%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD009-3 : 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 : n017.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 01:15:35 PM UTC 2026
% Result : Unsatisfiable 1.10s 1.71s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 10 unt; 0 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 89 ( 44 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?; 28 :)
% 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/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
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(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(f20,axiom,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
fof(f30,negated_conjecture,
! [X0] : ~ product(a,X0,b),
file('/export/starexec/sandbox2/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_98,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,multiply(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_105,plain,
defined(a),
inference(cnf_transformation,[],[f27]) ).
tcf(c_106,plain,
defined(b),
inference(cnf_transformation,[],[f28]) ).
tcf(c_107,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[],[f29]) ).
tcf(c_108,negated_conjecture,
! [X0: $i] : ~ product(a,X0,b),
inference(cnf_transformation,[],[f30]) ).
tcf(c_285,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_286,plain,
( defined(multiplicative_inverse(a))
| sum(additive_identity,a,additive_identity)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_337,plain,
! [X0: $i,X1: $i] :
( product(a,X0,X1)
| ~ product(X0,a,X1) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( product(X0,X4,b)
| ~ product(X2,X3,b)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_467,plain,
( product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_478,plain,
( product(multiplicative_identity,b,b)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_564,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X2,b)
| ~ product(multiplicative_identity,b,b)
| ~ product(X1,b,X2)
| ~ product(X0,X1,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_345]) ).
tcf(c_1348,plain,
! [X0: $i,X1: $i] :
( product(X1,multiply(X0,b),b)
| ~ product(multiplicative_identity,b,b)
| ~ product(X1,X0,multiplicative_identity)
| ~ product(X0,b,multiply(X0,b)) ),
inference(instantiation,[status(thm)],[c_564]) ).
tcf(c_2556,plain,
! [X0: $i] :
( product(X0,b,multiply(X0,b))
| ~ defined(b)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_2851,plain,
( product(a,multiply(multiplicative_inverse(a),b),b)
| ~ product(multiplicative_identity,b,b)
| ~ product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_inverse(a),b,multiply(multiplicative_inverse(a),b)) ),
inference(instantiation,[status(thm)],[c_1348]) ).
tcf(c_6392,plain,
( product(multiplicative_inverse(a),b,multiply(multiplicative_inverse(a),b))
| ~ defined(b)
| ~ defined(multiplicative_inverse(a)) ),
inference(instantiation,[status(thm)],[c_2556]) ).
tcf(c_11816,plain,
~ product(a,multiply(multiplicative_inverse(a),b),b),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_11817,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11816,c_6392,c_2851,c_478,c_467,c_285,c_286,c_107,c_105,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD009-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n017.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 : Fri Sep 25 10:30:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.10/1.71 % SZS status Started for theBenchmark.p
% 1.10/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.10/1.71
% 1.10/1.71 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.10/1.71
% 1.10/1.71 % ------ iProver source info
% 1.10/1.71
% 1.10/1.71 % git: date: 2026-07-19 20:42:38 +0200
% 1.10/1.71 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.10/1.71 % git: non_committed_changes: false
% 1.10/1.71
% 1.10/1.71 % ------ Parsing...% successful
% 1.10/1.71
% 1.10/1.71
% 1.10/1.71 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.10/1.71
% 1.10/1.71 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.10/1.71
% 1.10/1.71 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.10/1.71 % ------ Proving...
% 1.10/1.71 % ------ Problem Properties
% 1.10/1.71
% 1.10/1.71 %
% 1.10/1.71 % clauses 30
% 1.10/1.71 % conjectures 2
% 1.10/1.71 % EPR 22
% 1.10/1.71 % Horn 27
% 1.10/1.71 % unary 7
% 1.10/1.71 % binary 6
% 1.10/1.71 % lits 81
% 1.10/1.71 % lits eq 0
% 1.10/1.71 % fd_pure 0
% 1.10/1.71 % fd_pseudo 0
% 1.10/1.71 % fd_cond 0
% 1.10/1.71 % fd_pseudo_cond 0
% 1.10/1.71 % AC symbols 0
% 1.10/1.71
% 1.10/1.71 % ------ Input Options Time Limit: Unbounded
% 1.10/1.71
% 1.10/1.71
% 1.10/1.71 % ------
% 1.10/1.71 % Current options:
% 1.10/1.71 % ------
% 1.10/1.71
% 1.10/1.71
% 1.10/1.71 %
% 1.10/1.71
% 1.10/1.71 % ------ Proving...
% 1.10/1.71 %
% 1.10/1.71
% 1.10/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.10/1.71
% 1.10/1.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.10/1.71
% 1.10/1.71
%------------------------------------------------------------------------------