%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD010-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n009.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 01:15:36 PM UTC 2026
% Result : Unsatisfiable 2.04s 1.20s
% Output : CNFRefutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 53 ( 18 unt; 1 def)
% Number of atoms : 155 ( 1 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 143 ( 72 ~; 71 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 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; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 74 ( 0 sgn 74 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
fof(f7,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
fof(f8,axiom,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
fof(f9,axiom,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
fof(f10,axiom,
! [X2,X0,X1] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X4,X6,X1)
| ~ product(X3,X6,X0)
| ~ product(X5,X6,X2)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
fof(f18,axiom,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
fof(f27,negated_conjecture,
~ sum(additive_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_1) ).
fof(f28,negated_conjecture,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_2) ).
tcf(c_79,plain,
! [X0: $i] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X2,X5,X4)
| ~ product(X1,X5,X3)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_84,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_85,plain,
! [X0: $i] :
( sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sum(X4,X5,X6)
| ~ product(X2,X3,X6)
| ~ product(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_90,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f14]) ).
tcf(c_93,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[],[f17]) ).
tcf(c_94,plain,
! [X0: $i] :
( defined(multiplicative_inverse(X0))
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_103,negated_conjecture,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(cnf_transformation,[],[f27]) ).
tcf(c_104,negated_conjecture,
~ sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity),
inference(cnf_transformation,[],[f28]) ).
tcf(c_273,definition,
iPr_def_10 = multiplicative_inverse(multiplicative_identity),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_274,negated_conjecture,
~ sum(additive_identity,iPr_def_10,multiplicative_identity),
inference(demodulation,[status(thm)],[c_104,c_273]) ).
tcf(c_275,negated_conjecture,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_741,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,X0)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_84,c_86]) ).
tcf(c_744,plain,
( product(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_741]) ).
tcf(c_788,plain,
( defined(multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_identity) ),
inference(superposition,[status(thm)],[c_94,c_275]) ).
tcf(c_791,plain,
( defined(iPr_def_10)
| ~ defined(multiplicative_identity) ),
inference(light_normalisation,[status(thm)],[c_788,c_273]) ).
tcf(c_792,plain,
defined(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_791,c_93]) ).
tcf(c_826,plain,
( product(iPr_def_10,multiplicative_identity,multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity) ),
inference(superposition,[status(thm)],[c_273,c_85]) ).
tcf(c_828,plain,
product(iPr_def_10,multiplicative_identity,multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_826,c_275,c_93]) ).
tcf(c_832,plain,
product(multiplicative_identity,iPr_def_10,multiplicative_identity),
inference(superposition,[status(thm)],[c_828,c_86]) ).
tcf(c_1312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(additive_identity,iPr_def_10,multiplicative_identity)
| ~ product(X2,X3,multiplicative_identity)
| ~ product(X1,X3,iPr_def_10)
| ~ product(X0,X3,additive_identity)
| ~ sum(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_1331,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(iPr_def_10,X1,X2)
| ~ product(multiplicative_identity,X0,X2)
| ~ product(multiplicative_identity,X0,X1) ),
inference(superposition,[status(thm)],[c_828,c_82]) ).
tcf(c_1333,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(multiplicative_identity,X2,X1)
| ~ product(iPr_def_10,X0,X2)
| ~ product(multiplicative_identity,X0,X1) ),
inference(superposition,[status(thm)],[c_832,c_82]) ).
tcf(c_1391,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X1,multiplicative_identity)
| ~ product(multiplicative_identity,X0,X2)
| ~ product(X0,X1,iPr_def_10) ),
inference(superposition,[status(thm)],[c_832,c_83]) ).
tcf(c_1689,plain,
! [X0: $i,X1: $i] :
( product(iPr_def_10,X0,X1)
| ~ defined(X0)
| ~ product(multiplicative_identity,X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_1331]) ).
tcf(c_1770,plain,
( sum(additive_identity,multiplicative_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_1787,plain,
( product(iPr_def_10,iPr_def_10,multiplicative_identity)
| ~ defined(iPr_def_10) ),
inference(superposition,[status(thm)],[c_832,c_1689]) ).
tcf(c_1789,plain,
product(iPr_def_10,iPr_def_10,multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_1787,c_792]) ).
tcf(c_1809,plain,
! [X0: $i,X1: $i] :
( product(multiplicative_identity,X1,X0)
| ~ defined(X0)
| ~ product(iPr_def_10,X0,X1) ),
inference(superposition,[status(thm)],[c_84,c_1333]) ).
tcf(c_1895,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,multiplicative_identity)
| ~ product(iPr_def_10,X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_832,c_1391]) ).
tcf(c_1936,plain,
( product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ defined(iPr_def_10) ),
inference(superposition,[status(thm)],[c_741,c_1895]) ).
tcf(c_1937,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_1936,c_792]) ).
tcf(c_2314,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,iPr_def_10,multiplicative_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(X1,multiplicative_identity,multiplicative_identity)
| ~ product(X0,multiplicative_identity,iPr_def_10)
| ~ sum(additive_identity,X0,X1) ),
inference(instantiation,[status(thm)],[c_1312]) ).
tcf(c_4162,plain,
! [X0: $i] :
( sum(additive_identity,iPr_def_10,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_identity,iPr_def_10)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(X0,multiplicative_identity,multiplicative_identity)
| ~ sum(additive_identity,multiplicative_identity,X0) ),
inference(instantiation,[status(thm)],[c_2314]) ).
tcf(c_6839,plain,
( product(multiplicative_identity,multiplicative_identity,iPr_def_10)
| ~ defined(iPr_def_10) ),
inference(superposition,[status(thm)],[c_1789,c_1809]) ).
tcf(c_6874,plain,
product(multiplicative_identity,multiplicative_identity,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_6839,c_792]) ).
tcf(c_14547,plain,
( sum(additive_identity,iPr_def_10,multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_identity,iPr_def_10)
| ~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ sum(additive_identity,multiplicative_identity,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_4162]) ).
tcf(c_14548,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_14547,c_6874,c_1937,c_1770,c_744,c_274,c_90,c_93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD010-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 10:34:59 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 2.04/1.20 % SZS status Started for theBenchmark.p
% 2.04/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.04/1.20
% 2.04/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.04/1.20
% 2.04/1.20 % ------ iProver source info
% 2.04/1.20
% 2.04/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 2.04/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.04/1.20 % git: non_committed_changes: false
% 2.04/1.20
% 2.04/1.20 % ------ Parsing...% successful
% 2.04/1.20
% 2.04/1.20
% 2.04/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.04/1.20
% 2.04/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.04/1.20
% 2.04/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.04/1.20
% 2.04/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.04/1.20 % ------ Proving...
% 2.04/1.20 % ------ Problem Properties
% 2.04/1.20
% 2.04/1.20 %
% 2.04/1.20 % clauses 29
% 2.04/1.20 % conjectures 2
% 2.04/1.20 % EPR 20
% 2.04/1.20 % Horn 26
% 2.04/1.20 % unary 6
% 2.04/1.20 % binary 6
% 2.04/1.20 % lits 80
% 2.04/1.20 % lits eq 1
% 2.04/1.20 % fd_pure 0
% 2.04/1.20 % fd_pseudo 0
% 2.04/1.20 % fd_cond 0
% 2.04/1.20 % fd_pseudo_cond 0
% 2.04/1.20 % AC symbols 0
% 2.04/1.20
% 2.04/1.20 % ------ Schedule dynamic 5 is on
% 2.04/1.20
% 2.04/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.04/1.20
% 2.04/1.20
% 2.04/1.20 % ------
% 2.04/1.20 % Current options:
% 2.04/1.20 % ------
% 2.04/1.20
% 2.04/1.20
% 2.04/1.20 %
% 2.04/1.20
% 2.04/1.20 % ------ Proving...
% 2.04/1.20 %
% 2.04/1.20
% 2.04/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.04/1.20
% 2.04/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.04/1.20
% 2.04/1.20
%------------------------------------------------------------------------------