%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ITP010+4 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 07:41:23 AM UTC 2026
% Result : Theorem 13.47s 7.77s
% Output : CNFRefutation 13.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1
% Syntax : Number of formulae : 3 ( 1 unt; 0 def)
% Number of atoms : 5 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 0 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm_2Ecardinal_2ECARD__NOT__LE,conjecture,
! [A_27a,A_27b,V0s_2E0,V1t_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) ),
file('theBenchmark.p',thm_2Ecardinal_2ECARD__NOT__LE) ).
fof(thm_2Ecardinal_2ECARD__NOT__LE_neg,negated_conjecture,
~ ! [A_27a,A_27b,V0s_2E0,V1t_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) ),
inference(assume_negation,[status(cth)],[thm_2Ecardinal_2ECARD__NOT__LE]) ).
cnf(c_5941,negated_conjecture,
$false,
inference(clausify,[status(thm)],[thm_2Ecardinal_2ECARD__NOT__LE_neg]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP010+4 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n008.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Fri Sep 25 17:13:56 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.37 % Process 1513016 was started by sandbox2 on n008,
% 0.11/5.37 % Fri Sep 25 17:13:56 2026
% 0.11/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 13.47/7.77
% 13.47/7.77 % SInE (scan): 1551 to sos (tol 1.5x), 450 to usable (tol 2.0x), 8762 zapped, of 10763 axioms (depth 3).
% 13.47/7.77
% 13.47/7.77 % From the command line: assign(max_seconds, 300).
% 13.47/7.77
% 13.47/7.77 % SZS status Theorem for theBenchmark
% 13.47/7.77
% 13.47/7.77 % Proof 1 at 1.30 (+ 0.37) seconds.
% 13.47/7.77 % Length of proof is 2.
% 13.47/7.77 % Level of proof is 1.
% 13.47/7.77 % Maximum clause weight is 0.000.
% 13.47/7.77 % Given clauses 0.
% 13.47/7.77
% 13.47/7.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------