%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV377+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 09:07:35 AM UTC 2026
% Result : Theorem 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 10 unt; 0 def)
% Number of atoms : 24 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 1 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 33 ( 7 sgn 17 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax40,axiom,
! [U,V] :
( ok(triple(U,V,bad))
<=> $false ),
file('theBenchmark.p',ax40) ).
fof(ax41,axiom,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> W = bad ),
file('theBenchmark.p',ax41) ).
fof(ax42,axiom,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
file('theBenchmark.p',ax42) ).
fof(l13_co,conjecture,
! [U,V,W,X] :
( ~ ok(triple(U,V,W))
=> ~ ok(insert_cpq(triple(U,V,W),X)) ),
file('theBenchmark.p',l13_co) ).
fof(l13_co_neg,negated_conjecture,
~ ! [U,V,W,X] :
( ~ ok(triple(U,V,W))
=> ~ ok(insert_cpq(triple(U,V,W),X)) ),
inference(assume_negation,[status(cth)],[l13_co]) ).
cnf(c_78,plain,
~ ok(triple(A,B,bad)),
inference(clausify,[status(thm)],[ax40]) ).
cnf(c_79,plain,
( bad = C
| ok(triple(A,B,C)) ),
inference(clausify,[status(thm)],[ax41]) ).
cnf(c_80,plain,
triple(insert_pqp(A,B),insert_slb(C,pair(B,bottom)),D) = insert_cpq(triple(A,C,D),B),
inference(clausify,[status(thm)],[ax42]) ).
fof(nnf_41,plain,
? [U,V,W,X] :
( ok(insert_cpq(triple(U,V,W),X))
& ~ ok(triple(U,V,W)) ),
inference(fof_nnf,[status(thm)],[l13_co_neg]) ).
fof(sk_l13_co_neg,plain,
( ok(insert_cpq(triple(sK0,sK1,sK2),sK3))
& ~ ok(triple(sK0,sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK2),skolemize(X,sK3)],[nnf_41]) ).
cnf(c_97,negated_conjecture,
~ ok(triple(sK0,sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_l13_co_neg]) ).
cnf(c_98,negated_conjecture,
ok(insert_cpq(triple(sK0,sK1,sK2),sK3)),
inference(split_conjunct,[status(thm)],[sk_l13_co_neg]) ).
cnf(c_129,plain,
~ ok(insert_cpq(triple(A,B,bad),C)),
inference(paramod,[status(thm)],[c_80,c_78]) ).
cnf(c_168,negated_conjecture,
bad = sK2,
inference(resolve,[status(thm)],[c_97,c_79]) ).
cnf(c_166,negated_conjecture,
sK2 = bad,
inference(copy,[status(thm)],[c_168]) ).
cnf(c_169,negated_conjecture,
ok(insert_cpq(triple(sK0,sK1,bad),sK3)),
inference(paramod,[status(thm)],[c_166,c_98]) ).
cnf(c_167,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_129,c_169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV377+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 13:42:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 1869520 was started by sandbox on n002,
% 0.11/0.38 % Sat Sep 26 13:42:06 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 0.11/0.42
% 0.11/0.42 % SZS status Theorem for theBenchmark
% 0.11/0.42
% 0.11/0.42 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.11/0.42 % Length of proof is 12.
% 0.11/0.42 % Level of proof is 3.
% 0.11/0.42 % Maximum clause weight is 17.000.
% 0.11/0.42 % Given clauses 50.
% 0.11/0.42
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------