%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD031-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.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 01:15:42 PM UTC 2026
% Result : Unsatisfiable 2.25s 1.29s
% Output : CNFRefutation 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 16 unt; 1 def)
% Number of atoms : 68 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 53 ( 27 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
fof(f8,axiom,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
fof(f18,axiom,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,negated_conjecture,
product(multiplicative_identity,a,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_2) ).
fof(f29,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_3) ).
fof(f30,negated_conjecture,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_4) ).
tcf(c_84,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_86,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_87,plain,
! [X0: $i] :
( sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_96,plain,
! [X0: $i] :
( defined(multiplicative_inverse(X0))
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_105,plain,
defined(a),
inference(cnf_transformation,[],[f27]) ).
tcf(c_106,negated_conjecture,
product(multiplicative_identity,a,multiplicative_identity),
inference(cnf_transformation,[],[f28]) ).
tcf(c_107,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[],[f29]) ).
tcf(c_108,negated_conjecture,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_281,definition,
iPr_def_10 = multiplicative_inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_282,negated_conjecture,
~ product(multiplicative_identity,multiplicative_identity,iPr_def_10),
inference(demodulation,[status(thm)],[c_108,c_281]) ).
tcf(c_283,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_284,negated_conjecture,
product(multiplicative_identity,a,multiplicative_identity),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_791,plain,
( defined(multiplicative_inverse(a))
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_96,c_283]) ).
tcf(c_793,plain,
( defined(iPr_def_10)
| ~ defined(a) ),
inference(light_normalisation,[status(thm)],[c_791,c_281]) ).
tcf(c_794,plain,
defined(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_793,c_105]) ).
tcf(c_824,plain,
( sum(additive_identity,a,additive_identity)
| product(iPr_def_10,a,multiplicative_identity)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_281,c_87]) ).
tcf(c_826,plain,
product(iPr_def_10,a,multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_824,c_283,c_105]) ).
tcf(c_875,plain,
product(a,iPr_def_10,multiplicative_identity),
inference(superposition,[status(thm)],[c_826,c_88]) ).
tcf(c_1227,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(multiplicative_identity,X1,X2)
| ~ product(multiplicative_identity,X0,X2)
| ~ product(a,X0,X1) ),
inference(superposition,[status(thm)],[c_284,c_84]) ).
tcf(c_1341,plain,
! [X0: $i] :
( product(multiplicative_identity,multiplicative_identity,X0)
| ~ product(multiplicative_identity,iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_875,c_1227]) ).
tcf(c_1369,plain,
( product(multiplicative_identity,multiplicative_identity,iPr_def_10)
| ~ defined(iPr_def_10) ),
inference(superposition,[status(thm)],[c_86,c_1341]) ).
tcf(c_1372,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1369,c_282,c_794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD031-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n005.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 10:45:05 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 2.25/1.29 % SZS status Started for theBenchmark.p
% 2.25/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.25/1.29
% 2.25/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.25/1.29
% 2.25/1.29 % ------ iProver source info
% 2.25/1.29
% 2.25/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.25/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.25/1.29 % git: non_committed_changes: false
% 2.25/1.29
% 2.25/1.29 % ------ Parsing...% successful
% 2.25/1.29
% 2.25/1.29
% 2.25/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.25/1.29
% 2.25/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.25/1.29
% 2.25/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.25/1.29
% 2.25/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.25/1.29 % ------ Proving...
% 2.25/1.29 % ------ Problem Properties
% 2.25/1.29
% 2.25/1.29 %
% 2.25/1.29 % clauses 31
% 2.25/1.29 % conjectures 3
% 2.25/1.29 % EPR 22
% 2.25/1.29 % Horn 28
% 2.25/1.29 % unary 8
% 2.25/1.29 % binary 6
% 2.25/1.29 % lits 82
% 2.25/1.29 % lits eq 1
% 2.25/1.29 % fd_pure 0
% 2.25/1.29 % fd_pseudo 0
% 2.25/1.29 % fd_cond 0
% 2.25/1.29 % fd_pseudo_cond 0
% 2.25/1.29 % AC symbols 0
% 2.25/1.29
% 2.25/1.29 % ------ Schedule dynamic 5 is on
% 2.25/1.29
% 2.25/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.25/1.29
% 2.25/1.29
% 2.25/1.29 % ------
% 2.25/1.29 % Current options:
% 2.25/1.29 % ------
% 2.25/1.29
% 2.25/1.29
% 2.25/1.29 %
% 2.25/1.29
% 2.25/1.29 % ------ Proving...
% 2.25/1.29 %
% 2.25/1.29
% 2.25/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.25/1.29
% 2.25/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.25/1.29
% 2.25/1.29
%------------------------------------------------------------------------------