%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : ITP019+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 : Thu Sep 24 08:45:35 AM UTC 2026
% Result : Theorem 0.22s 0.48s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 46 ( 30 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 47 ( 21 ~; 10 |; 10 &)
% ( 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 : 8 ( 0 sgn 5 !; 2 ?)
% 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(f_32_1,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) )
& ( 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(fof_nnf,[status(thm)],[conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0]) ).
fof(f_32_2,plain,
! [U_39] :
( ( ( ap(c_2Ecomplex_2Ecomplex__inv,U_39) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| U_39 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) )
& ( U_39 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ap(c_2Ecomplex_2Ecomplex__inv,U_39) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) )
| ~ mem(U_39,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( U_39 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ap(c_2Ecomplex_2Ecomplex__inv,U_39) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ~ mem(U_39,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,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(negate,[status(cth)],[conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ]) ).
fof(f_33_2,negated_conjecture,
? [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(fof_nnf,[status(thm)],[f_33_1]) ).
fof(f_33_3,negated_conjecture,
? [U_40] :
( ap(c_2Ecomplex_2Ecomplex__inv,U_40) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& U_40 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& mem(U_40,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(variable_rename,[status(thm)],[f_33_2]) ).
fof(f_33_4,negated_conjecture,
( ap(c_2Ecomplex_2Ecomplex__inv,sK4) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& sK4 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& mem(sK4,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_40,sK4)],[f_33_3]) ).
fof(f_33_5,negated_conjecture,
( ap(c_2Ecomplex_2Ecomplex__inv,sK4) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& sK4 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
& mem(sK4,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(definitional_conversion,[status(esa)],[f_33_4]) ).
cnf(f_33_6,negated_conjecture,
mem(sK4,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_7,negated_conjecture,
sK4 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(f_33_8,negated_conjecture,
ap(c_2Ecomplex_2Ecomplex__inv,sK4) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(clausify,[status(thm)],[f_33_5]) ).
cnf(t1,plain,
sK4 != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(start,[status(thm),parent(0:0)],[f_33_7]) ).
cnf(t2,plain,
( ap(c_2Ecomplex_2Ecomplex__inv,sK4) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ~ mem(sK4,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| sK4 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ),
inference(extension,[status(thm),parent(t1:1)],[f_32_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
mem(sK4,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(extension,[status(thm),parent(t2:2)],[f_33_6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
ap(c_2Ecomplex_2Ecomplex__inv,sK4) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
inference(extension,[status(thm),parent(t2:3)],[f_33_8]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 11:29:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.22/0.48 % SZS status Theorem for theBenchmark
% 0.22/0.48 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------