%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD026-3 : 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 : n020.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 01:15:40 PM UTC 2026
% Result : Unsatisfiable 3.57s 1.19s
% Output : CNFRefutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 14
% Syntax : Number of formulae : 55 ( 15 unt; 0 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 159 ( 78 ~; 81 |; 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 : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X2,X0,X1] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
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(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/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/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/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,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
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,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_4) ).
fof(f31,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_5) ).
tcf(c_80,plain,
defined(a),
inference(cnf_transformation,[],[f27]) ).
tcf(c_81,plain,
defined(b),
inference(cnf_transformation,[],[f28]) ).
tcf(c_82,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[],[f29]) ).
tcf(c_83,negated_conjecture,
product(multiplicative_identity,a,b),
inference(cnf_transformation,[],[f30]) ).
tcf(c_84,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
inference(cnf_transformation,[],[f31]) ).
tcf(c_86,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f14]) ).
tcf(c_89,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,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_93,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[],[f17]) ).
tcf(c_94,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_95,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,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_98,plain,
! [X0: $i] :
( defined(multiplicative_inverse(X0))
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_99,plain,
! [X0: $i] :
( sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_100,plain,
( product(multiplicative_identity,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_199,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_200,plain,
( sum(additive_identity,a,additive_identity)
| ~ sum(a,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_203,plain,
! [X0: $i] :
( product(X0,multiplicative_identity,X0)
| ~ product(multiplicative_identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_204,plain,
( product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(multiplicative_identity,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_203]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(b,X0,X2)
| ~ product(multiplicative_identity,a,b)
| ~ product(multiplicative_identity,X1,X2)
| ~ product(a,X0,X1) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_224,plain,
( product(a,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(a,additive_identity,additive_identity)
| ~ product(X2,X3,additive_identity)
| ~ product(X1,X3,additive_identity)
| ~ product(X0,X3,a)
| ~ sum(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_267,plain,
! [X0: $i] :
( product(b,multiplicative_identity,X0)
| ~ product(multiplicative_identity,a,b)
| ~ product(a,multiplicative_identity,a)
| ~ product(multiplicative_identity,a,X0) ),
inference(instantiation,[status(thm)],[c_210]) ).
tcf(c_268,plain,
( product(a,multiplicative_identity,a)
| ~ product(multiplicative_identity,a,a) ),
inference(instantiation,[status(thm)],[c_203]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i] :
( sum(b,X0,X1)
| ~ sum(X0,b,X1) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_278,plain,
( sum(b,additive_identity,additive_identity)
| ~ sum(additive_identity,b,additive_identity) ),
inference(instantiation,[status(thm)],[c_277]) ).
tcf(c_329,plain,
( product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ defined(multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_377,plain,
! [X0: $i] :
( product(b,multiplicative_inverse(a),X0)
| ~ product(multiplicative_identity,a,b)
| ~ product(multiplicative_identity,multiplicative_identity,X0)
| ~ product(a,multiplicative_inverse(a),multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_210]) ).
tcf(c_398,plain,
( product(multiplicative_identity,a,a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_645,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_646,plain,
( defined(multiplicative_inverse(b))
| sum(additive_identity,b,additive_identity)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_1577,plain,
( product(b,multiplicative_identity,a)
| ~ product(multiplicative_identity,a,b)
| ~ product(multiplicative_identity,a,a)
| ~ product(a,multiplicative_identity,a) ),
inference(instantiation,[status(thm)],[c_267]) ).
tcf(c_1578,plain,
! [X0: $i,X1: $i] :
( sum(a,additive_identity,additive_identity)
| ~ product(b,multiplicative_identity,a)
| ~ product(X1,multiplicative_identity,additive_identity)
| ~ product(X0,multiplicative_identity,additive_identity)
| ~ sum(b,X0,X1) ),
inference(instantiation,[status(thm)],[c_230]) ).
tcf(c_1579,plain,
( sum(a,additive_identity,additive_identity)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(b,multiplicative_identity,a)
| ~ sum(b,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_1578]) ).
tcf(c_2025,plain,
( product(b,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,a,b)
| ~ product(a,multiplicative_inverse(a),multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_377]) ).
tcf(c_3235,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(multiplicative_identity,X2,X1)
| ~ product(b,X2,X0)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(multiplicative_inverse(b),X0,X1) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_12480,plain,
( product(multiplicative_inverse(b),multiplicative_identity,multiplicative_inverse(b))
| ~ product(multiplicative_identity,multiplicative_inverse(b),multiplicative_inverse(b)) ),
inference(instantiation,[status(thm)],[c_203]) ).
tcf(c_12502,plain,
( product(multiplicative_identity,multiplicative_inverse(b),multiplicative_inverse(b))
| ~ defined(multiplicative_inverse(b)) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_13262,plain,
! [X0: $i] :
( product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b))
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(b,multiplicative_inverse(a),X0)
| ~ product(multiplicative_inverse(b),X0,multiplicative_inverse(b)) ),
inference(instantiation,[status(thm)],[c_3235]) ).
tcf(c_17174,plain,
( product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b))
| ~ product(b,multiplicative_inverse(a),multiplicative_identity)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity)
| ~ product(multiplicative_inverse(b),multiplicative_identity,multiplicative_inverse(b)) ),
inference(instantiation,[status(thm)],[c_13262]) ).
tcf(c_17175,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_17174,c_12502,c_12480,c_2025,c_1579,c_1577,c_645,c_646,c_398,c_329,c_278,c_268,c_224,c_204,c_200,c_199,c_100,c_84,c_82,c_83,c_80,c_81,c_86,c_93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD026-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 10:43:50 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...
% 3.57/1.19 % SZS status Started for theBenchmark.p
% 3.57/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.57/1.19
% 3.57/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.57/1.19
% 3.57/1.19 % ------ iProver source info
% 3.57/1.19
% 3.57/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.57/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.57/1.19 % git: non_committed_changes: false
% 3.57/1.19
% 3.57/1.19 % ------ Parsing...% successful
% 3.57/1.19
% 3.57/1.19
% 3.57/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.57/1.19
% 3.57/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.57/1.19
% 3.57/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.57/1.19 % ------ Proving...
% 3.57/1.19 % ------ Problem Properties
% 3.57/1.19
% 3.57/1.19 %
% 3.57/1.19 % clauses 20
% 3.57/1.19 % conjectures 3
% 3.57/1.19 % EPR 17
% 3.57/1.19 % Horn 18
% 3.57/1.19 % unary 8
% 3.57/1.19 % binary 4
% 3.57/1.19 % lits 48
% 3.57/1.19 % lits eq 0
% 3.57/1.19 % fd_pure 0
% 3.57/1.19 % fd_pseudo 0
% 3.57/1.19 % fd_cond 0
% 3.57/1.19 % fd_pseudo_cond 0
% 3.57/1.19 % AC symbols 0
% 3.57/1.19
% 3.57/1.19 % ------ Schedule dynamic 5 is on
% 3.57/1.19
% 3.57/1.19 % ------ no equalities: superposition off
% 3.57/1.19
% 3.57/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.57/1.19
% 3.57/1.19
% 3.57/1.19 % ------
% 3.57/1.19 % Current options:
% 3.57/1.19 % ------
% 3.57/1.19
% 3.57/1.19
% 3.57/1.19 %
% 3.57/1.19
% 3.57/1.19 % ------ Proving...
% 3.57/1.19 %
% 3.57/1.19
% 3.57/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.57/1.19
% 3.57/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.57/1.19
% 3.57/1.19
%------------------------------------------------------------------------------