,nil)
| ssList(sk7) ),
inference(paramod,[status(thm)],[c_226,c_9052]) ).
cnf(c_13829,plain,
( ~ segmentP(sk4,nil)
| ssList(sk7) ),
inference(copy,[status(thm)],[c_13828]) ).
cnf(c_12898,plain,
ssList(sk7),
inference(resolve,[status(thm)],[c_7272,c_13829]) ).
cnf(c_12913,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk6)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_12898,c_8375]) ).
cnf(c_13830,plain,
( ssList(sk6)
| ~ segmentP(sk4,nil)
| ssList(sk6) ),
inference(paramod,[status(thm)],[c_224,c_9053]) ).
cnf(c_13831,plain,
( ~ segmentP(sk4,nil)
| ssList(sk6) ),
inference(copy,[status(thm)],[c_13830]) ).
cnf(c_13178,plain,
ssList(sk6),
inference(resolve,[status(thm)],[c_7272,c_13831]) ).
cnf(c_13183,plain,
( segmentP(sk4,sk3)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_13178,c_12913]) ).
cnf(c_13832,plain,
( ssItem(sk5)
| ~ segmentP(sk4,nil)
| ssItem(sk5) ),
inference(paramod,[status(thm)],[c_210,c_9054]) ).
cnf(c_13833,plain,
( ~ segmentP(sk4,nil)
| ssItem(sk5) ),
inference(copy,[status(thm)],[c_13832]) ).
cnf(c_13429,plain,
ssItem(sk5),
inference(resolve,[status(thm)],[c_7272,c_13833]) ).
cnf(c_13437,plain,
( app(sk3,cons(sk5,nil)) != nil
| sk4 = nil ),
inference(resolve,[status(thm)],[c_13429,c_10153]) ).
cnf(c_13462,plain,
( singletonP(sk3)
| sk3 = nil ),
inference(resolve,[status(thm)],[c_13429,c_8350]) ).
cnf(c_13475,plain,
( singletonP(sk3)
| sk4 = nil ),
inference(resolve,[status(thm)],[c_13429,c_7924]) ).
cnf(c_13834,plain,
( ~ segmentP(sk4,nil)
| sk4 != nil
| singletonP(sk3) ),
inference(paramod,[status(thm)],[c_13462,c_321]) ).
cnf(c_13687,plain,
( sk4 != nil
| singletonP(sk3) ),
inference(resolve,[status(thm)],[c_7272,c_13834]) ).
cnf(c_13835,plain,
( singletonP(sk3)
| singletonP(sk3) ),
inference(resolve,[status(thm)],[c_13687,c_13475]) ).
cnf(c_13775,plain,
singletonP(sk3),
inference(copy,[status(thm)],[c_13835]) ).
cnf(c_13777,plain,
cons(sk5,nil) = sk3,
inference(resolve,[status(thm)],[c_13775,c_8444]) ).
cnf(c_13779,plain,
~ segmentP(sk4,sk3),
inference(resolve,[status(thm)],[c_13775,c_236]) ).
cnf(c_13789,plain,
( app(sk3,sk3) != nil
| sk4 = nil ),
inference(paramod,[status(thm)],[c_13777,c_13437]) ).
cnf(c_13801,plain,
sk3 = nil,
inference(resolve,[status(thm)],[c_13779,c_13183]) ).
cnf(c_13836,plain,
( app(nil,sk3) != nil
| sk4 = nil ),
inference(paramod,[status(thm)],[c_13801,c_13789]) ).
cnf(c_13837,plain,
( app(nil,nil) != nil
| sk4 = nil ),
inference(paramod,[status(thm)],[c_13801,c_13836]) ).
cnf(c_13838,plain,
( nil != nil
| sk4 = nil ),
inference(paramod,[status(thm)],[c_1137,c_13837]) ).
cnf(c_13807,plain,
sk4 = nil,
inference(copy,[status(thm)],[c_13838]) ).
cnf(c_13839,plain,
~ segmentP(nil,sk3),
inference(paramod,[status(thm)],[c_13807,c_13779]) ).
cnf(c_13840,plain,
~ segmentP(nil,nil),
inference(paramod,[status(thm)],[c_13801,c_13839]) ).
cnf(c_13812,plain,
$false,
inference(resolve,[status(thm)],[c_887,c_13840]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC389-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n008.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 12:57:24 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 3721991 was started by sandbox on n008,
% 0.16/0.42 % Sat Sep 26 12:57:24 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 113.38/15.76
% 113.38/15.76 % given #500 (I,wt=34): 572 app(app(A,cons(B,C)),cons(D,A)) != C | -ssList(A) | -ssList(C) | -ssItem(D) | -ssItem(B) | -totalorderedP(C) | leq(B,D). [factor(382,c,g)].
% 113.38/15.76
% 113.38/15.76 % SZS status Unsatisfiable for theBenchmark
% 113.38/15.76
% 113.38/15.76 % Proof 1 at 5.44 (+ 1.71) seconds.
% 113.38/15.76 % Length of proof is 67.
% 113.38/15.76 % Level of proof is 11.
% 113.38/15.76 % Maximum clause weight is 31.000.
% 113.38/15.76 % Given clauses 937.
% 113.38/15.76
% 113.38/15.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------