%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD036-3 : 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 : n001.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 01:15:43 PM UTC 2026
% Result : Unsatisfiable 1.11s 1.20s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 13 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 87 ( 44 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?; 25 :)
% 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(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/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
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(f28,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,axiom,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
fof(f31,negated_conjecture,
product(a,c,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_5) ).
fof(f32,negated_conjecture,
product(b,c,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_6) ).
fof(f33,negated_conjecture,
~ product(multiplicative_identity,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_7) ).
fof(f34,negated_conjecture,
~ sum(additive_identity,c,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_8) ).
tcf(c_88,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_89,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_90,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_91,plain,
! [X0: $i] :
( sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_110,plain,
defined(b),
inference(cnf_transformation,[],[f28]) ).
tcf(c_111,plain,
defined(c),
inference(cnf_transformation,[],[f29]) ).
tcf(c_113,negated_conjecture,
product(a,c,u),
inference(cnf_transformation,[],[f31]) ).
tcf(c_114,negated_conjecture,
product(b,c,u),
inference(cnf_transformation,[],[f32]) ).
tcf(c_115,negated_conjecture,
~ product(multiplicative_identity,a,b),
inference(cnf_transformation,[],[f33]) ).
tcf(c_116,negated_conjecture,
~ sum(additive_identity,c,additive_identity),
inference(cnf_transformation,[],[f34]) ).
tcf(c_302,plain,
( sum(additive_identity,c,additive_identity)
| product(multiplicative_inverse(c),c,multiplicative_identity)
| ~ defined(c) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_305,plain,
( product(c,a,u)
| ~ product(a,c,u) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_306,plain,
( product(c,b,u)
| ~ product(b,c,u) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(multiplicative_identity,X2,X1)
| ~ product(c,X2,X0)
| ~ product(multiplicative_inverse(c),c,multiplicative_identity)
| ~ product(multiplicative_inverse(c),X0,X1) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_340,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(multiplicative_inverse(c),X1,X2)
| ~ product(multiplicative_identity,X0,X2)
| ~ product(c,X0,X1)
| ~ product(multiplicative_inverse(c),c,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_773,plain,
( product(multiplicative_identity,b,b)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_1880,plain,
! [X0: $i] :
( product(multiplicative_identity,a,b)
| ~ product(c,a,X0)
| ~ product(multiplicative_inverse(c),c,multiplicative_identity)
| ~ product(multiplicative_inverse(c),X0,b) ),
inference(instantiation,[status(thm)],[c_339]) ).
tcf(c_2060,plain,
! [X0: $i] :
( product(multiplicative_inverse(c),u,X0)
| ~ product(c,b,u)
| ~ product(multiplicative_identity,b,X0)
| ~ product(multiplicative_inverse(c),c,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_340]) ).
tcf(c_5015,plain,
( product(multiplicative_identity,a,b)
| ~ product(c,a,u)
| ~ product(multiplicative_inverse(c),u,b)
| ~ product(multiplicative_inverse(c),c,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_1880]) ).
tcf(c_7211,plain,
( product(multiplicative_inverse(c),u,b)
| ~ product(multiplicative_identity,b,b)
| ~ product(c,b,u)
| ~ product(multiplicative_inverse(c),c,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_2060]) ).
tcf(c_7212,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7211,c_5015,c_773,c_306,c_305,c_302,c_115,c_116,c_113,c_114,c_110,c_111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD036-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n001.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 10:52:42 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.11/1.20 % SZS status Started for theBenchmark.p
% 1.11/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 1.11/1.20
% 1.11/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.11/1.20
% 1.11/1.20 % ------ iProver source info
% 1.11/1.20
% 1.11/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 1.11/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.11/1.20 % git: non_committed_changes: false
% 1.11/1.20
% 1.11/1.20 % ------ Parsing...% successful
% 1.11/1.20
% 1.11/1.20
% 1.11/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.11/1.20
% 1.11/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.11/1.20
% 1.11/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.11/1.20 % ------ Proving...
% 1.11/1.20 % ------ Problem Properties
% 1.11/1.20
% 1.11/1.20 %
% 1.11/1.20 % clauses 34
% 1.11/1.20 % conjectures 4
% 1.11/1.20 % EPR 26
% 1.11/1.20 % Horn 31
% 1.11/1.20 % unary 11
% 1.11/1.20 % binary 6
% 1.11/1.20 % lits 85
% 1.11/1.20 % lits eq 0
% 1.11/1.20 % fd_pure 0
% 1.11/1.20 % fd_pseudo 0
% 1.11/1.20 % fd_cond 0
% 1.11/1.20 % fd_pseudo_cond 0
% 1.11/1.20 % AC symbols 0
% 1.11/1.20
% 1.11/1.20 % ------ Schedule dynamic 5 is on
% 1.11/1.20
% 1.11/1.20 % ------ no equalities: superposition off
% 1.11/1.20
% 1.11/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.11/1.20
% 1.11/1.20
% 1.11/1.20 % ------
% 1.11/1.20 % Current options:
% 1.11/1.20 % ------
% 1.11/1.20
% 1.11/1.20
% 1.11/1.20 %
% 1.11/1.20
% 1.11/1.20 % ------ Proving...
% 1.11/1.20 %
% 1.11/1.20
% 1.11/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 1.11/1.20
% 1.11/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.66/1.20
% 1.66/1.20
%------------------------------------------------------------------------------