%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP019+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n003.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 01:47:52 PM UTC 2026
% Result : Theorem 2.80s 1.26s
% Output : CNFRefutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 16 unt; 3 def)
% Number of atoms : 69 ( 37 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 48 ( 23 ~; 11 |; 7 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 8 !; 2 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
fof(f32,axiom,
! [X0] :
( mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( ap(c_2Ecomplex_2Ecomplex__inv,X0) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
<=> X0 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
fof(f33,conjecture,
! [X0] :
( mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( 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) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
=> ( 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) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f55,plain,
! [X0] :
( ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| ( ap(c_2Ecomplex_2Ecomplex__inv,X0) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
<=> X0 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f56,plain,
? [X0] :
( mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
& 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) ),
inference(ennf_transformation,[],[f34]) ).
fof(f57,plain,
? [X0] :
( mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
& 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) ),
inference(flattening,[],[f56]) ).
fof(f74,plain,
! [X0] :
( ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| ( ( ap(c_2Ecomplex_2Ecomplex__inv,X0) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| X0 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) )
& ( ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != X0
| ap(c_2Ecomplex_2Ecomplex__inv,X0) = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f75,plain,
( mem(sK3,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
& ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != sK3
& ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = ap(c_2Ecomplex_2Ecomplex__inv,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f57]) ).
fof(f122,plain,
! [X0] :
( ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| ap(c_2Ecomplex_2Ecomplex__inv,X0) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)
| ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0 ),
inference(cnf_transformation,[],[f74]) ).
fof(f124,plain,
mem(sK3,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(cnf_transformation,[],[f75]) ).
fof(f125,plain,
ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != sK3,
inference(cnf_transformation,[],[f75]) ).
fof(f126,plain,
ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = ap(c_2Ecomplex_2Ecomplex__inv,sK3),
inference(cnf_transformation,[],[f75]) ).
tcf(c_89,plain,
! [X0: $i] :
( ( ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0 )
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| ( ap(c_2Ecomplex_2Ecomplex__inv,X0) != ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) ) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_90,negated_conjecture,
ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = ap(c_2Ecomplex_2Ecomplex__inv,sK3),
inference(cnf_transformation,[],[f126]) ).
tcf(c_91,negated_conjecture,
ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != sK3,
inference(cnf_transformation,[],[f125]) ).
tcf(c_92,negated_conjecture,
mem(sK3,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)),
inference(cnf_transformation,[],[f124]) ).
tcf(c_545,definition,
iPr_def_10 = ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_546,definition,
iPr_def_11 = ap(c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_547,definition,
iPr_def_12 = ap(c_2Ecomplex_2Ecomplex__inv,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_548,negated_conjecture,
mem(sK3,iPr_def_10),
inference(demodulation,[status(thm)],[c_92,c_545]) ).
tcf(c_549,negated_conjecture,
iPr_def_11 != sK3,
inference(demodulation,[status(thm)],[c_91,c_546]) ).
tcf(c_550,negated_conjecture,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_90,c_547]) ).
tcf(c_1127,plain,
ap(c_2Ecomplex_2Ecomplex__inv,sK3) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_547,c_550]) ).
tcf(c_2124,plain,
! [X0: $i] :
( ( X0 = iPr_def_11 )
| ~ mem(X0,iPr_def_10)
| ( ap(c_2Ecomplex_2Ecomplex__inv,X0) != iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_89,c_545,c_546]) ).
tcf(c_2134,plain,
( ( sK3 = iPr_def_11 )
| ~ mem(sK3,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1127,c_2124]) ).
tcf(c_2136,plain,
sK3 = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_2134,c_548]) ).
tcf(c_2140,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_549,c_2136]) ).
tcf(c_2142,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_2140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 17:46:36 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 2.80/1.26 % SZS status Started for theBenchmark.p
% 2.80/1.26 % SZS status Theorem for theBenchmark.p
% 2.80/1.26
% 2.80/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.80/1.26
% 2.80/1.26 % ------ iProver source info
% 2.80/1.26
% 2.80/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 2.80/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.80/1.26 % git: non_committed_changes: false
% 2.80/1.26
% 2.80/1.26 % ------ Parsing...
% 2.80/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.80/1.26
% 2.80/1.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.80/1.26
% 2.80/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.80/1.26
% 2.80/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.80/1.26 % ------ Proving...
% 2.80/1.26 % ------ Problem Properties
% 2.80/1.26
% 2.80/1.26 %
% 2.80/1.26 % clauses 47
% 2.80/1.26 % conjectures 3
% 2.80/1.26 % EPR 14
% 2.80/1.26 % Horn 41
% 2.80/1.26 % unary 20
% 2.80/1.26 % binary 5
% 2.80/1.26 % lits 117
% 2.80/1.26 % lits eq 16
% 2.80/1.26 % fd_pure 0
% 2.80/1.26 % fd_pseudo 0
% 2.80/1.26 % fd_cond 1
% 2.80/1.26 % fd_pseudo_cond 5
% 2.80/1.26 % AC symbols 0
% 2.80/1.26
% 2.80/1.26 % ------ Schedule dynamic 5 is on
% 2.80/1.26
% 2.80/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.80/1.26
% 2.80/1.26
% 2.80/1.26 % ------
% 2.80/1.26 % Current options:
% 2.80/1.26 % ------
% 2.80/1.26
% 2.80/1.26
% 2.80/1.26 %
% 2.80/1.26
% 2.80/1.26 % ------ Proving...
% 2.80/1.26 %
% 2.80/1.26
% 2.80/1.26 % SZS status Theorem for theBenchmark.p
% 2.80/1.26
% 2.80/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.80/1.26
% 2.80/1.26
%------------------------------------------------------------------------------