%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV389+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 09:07:37 AM UTC 2026
% Result : Theorem 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 35 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 18 ~; 9 |; 5 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 23 ( 0 sgn 10 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax52,axiom,
! [U] : removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U)),
file('theBenchmark.p',ax52) ).
fof(l25_l40,axiom,
! [U,V,W] :
( ( ok(removemin_cpq_eff(triple(U,V,W)))
& check_cpq(removemin_cpq_eff(triple(U,V,W))) )
=> check_cpq(triple(U,V,W)) ),
file('theBenchmark.p',l25_l40) ).
fof(l25_co,conjecture,
! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
=> ( ~ ok(removemin_cpq_eff(triple(U,V,W)))
| ~ check_cpq(removemin_cpq_eff(triple(U,V,W))) ) ),
file('theBenchmark.p',l25_co) ).
fof(l25_co_neg,negated_conjecture,
~ ! [U,V,W] :
( ~ check_cpq(triple(U,V,W))
=> ( ~ ok(removemin_cpq_eff(triple(U,V,W)))
| ~ check_cpq(removemin_cpq_eff(triple(U,V,W))) ) ),
inference(assume_negation,[status(cth)],[l25_co]) ).
cnf(c_96,plain,
removemin_cpq_eff(A) = remove_cpq(findmin_cpq_eff(A),findmin_cpq_res(A)),
inference(clausify,[status(thm)],[ax52]) ).
cnf(c_98,plain,
( check_cpq(triple(A,B,C))
| ~ ok(removemin_cpq_eff(triple(A,B,C)))
| ~ check_cpq(removemin_cpq_eff(triple(A,B,C))) ),
inference(clausify,[status(thm)],[l25_l40]) ).
cnf(c_178,plain,
( check_cpq(triple(A,B,C))
| ~ ok(removemin_cpq_eff(triple(A,B,C)))
| ~ check_cpq(remove_cpq(findmin_cpq_eff(triple(A,B,C)),findmin_cpq_res(triple(A,B,C)))) ),
inference(paramod,[status(thm)],[c_96,c_98]) ).
cnf(c_99,plain,
( check_cpq(triple(A,B,C))
| ~ ok(remove_cpq(findmin_cpq_eff(triple(A,B,C)),findmin_cpq_res(triple(A,B,C))))
| ~ check_cpq(remove_cpq(findmin_cpq_eff(triple(A,B,C)),findmin_cpq_res(triple(A,B,C)))) ),
inference(paramod,[status(thm)],[c_96,c_178]) ).
fof(nnf_42,plain,
? [U,V,W] :
( ok(removemin_cpq_eff(triple(U,V,W)))
& check_cpq(removemin_cpq_eff(triple(U,V,W)))
& ~ check_cpq(triple(U,V,W)) ),
inference(fof_nnf,[status(thm)],[l25_co_neg]) ).
fof(sk_l25_co_neg,plain,
( ok(removemin_cpq_eff(triple(sK0,sK1,sK2)))
& check_cpq(removemin_cpq_eff(triple(sK0,sK1,sK2)))
& ~ check_cpq(triple(sK0,sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK2)],[nnf_42]) ).
cnf(c_100,negated_conjecture,
~ check_cpq(triple(sK0,sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_l25_co_neg]) ).
cnf(c_101,negated_conjecture,
check_cpq(removemin_cpq_eff(triple(sK0,sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_l25_co_neg]) ).
cnf(c_102,negated_conjecture,
check_cpq(remove_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))),
inference(paramod,[status(thm)],[c_96,c_101]) ).
cnf(c_103,negated_conjecture,
ok(removemin_cpq_eff(triple(sK0,sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_l25_co_neg]) ).
cnf(c_104,negated_conjecture,
ok(remove_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))),
inference(paramod,[status(thm)],[c_96,c_103]) ).
cnf(c_179,negated_conjecture,
( check_cpq(triple(sK0,sK1,sK2))
| ~ ok(remove_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))) ),
inference(resolve,[status(thm)],[c_99,c_102]) ).
cnf(c_180,negated_conjecture,
~ ok(remove_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))),
inference(resolve,[status(thm)],[c_179,c_100]) ).
cnf(c_177,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_104,c_180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV389+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 13:39:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.37 % Process 2863543 was started by sandbox2 on n013,
% 0.14/0.37 % Sat Sep 26 13:39:51 2026
% 0.14/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.41
% 0.14/0.41 % SZS status Theorem for theBenchmark
% 0.14/0.41
% 0.14/0.41 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.14/0.41 % Length of proof is 12.
% 0.14/0.41 % Level of proof is 3.
% 0.14/0.41 % Maximum clause weight is 29.000.
% 0.14/0.41 % Given clauses 52.
% 0.14/0.41
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------