%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ITP019+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 : n020.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 01:44:18 PM UTC 2026
% Result : Theorem 36.36s 5.80s
% Output : Proof 36.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 5 unt; 0 def)
% Number of atoms : 35 ( 25 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 38 ( 17 ~; 9 |; 6 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,conjecture,
! [V0z] :
( mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( V0z != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
=> ap(c_2Ecomplex_2Ecomplex__inv,V0z) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
fof(f32_neg,negated_conjecture,
~ ! [V0z] :
( mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( V0z != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
=> ap(c_2Ecomplex_2Ecomplex__inv,V0z) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f32_nnf,plain,
? [V0z] :
( ap(c_2Ecomplex_2Ecomplex__inv,V0z) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& V0z != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(nnf_transformation,[status(thm)],[f32_neg]) ).
fof(f32_sk,plain,
( ap(c_2Ecomplex_2Ecomplex__inv,sk3) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& sk3 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& mem(sk3,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f32_nnf]) ).
cnf(c61,plain,
mem(sk3,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f31,axiom,
! [V0z] :
( mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( ap(c_2Ecomplex_2Ecomplex__inv,V0z) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
<=> V0z = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
fof(f31_nnf,plain,
! [V0z] :
( ( ( V0z != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ap(c_2Ecomplex_2Ecomplex__inv,V0z) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) )
& ( V0z = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ap(c_2Ecomplex_2Ecomplex__inv,V0z) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) )
| ~ mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [V0z] :
( ( ( V0z != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ap(c_2Ecomplex_2Ecomplex__inv,V0z) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) )
& ( V0z = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ap(c_2Ecomplex_2Ecomplex__inv,V0z) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) )
| ~ mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c59,plain,
( X0 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ap(c_2Ecomplex_2Ecomplex__inv,X0) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p161,plain,
( sk3 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ap(c_2Ecomplex_2Ecomplex__inv,sk3) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ),
inference(resolution,[status(thm)],[c61,c59]) ).
cnf(c63,plain,
ap(c_2Ecomplex_2Ecomplex__inv,sk3) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p281,plain,
sk3 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(resolution,[status(thm)],[p161,c63]) ).
cnf(c62,plain,
sk3 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p1334,plain,
$false,
inference(resolution,[status(thm)],[p281,c62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ITP019+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.43 % Computer : n020.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Wed Sep 23 17:45:34 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 36.36/5.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.36/5.80 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------