%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ITP010+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 27.08s 3.90s
% Output : Proof 27.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 3 unt; 0 def)
% Number of atoms : 35 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 38 ( 12 ~; 4 |; 12 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 8 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f40,conjecture,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
fof(f40_neg,negated_conjecture,
~ ! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t] :
( mem(V1t,arr(A_27b,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f40_nnf,plain,
? [A_27a] :
( ? [A_27b] :
( ? [V0s] :
( ? [V1t] :
( ( ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
& p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) )
| ( p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
& ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) )
& mem(V1t,arr(A_27b,bool)) )
& mem(V0s,arr(A_27a,bool)) )
& ne(A_27b) )
& ne(A_27a) ),
inference(nnf_transformation,[status(thm)],[f40_neg]) ).
fof(f40_sk,plain,
( ( ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sk3,sk4),sk5),sk6))
& p(ap(ap(c_2Ecardinal_2Ecardleq(sk3,sk4),sk5),sk6)) )
| ( p(ap(ap(c_2Ecardinal_2Ecardleq(sk3,sk4),sk5),sk6))
& ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sk3,sk4),sk5),sk6)) ) )
& mem(sk6,arr(sk4,bool))
& mem(sk5,arr(sk3,bool))
& ne(sk4)
& ne(sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5,sk6])],[f40_nnf]) ).
cnf(c274,plain,
( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sk3,sk4),sk5),sk6))
| ~ p(ap(ap(c_2Ecardinal_2Ecardleq(sk3,sk4),sk5),sk6)) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p278,plain,
~ p(ap(ap(c_2Ecardinal_2Ecardleq(sk3,sk4),sk5),sk6)),
inference(factoring,[status(thm)],[c274]) ).
cnf(c275,plain,
( p(ap(ap(c_2Ecardinal_2Ecardleq(sk3,sk4),sk5),sk6))
| p(ap(ap(c_2Ecardinal_2Ecardleq(sk3,sk4),sk5),sk6)) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p277,plain,
p(ap(ap(c_2Ecardinal_2Ecardleq(sk3,sk4),sk5),sk6)),
inference(factoring,[status(thm)],[c275]) ).
cnf(p279,plain,
$false,
inference(resolution,[status(thm)],[p278,p277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP010+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n017.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
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Wed Sep 23 17:30:16 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.08/3.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.08/3.90 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------