%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC002-1 : 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 08:56:30 AM UTC 2026
% Result : Unsatisfiable 32.55s 4.66s
% Output : CNFRefutation 32.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 82 ( 18 unt; 0 def)
% Number of atoms : 279 ( 76 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 405 ( 208 ~; 197 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 56 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1_28,axiom,
! [VAR_0] :
( ~ neq(sk4,nil)
| ~ geq(VAR_0,sk6)
| ~ memberP(sk4,VAR_0)
| sk6 = VAR_0
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_28) ).
cnf(c_51,plain,
( ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| sk6 = A
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_28]) ).
fof(co1_27,axiom,
( ~ neq(sk4,nil)
| app(sk7,sk8) = sk3 ),
file('theBenchmark.p',co1_27) ).
cnf(c_52,plain,
( ~ neq(sk4,nil)
| app(sk7,sk8) = sk3 ),
inference(clausify,[status(thm)],[co1_27]) ).
fof(co1_26,axiom,
( ~ neq(sk4,nil)
| app(app(sk7,cons(sk6,nil)),sk8) = sk4 ),
file('theBenchmark.p',co1_26) ).
cnf(c_53,plain,
( ~ neq(sk4,nil)
| app(app(sk7,cons(sk6,nil)),sk8) = sk4 ),
inference(clausify,[status(thm)],[co1_26]) ).
fof(co1_25,axiom,
( ~ neq(sk4,nil)
| ssList(sk8) ),
file('theBenchmark.p',co1_25) ).
cnf(c_54,plain,
( ~ neq(sk4,nil)
| ssList(sk8) ),
inference(clausify,[status(thm)],[co1_25]) ).
fof(co1_24,axiom,
( ~ neq(sk4,nil)
| ssList(sk7) ),
file('theBenchmark.p',co1_24) ).
cnf(c_55,plain,
( ~ neq(sk4,nil)
| ssList(sk7) ),
inference(clausify,[status(thm)],[co1_24]) ).
fof(co1_23,axiom,
( ~ neq(sk4,nil)
| ssItem(sk6) ),
file('theBenchmark.p',co1_23) ).
cnf(c_56,plain,
( ~ neq(sk4,nil)
| ssItem(sk6) ),
inference(clausify,[status(thm)],[co1_23]) ).
fof(co1_22,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ neq(sk4,nil)
| VAR_0 != sk5(VAR_2,VAR_1,VAR_0)
| app(VAR_1,VAR_2) != sk1
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sk2
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_22) ).
cnf(c_57,plain,
( ~ neq(sk4,nil)
| A != sk5(C,B,A)
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_22]) ).
cnf(c_58,plain,
( ~ neq(sk4,nil)
| sk5(C,B,A) != A
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(copy,[status(thm)],[c_57]) ).
fof(co1_21,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ neq(sk4,nil)
| geq(sk5(VAR_2,VAR_1,VAR_0),VAR_0)
| app(VAR_1,VAR_2) != sk1
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sk2
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_21) ).
cnf(c_59,plain,
( ~ neq(sk4,nil)
| geq(sk5(C,B,A),A)
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_21]) ).
fof(co1_20,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ neq(sk4,nil)
| memberP(sk2,sk5(VAR_2,VAR_1,VAR_0))
| app(VAR_1,VAR_2) != sk1
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sk2
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_20) ).
cnf(c_60,plain,
( ~ neq(sk4,nil)
| memberP(sk2,sk5(C,B,A))
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_20]) ).
fof(co1_19,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ neq(sk4,nil)
| ssItem(sk5(VAR_2,VAR_1,VAR_0))
| app(VAR_1,VAR_2) != sk1
| app(app(VAR_1,cons(VAR_0,nil)),VAR_2) != sk2
| ~ ssList(VAR_2)
| ~ ssList(VAR_1)
| ~ ssItem(VAR_0) ),
file('theBenchmark.p',co1_19) ).
cnf(c_61,plain,
( ~ neq(sk4,nil)
| ssItem(sk5(C,B,A))
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(clausify,[status(thm)],[co1_19]) ).
fof(co1_7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('theBenchmark.p',co1_7) ).
cnf(c_74,plain,
( neq(sk2,nil)
| neq(sk2,nil) ),
inference(clausify,[status(thm)],[co1_7]) ).
cnf(c_75,plain,
neq(sk2,nil),
inference(copy,[status(thm)],[c_74]) ).
fof(co1_6,axiom,
sk1 = sk3,
file('theBenchmark.p',co1_6) ).
cnf(c_76,plain,
sk1 = sk3,
inference(clausify,[status(thm)],[co1_6]) ).
cnf(c_77,plain,
sk3 = sk1,
inference(copy,[status(thm)],[c_76]) ).
fof(co1_5,axiom,
sk2 = sk4,
file('theBenchmark.p',co1_5) ).
cnf(c_78,plain,
sk2 = sk4,
inference(clausify,[status(thm)],[co1_5]) ).
cnf(c_79,plain,
sk4 = sk2,
inference(copy,[status(thm)],[c_78]) ).
cnf(c_15183,plain,
( ~ neq(sk4,nil)
| app(sk7,sk8) = sk1 ),
inference(paramod,[status(thm)],[c_77,c_52]) ).
cnf(c_15184,plain,
( ~ neq(sk2,nil)
| app(sk7,sk8) = sk1 ),
inference(paramod,[status(thm)],[c_79,c_15183]) ).
cnf(c_343,plain,
app(sk7,sk8) = sk1,
inference(resolve,[status(thm)],[c_75,c_15184]) ).
cnf(c_15185,plain,
( ~ neq(sk2,nil)
| ssItem(sk5(C,B,A))
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_79,c_61]) ).
cnf(c_344,plain,
( ssItem(sk5(C,B,A))
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_75,c_15185]) ).
cnf(c_15186,plain,
( ~ neq(sk2,nil)
| memberP(sk2,sk5(C,B,A))
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_79,c_60]) ).
cnf(c_345,plain,
( memberP(sk2,sk5(C,B,A))
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_75,c_15186]) ).
cnf(c_15187,plain,
( ~ neq(sk2,nil)
| geq(sk5(C,B,A),A)
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_79,c_59]) ).
cnf(c_346,plain,
( geq(sk5(C,B,A),A)
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_75,c_15187]) ).
cnf(c_15188,plain,
( ~ neq(sk2,nil)
| sk5(C,B,A) != A
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_79,c_58]) ).
cnf(c_347,plain,
( sk5(C,B,A) != A
| app(B,C) != sk1
| app(app(B,cons(A,nil)),C) != sk2
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_75,c_15188]) ).
cnf(c_15189,plain,
( ~ neq(sk2,nil)
| ssItem(sk6) ),
inference(paramod,[status(thm)],[c_79,c_56]) ).
cnf(c_348,plain,
ssItem(sk6),
inference(resolve,[status(thm)],[c_75,c_15189]) ).
cnf(c_15190,plain,
( ~ neq(sk2,nil)
| ssList(sk7) ),
inference(paramod,[status(thm)],[c_79,c_55]) ).
cnf(c_349,plain,
ssList(sk7),
inference(resolve,[status(thm)],[c_75,c_15190]) ).
cnf(c_15191,plain,
( ~ neq(sk2,nil)
| ssList(sk8) ),
inference(paramod,[status(thm)],[c_79,c_54]) ).
cnf(c_350,plain,
ssList(sk8),
inference(resolve,[status(thm)],[c_75,c_15191]) ).
cnf(c_15192,plain,
( ~ neq(sk4,nil)
| app(app(sk7,cons(sk6,nil)),sk8) = sk2 ),
inference(paramod,[status(thm)],[c_79,c_53]) ).
cnf(c_15193,plain,
( ~ neq(sk2,nil)
| app(app(sk7,cons(sk6,nil)),sk8) = sk2 ),
inference(paramod,[status(thm)],[c_79,c_15192]) ).
cnf(c_351,plain,
app(app(sk7,cons(sk6,nil)),sk8) = sk2,
inference(resolve,[status(thm)],[c_75,c_15193]) ).
cnf(c_15194,plain,
( ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk2,A)
| sk6 = A
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_79,c_51]) ).
cnf(c_15195,plain,
( ~ neq(sk2,nil)
| ~ geq(A,sk6)
| ~ memberP(sk2,A)
| sk6 = A
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_79,c_15194]) ).
cnf(c_352,plain,
( ~ geq(A,sk6)
| ~ memberP(sk2,A)
| sk6 = A
| ~ ssItem(A) ),
inference(resolve,[status(thm)],[c_75,c_15195]) ).
cnf(c_15196,plain,
( sk5(sk8,sk7,sk6) != sk6
| app(sk7,sk8) != sk1
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_351,c_347]) ).
cnf(c_15197,plain,
( sk5(sk8,sk7,sk6) != sk6
| sk1 != sk1
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(paramod,[status(thm)],[c_343,c_15196]) ).
cnf(c_15198,plain,
( sk5(sk8,sk7,sk6) != sk6
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(copy,[status(thm)],[c_15197]) ).
cnf(c_15199,plain,
( sk5(sk8,sk7,sk6) != sk6
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_348,c_15198]) ).
cnf(c_15200,plain,
( sk5(sk8,sk7,sk6) != sk6
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_349,c_15199]) ).
cnf(c_8402,plain,
sk5(sk8,sk7,sk6) != sk6,
inference(resolve,[status(thm)],[c_350,c_15200]) ).
cnf(c_15201,plain,
( geq(sk5(sk8,sk7,sk6),sk6)
| app(sk7,sk8) != sk1
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_351,c_346]) ).
cnf(c_15202,plain,
( geq(sk5(sk8,sk7,sk6),sk6)
| sk1 != sk1
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(paramod,[status(thm)],[c_343,c_15201]) ).
cnf(c_15203,plain,
( geq(sk5(sk8,sk7,sk6),sk6)
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(copy,[status(thm)],[c_15202]) ).
cnf(c_15204,plain,
( geq(sk5(sk8,sk7,sk6),sk6)
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_348,c_15203]) ).
cnf(c_15205,plain,
( geq(sk5(sk8,sk7,sk6),sk6)
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_349,c_15204]) ).
cnf(c_8403,plain,
geq(sk5(sk8,sk7,sk6),sk6),
inference(resolve,[status(thm)],[c_350,c_15205]) ).
cnf(c_15206,plain,
( memberP(sk2,sk5(sk8,sk7,sk6))
| app(sk7,sk8) != sk1
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_351,c_345]) ).
cnf(c_15207,plain,
( memberP(sk2,sk5(sk8,sk7,sk6))
| sk1 != sk1
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(paramod,[status(thm)],[c_343,c_15206]) ).
cnf(c_15208,plain,
( memberP(sk2,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(copy,[status(thm)],[c_15207]) ).
cnf(c_15209,plain,
( memberP(sk2,sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_348,c_15208]) ).
cnf(c_15210,plain,
( memberP(sk2,sk5(sk8,sk7,sk6))
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_349,c_15209]) ).
cnf(c_8404,plain,
memberP(sk2,sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_350,c_15210]) ).
cnf(c_15211,plain,
( ssItem(sk5(sk8,sk7,sk6))
| app(sk7,sk8) != sk1
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(resolve,[status(thm)],[c_351,c_344]) ).
cnf(c_15212,plain,
( ssItem(sk5(sk8,sk7,sk6))
| sk1 != sk1
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(paramod,[status(thm)],[c_343,c_15211]) ).
cnf(c_15213,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssItem(sk6) ),
inference(copy,[status(thm)],[c_15212]) ).
cnf(c_15214,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8)
| ~ ssList(sk7) ),
inference(resolve,[status(thm)],[c_348,c_15213]) ).
cnf(c_15215,plain,
( ssItem(sk5(sk8,sk7,sk6))
| ~ ssList(sk8) ),
inference(resolve,[status(thm)],[c_349,c_15214]) ).
cnf(c_8405,plain,
ssItem(sk5(sk8,sk7,sk6)),
inference(resolve,[status(thm)],[c_350,c_15215]) ).
cnf(c_15216,plain,
( ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk2,sk5(sk8,sk7,sk6))
| sk6 = sk5(sk8,sk7,sk6) ),
inference(resolve,[status(thm)],[c_8405,c_352]) ).
cnf(c_15217,plain,
( ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk2,sk5(sk8,sk7,sk6))
| sk5(sk8,sk7,sk6) = sk6 ),
inference(copy,[status(thm)],[c_15216]) ).
cnf(c_15218,plain,
( ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk2,sk5(sk8,sk7,sk6)) ),
inference(resolve,[status(thm)],[c_8402,c_15217]) ).
cnf(c_15219,plain,
~ geq(sk5(sk8,sk7,sk6),sk6),
inference(resolve,[status(thm)],[c_8404,c_15218]) ).
cnf(c_15182,plain,
$false,
inference(resolve,[status(thm)],[c_8403,c_15219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC002-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 12:03:19 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1484915 was started by sandbox2 on n020,
% 0.10/0.37 % Sat Sep 26 12:03:19 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 32.55/4.66
% 32.55/4.66 % given #500 (I,wt=37): 581 app(app(A,cons(B,C)),cons(B,C)) != D | -ssList(C) | -ssList(A) | -ssItem(B) | -ssList(D) | lt(B,B) | -lt(skaf59(D),skaf60(D)). [factor(310,d,e),merge(g)].
% 32.55/4.66
% 32.55/4.66 % given #1000 (T,wt=8): 6803 segmentP(skaf81(A),nil). [resolve(229,a,187,a)].
% 32.55/4.66
% 32.55/4.66 % SZS status Unsatisfiable for theBenchmark
% 32.55/4.66
% 32.55/4.66 % Proof 1 at 3.17 (+ 0.98) seconds.
% 32.55/4.66 % Length of proof is 32.
% 32.55/4.66 % Level of proof is 4.
% 32.55/4.66 % Maximum clause weight is 39.000.
% 32.55/4.66 % Given clauses 1374.
% 32.55/4.66
% 32.55/4.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------