%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ITP010+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 : Fri Sep 25 01:44:08 PM UTC 2026
% Result : Theorem 26.39s 3.75s
% Output : Proof 26.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 3 unt; 0 def)
% Number of atoms : 19 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 22 ( 12 ~; 4 |; 4 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f39,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('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecardinal_2ECARD__NOT__LE) ).
fof(f39_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(negated_conjecture,[status(cth)],[f39]) ).
fof(f39_nnf,plain,
? [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)))) )
| ( 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(nnf_transformation,[status(thm)],[f39_neg]) ).
fof(f39_sk,plain,
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk6),s(tyop_2Emin_2Efun(sk5,tyop_2Emin_2Ebool),sk7))))
& p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk6),s(tyop_2Emin_2Efun(sk5,tyop_2Emin_2Ebool),sk7)))) )
| ( p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk6),s(tyop_2Emin_2Efun(sk5,tyop_2Emin_2Ebool),sk7))))
& ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk6),s(tyop_2Emin_2Efun(sk5,tyop_2Emin_2Ebool),sk7)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6,sk7])],[f39_nnf]) ).
cnf(c298,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk6),s(tyop_2Emin_2Efun(sk5,tyop_2Emin_2Ebool),sk7))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk6),s(tyop_2Emin_2Efun(sk5,tyop_2Emin_2Ebool),sk7)))) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(p302,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk6),s(tyop_2Emin_2Efun(sk5,tyop_2Emin_2Ebool),sk7)))),
inference(factoring,[status(thm)],[c298]) ).
cnf(c299,plain,
( p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk6),s(tyop_2Emin_2Efun(sk5,tyop_2Emin_2Ebool),sk7))))
| p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk6),s(tyop_2Emin_2Efun(sk5,tyop_2Emin_2Ebool),sk7)))) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(p301,plain,
p(s(tyop_2Emin_2Ebool,c_2Ecardinal_2Ecardleq_2E2(s(tyop_2Emin_2Efun(sk4,tyop_2Emin_2Ebool),sk6),s(tyop_2Emin_2Efun(sk5,tyop_2Emin_2Ebool),sk7)))),
inference(factoring,[status(thm)],[c299]) ).
cnf(p303,plain,
$false,
inference(resolution,[status(thm)],[p302,p301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP010+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 17:40:08 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.39/3.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.39/3.75 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------