%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ITP019+5 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /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 07:38:11 AM UTC 2026
% Result : Theorem 86.64s 23.67s
% Output : CNFRefutation 86.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 13 unt; 0 def)
% Number of atoms : 39 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_thm_2Ecomplex_2ECOMPLEX__MUL__RID,axiom,
! [X0] :
( mem(X0,'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'))
=> ap(ap('c$u2Ecomplex$u2Ecomplex$u$umul',X0),ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum',ap('c$u2Earithmetic$u2ENUMERAL',ap('c$u2Earithmetic$u2EBIT1','c$u2Earithmetic$u2EZERO')))) = X0 ) ).
fof(conj_thm_2Ecomplex_2ECOMPLEX__MUL__RINV,axiom,
! [X0] :
( mem(X0,'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'))
=> ( X0 != ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0')
=> ap(ap('c$u2Ecomplex$u2Ecomplex$u$umul',X0),ap('c$u2Ecomplex$u2Ecomplex$u$uinv',X0)) = ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum',ap('c$u2Earithmetic$u2ENUMERAL',ap('c$u2Earithmetic$u2EBIT1','c$u2Earithmetic$u2EZERO'))) ) ) ).
fof(conj_thm_2Ecomplex_2ECOMPLEX__MUL__RZERO,axiom,
! [X0] :
( mem(X0,'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'))
=> ap(ap('c$u2Ecomplex$u2Ecomplex$u$umul',X0),ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0')) = ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0') ) ).
fof(ax_thm_2Earithmetic_2EALT__ZERO,axiom,
'c$u2Earithmetic$u2EZERO' = 'c$u2Enum$u2E0' ).
fof(conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ,conjecture,
! [X0] :
( mem(X0,'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'))
=> ( X0 != ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0')
=> ap('c$u2Ecomplex$u2Ecomplex$u$uinv',X0) != ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0') ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( mem(X0,'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal'))
=> ( X0 != ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0')
=> ap('c$u2Ecomplex$u2Ecomplex$u$uinv',X0) != ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0') ) ),
inference(negate_conjecture,[status(cth)],[conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ]) ).
cnf(c5,plain,
( ap(ap('c$u2Ecomplex$u2Ecomplex$u$umul',X0),ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum',ap('c$u2Earithmetic$u2ENUMERAL',ap('c$u2Earithmetic$u2EBIT1','c$u2Earithmetic$u2EZERO')))) = X0
| ~ mem(X0,'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal')) ),
inference(clausification,[status(esa)],[conj_thm_2Ecomplex_2ECOMPLEX__MUL__RID]) ).
cnf(c7,plain,
( ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0') = X0
| ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum',ap('c$u2Earithmetic$u2ENUMERAL',ap('c$u2Earithmetic$u2EBIT1','c$u2Earithmetic$u2EZERO'))) = ap(ap('c$u2Ecomplex$u2Ecomplex$u$umul',X0),ap('c$u2Ecomplex$u2Ecomplex$u$uinv',X0))
| ~ mem(X0,'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal')) ),
inference(clausification,[status(esa)],[conj_thm_2Ecomplex_2ECOMPLEX__MUL__RINV]) ).
cnf(c13,plain,
( ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0') = ap(ap('c$u2Ecomplex$u2Ecomplex$u$umul',X0),ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0'))
| ~ mem(X0,'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal')) ),
inference(clausification,[status(esa)],[conj_thm_2Ecomplex_2ECOMPLEX__MUL__RZERO]) ).
cnf(c41,plain,
'c$u2Enum$u2E0' = 'c$u2Earithmetic$u2EZERO',
inference(clausification,[status(esa)],[ax_thm_2Earithmetic_2EALT__ZERO]) ).
cnf(c44,plain,
mem(sK42,'ty$u2Epair$u2Eprod'('ty$u2Erealax$u2Ereal','ty$u2Erealax$u2Ereal')),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c45,plain,
ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0') = ap('c$u2Ecomplex$u2Ecomplex$u$uinv',sK42),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c46,plain,
ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0') != sK42,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0') = ap(ap('c$u2Ecomplex$u2Ecomplex$u$umul',sK42),ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0')),
inference(resolution,[status(thm)],[c13,c44]) ).
cnf(d1,plain,
( ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0') = sK42
| ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum',ap('c$u2Earithmetic$u2ENUMERAL',ap('c$u2Earithmetic$u2EBIT1','c$u2Earithmetic$u2EZERO'))) = ap(ap('c$u2Ecomplex$u2Ecomplex$u$umul',sK42),ap('c$u2Ecomplex$u2Ecomplex$u$uinv',sK42)) ),
inference(resolution,[status(thm)],[c7,c44]) ).
cnf(d2,plain,
( ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0') = sK42
| ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum',ap('c$u2Earithmetic$u2ENUMERAL',ap('c$u2Earithmetic$u2EBIT1','c$u2Enum$u2E0'))) = ap(ap('c$u2Ecomplex$u2Ecomplex$u$umul',sK42),ap('c$u2Ecomplex$u2Ecomplex$u$uinv',sK42)) ),
inference(demodulation,[status(thm)],[d1,c41]) ).
cnf(d3,plain,
( ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0') = sK42
| ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum',ap('c$u2Earithmetic$u2ENUMERAL',ap('c$u2Earithmetic$u2EBIT1','c$u2Enum$u2E0'))) = ap(ap('c$u2Ecomplex$u2Ecomplex$u$umul',sK42),ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0')) ),
inference(demodulation,[status(thm)],[d2,c45]) ).
cnf(d4,plain,
ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum',ap('c$u2Earithmetic$u2ENUMERAL',ap('c$u2Earithmetic$u2EBIT1','c$u2Enum$u2E0'))) = ap(ap('c$u2Ecomplex$u2Ecomplex$u$umul',sK42),ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0')),
inference(resolution,[status(thm)],[c46,d3]) ).
cnf(d5,plain,
ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum',ap('c$u2Earithmetic$u2ENUMERAL',ap('c$u2Earithmetic$u2EBIT1','c$u2Enum$u2E0'))) = ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0'),
inference(demodulation,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
ap(ap('c$u2Ecomplex$u2Ecomplex$u$umul',sK42),ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum',ap('c$u2Earithmetic$u2ENUMERAL',ap('c$u2Earithmetic$u2EBIT1','c$u2Earithmetic$u2EZERO')))) = sK42,
inference(resolution,[status(thm)],[c5,c44]) ).
cnf(d7,plain,
ap(ap('c$u2Ecomplex$u2Ecomplex$u$umul',sK42),ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum',ap('c$u2Earithmetic$u2ENUMERAL',ap('c$u2Earithmetic$u2EBIT1','c$u2Enum$u2E0')))) = sK42,
inference(demodulation,[status(thm)],[d6,c41]) ).
cnf(d8,plain,
ap(ap('c$u2Ecomplex$u2Ecomplex$u$umul',sK42),ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0')) = sK42,
inference(demodulation,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
ap('c$u2Ecomplex$u2Ecomplex$u$uof$u$unum','c$u2Enum$u2E0') = sK42,
inference(demodulation,[status(thm)],[d0,d8]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c46,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019+5 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n013.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
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 17:28:24 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 86.64/23.67 % SZS status Theorem for theBenchmark.p
% 86.64/23.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------