%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC001+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 : n006.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 08:56:29 AM UTC 2026
% Result : Theorem 14.42s 2.51s
% Output : CNFRefutation 14.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 9 unt; 0 def)
% Number of atoms : 142 ( 12 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 173 ( 60 ~; 58 |; 45 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 27 ( 0 sgn 14 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( duplicatefreeP(U)
& ! [Z] :
( ssItem(Z)
=> ( ( memberP(U,Z)
& memberP(V,Z) )
| ( ~ memberP(U,Z)
& ~ memberP(V,Z) ) ) ) )
| ? [Y] :
( ( ( memberP(X,Y)
& ~ memberP(W,Y) )
| ( memberP(W,Y)
& ~ memberP(X,Y) ) )
& ssItem(Y) )
| ~ duplicatefreeP(W)
| U != W
| V != X ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( duplicatefreeP(U)
& ! [Z] :
( ssItem(Z)
=> ( ( memberP(U,Z)
& memberP(V,Z) )
| ( ~ memberP(U,Z)
& ~ memberP(V,Z) ) ) ) )
| ? [Y] :
( ( ( memberP(X,Y)
& ~ memberP(W,Y) )
| ( memberP(W,Y)
& ~ memberP(X,Y) ) )
& ssItem(Y) )
| ~ duplicatefreeP(W)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ duplicatefreeP(U)
| ? [Z] :
( ( ~ memberP(U,Z)
| ~ memberP(V,Z) )
& ( memberP(U,Z)
| memberP(V,Z) )
& ssItem(Z) ) )
& ! [Y] :
( ( ( ~ memberP(X,Y)
| memberP(W,Y) )
& ( ~ memberP(W,Y)
| memberP(X,Y) ) )
| ~ ssItem(Y) )
& duplicatefreeP(W)
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg_sk,plain,
( ( ~ duplicatefreeP(sK2)
| ( ( ~ memberP(sK2,sK1)
| ~ memberP(sK0,sK1) )
& ( memberP(sK2,sK1)
| memberP(sK0,sK1) )
& ssItem(sK1) ) )
& ! [Y] :
( ( ( ~ memberP(sK4,Y)
| memberP(sK3,Y) )
& ( ~ memberP(sK3,Y)
| memberP(sK4,Y) ) )
| ~ ssItem(Y) )
& duplicatefreeP(sK3)
& sK3 = sK2
& sK4 = sK0
& ssList(sK4)
& ssList(sK3)
& ssList(sK0)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK3,sK4,sK1]),skolemize(U,sK2),skolemize(V,sK0),skolemize(W,sK3),skolemize(X,sK4),skolemize(Z,sK1)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ duplicatefreeP(sK2)
| ~ memberP(sK2,sK1)
| ~ memberP(sK0,sK1) )
& ( ~ duplicatefreeP(sK2)
| memberP(sK2,sK1)
| memberP(sK0,sK1) )
& ( ~ duplicatefreeP(sK2)
| ssItem(sK1) )
& ! [VAR_0] :
( ~ memberP(sK4,VAR_0)
| memberP(sK3,VAR_0)
| ~ ssItem(VAR_0) )
& ! [VAR_0] :
( ~ memberP(sK3,VAR_0)
| memberP(sK4,VAR_0)
| ~ ssItem(VAR_0) )
& duplicatefreeP(sK3)
& sK3 = sK2
& sK4 = sK0
& ssList(sK4)
& ssList(sK3)
& ssList(sK0)
& ssList(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_166,negated_conjecture,
( ~ duplicatefreeP(sK2)
| ~ memberP(sK2,sK1)
| ~ memberP(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_167,negated_conjecture,
( ~ duplicatefreeP(sK2)
| memberP(sK2,sK1)
| memberP(sK0,sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_168,negated_conjecture,
( ~ duplicatefreeP(sK2)
| ssItem(sK1) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_169,negated_conjecture,
( ~ memberP(sK4,A)
| memberP(sK3,A)
| ~ ssItem(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_170,negated_conjecture,
( ~ memberP(sK3,A)
| memberP(sK4,A)
| ~ ssItem(A) ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_171,negated_conjecture,
duplicatefreeP(sK3),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_172,negated_conjecture,
sK3 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_173,negated_conjecture,
sK4 = sK0,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_448,negated_conjecture,
duplicatefreeP(sK2),
inference(paramod,[status(thm)],[c_172,c_171]) ).
cnf(c_2437,negated_conjecture,
( ~ memberP(sK3,A)
| memberP(sK0,A)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_173,c_170]) ).
cnf(c_449,negated_conjecture,
( ~ memberP(sK2,A)
| memberP(sK0,A)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_172,c_2437]) ).
cnf(c_2438,negated_conjecture,
( ~ memberP(sK4,A)
| memberP(sK2,A)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_172,c_169]) ).
cnf(c_450,negated_conjecture,
( ~ memberP(sK0,A)
| memberP(sK2,A)
| ~ ssItem(A) ),
inference(paramod,[status(thm)],[c_173,c_2438]) ).
cnf(c_762,negated_conjecture,
ssItem(sK1),
inference(resolve,[status(thm)],[c_448,c_168]) ).
cnf(c_763,negated_conjecture,
( memberP(sK2,sK1)
| memberP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_448,c_167]) ).
cnf(c_764,negated_conjecture,
( ~ memberP(sK2,sK1)
| ~ memberP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_448,c_166]) ).
cnf(c_2439,negated_conjecture,
( memberP(sK2,sK1)
| ~ ssItem(sK1)
| memberP(sK2,sK1) ),
inference(resolve,[status(thm)],[c_763,c_450]) ).
cnf(c_2440,negated_conjecture,
( ~ ssItem(sK1)
| memberP(sK2,sK1) ),
inference(copy,[status(thm)],[c_2439]) ).
cnf(c_2433,negated_conjecture,
memberP(sK2,sK1),
inference(resolve,[status(thm)],[c_762,c_2440]) ).
cnf(c_2441,negated_conjecture,
( memberP(sK0,sK1)
| ~ ssItem(sK1)
| memberP(sK0,sK1) ),
inference(resolve,[status(thm)],[c_763,c_449]) ).
cnf(c_2442,negated_conjecture,
( ~ ssItem(sK1)
| memberP(sK0,sK1) ),
inference(copy,[status(thm)],[c_2441]) ).
cnf(c_2435,negated_conjecture,
memberP(sK0,sK1),
inference(resolve,[status(thm)],[c_762,c_2442]) ).
cnf(c_2443,negated_conjecture,
~ memberP(sK2,sK1),
inference(resolve,[status(thm)],[c_2435,c_764]) ).
cnf(c_2436,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2433,c_2443]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC001+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 12:01:55 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1200149 was started by sandbox2 on n006,
% 0.10/0.36 % Sat Sep 26 12:01:55 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 14.42/2.51
% 14.42/2.51 % given #500 (I,wt=31): 680 -ssList(A) | ssList(f40(A)) | -ssItem(B) | -ssItem(C) | app(A,cons(B,cons(C,A))) != A | C = B. [factor(377,a,e)].
% 14.42/2.51
% 14.42/2.51 % SZS status Theorem for theBenchmark
% 14.42/2.51
% 14.42/2.51 % Proof 1 at 1.71 (+ 0.23) seconds.
% 14.42/2.51 % Length of proof is 18.
% 14.42/2.51 % Level of proof is 5.
% 14.42/2.51 % Maximum clause weight is 10.000.
% 14.42/2.51 % Given clauses 583.
% 14.42/2.51
% 14.42/2.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------