%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC151+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 : n010.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 08:57:01 AM UTC 2026
% Result : Theorem 1.89s 0.72s
% Output : CNFRefutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 5 unt; 0 def)
% Number of atoms : 37 ( 9 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 39 ( 11 ~; 6 |; 14 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 12 ( 0 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( totalorderP(X)
| ~ totalorderP(V)
| 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)
=> ( totalorderP(X)
| ~ totalorderP(V)
| U != W
| V != X ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ~ totalorderP(X)
& totalorderP(V)
& W = U
& X = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg,plain,
( ~ totalorderP(sK0)
& totalorderP(sK1)
& sK3 = sK2
& sK0 = sK1
& ssList(sK0)
& ssList(sK3)
& ssList(sK1)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK1,sK3,sK0]),skolemize(U,sK2),skolemize(V,sK1),skolemize(W,sK3),skolemize(X,sK0)],[nnf_87]) ).
cnf(c_165,negated_conjecture,
~ totalorderP(sK0),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_166,negated_conjecture,
totalorderP(sK1),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_168,negated_conjecture,
sK0 = sK1,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_453,negated_conjecture,
~ totalorderP(sK1),
inference(paramod,[status(thm)],[c_168,c_165]) ).
cnf(c_452,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_166,c_453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC151+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.45 % Computer : n010.cluster.edu
% 0.16/0.45 % Model : x86_64 x86_64
% 0.16/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.45 % Memory : 8046.5625MB
% 0.16/0.45 % OS : Linux 6.8.0-71-generic
% 0.16/0.45 % CPULimit : 300
% 0.16/0.45 % WCLimit : 300
% 0.16/0.45 % DateTime : Sat Sep 26 12:21:18 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.45 % Process 3278694 was started by sandbox2 on n010,
% 0.16/0.45 % Sat Sep 26 12:21:18 2026
% 0.16/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.49
% 0.16/0.49 % From the command line: assign(max_seconds, 300).
% 1.89/0.72
% 1.89/0.72 % SZS status Theorem for theBenchmark
% 1.89/0.72
% 1.89/0.72 % Proof 1 at 0.21 (+ 0.01) seconds.
% 1.89/0.72 % Length of proof is 5.
% 1.89/0.72 % Level of proof is 2.
% 1.89/0.72 % Maximum clause weight is 3.000.
% 1.89/0.72 % Given clauses 0.
% 1.89/0.72
% 1.89/0.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------