%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ITP019+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 07:41:32 AM UTC 2026
% Result : Theorem 0.03s 0.58s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 25 ( 17 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 24 ( 11 ~; 3 |; 4 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 5 ( 0 sgn 3 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0,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('theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
fof(conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ,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('theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
fof(conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ_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(assume_negation,[status(cth)],[conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ]) ).
cnf(c_59,plain,
( ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = A
| ap(c_2Ecomplex_2Ecomplex__inv,A) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ~ mem(A,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(clausify,[status(thm)],[conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0]) ).
fof(nnf_19,plain,
? [V0z] :
( ap(c_2Ecomplex_2Ecomplex__inv,V0z) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != V0z
& mem(V0z,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(fof_nnf,[status(thm)],[conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ_neg]) ).
fof(sk_conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ_neg,plain,
( ap(c_2Ecomplex_2Ecomplex__inv,sK0) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != sK0
& mem(sK0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(V0z,sK0)],[nnf_19]) ).
cnf(c_61,negated_conjecture,
mem(sK0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(split_conjunct,[status(thm)],[sk_conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ_neg]) ).
cnf(c_62,negated_conjecture,
ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != sK0,
inference(split_conjunct,[status(thm)],[sk_conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ_neg]) ).
cnf(c_63,negated_conjecture,
ap(c_2Ecomplex_2Ecomplex__inv,sK0) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(split_conjunct,[status(thm)],[sk_conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ_neg]) ).
cnf(c_211,negated_conjecture,
( ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = sK0
| ap(c_2Ecomplex_2Ecomplex__inv,sK0) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ),
inference(resolve,[status(thm)],[c_61,c_59]) ).
cnf(c_212,negated_conjecture,
ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = sK0,
inference(resolve,[status(thm)],[c_63,c_211]) ).
cnf(c_210,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_62,c_212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.55 % Computer : n016.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.03/0.55 % CPULimit : 300
% 0.03/0.55 % WCLimit : 300
% 0.03/0.55 % DateTime : Fri Sep 25 17:33:00 UTC 2026
% 0.03/0.56 % CPUTime :
% 0.03/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.56 % Process 2953883 was started by sandbox on n016,
% 0.03/0.56 % Fri Sep 25 17:33:00 2026
% 0.03/0.56 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.57
% 0.03/0.57 % From the command line: assign(max_seconds, 300).
% 0.03/0.58
% 0.03/0.58 % SZS status Theorem for theBenchmark
% 0.03/0.58
% 0.03/0.58 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.03/0.58 % Length of proof is 7.
% 0.03/0.58 % Level of proof is 2.
% 0.03/0.58 % Maximum clause weight is 27.000.
% 0.03/0.58 % Given clauses 42.
% 0.03/0.58
% 0.03/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------