%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD040-3 : 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 : n016.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 01:15:44 PM UTC 2026
% Result : Unsatisfiable 25.78s 4.32s
% Output : CNFRefutation 25.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 60 ( 9 unt; 0 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 192 ( 94 ~; 98 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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; 3 con; 0-1 aty)
% Number of variables : 98 ( 0 sgn 98 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
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(f4,axiom,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
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(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(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,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_2) ).
fof(f29,negated_conjecture,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X2,X5,X4)
| ~ sum(X1,X5,X3)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_80,plain,
! [X0: $i] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_81,plain,
! [X0: $i] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_85,plain,
! [X0: $i] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_86,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,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_91,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f14]) ).
tcf(c_95,plain,
! [X0: $i] :
( defined(multiplicative_inverse(X0))
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_104,plain,
defined(a),
inference(cnf_transformation,[],[f27]) ).
tcf(c_105,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[],[f28]) ).
tcf(c_106,negated_conjecture,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
inference(cnf_transformation,[],[f29]) ).
tcf(c_109,plain,
( sum(additive_identity,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_117,plain,
( defined(multiplicative_inverse(a))
| sum(additive_identity,a,additive_identity)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_118,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_119,plain,
( sum(additive_identity,a,additive_identity)
| ~ sum(a,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sum(X2,X4,X1)
| ~ product(multiplicative_identity,X1,X1)
| ~ sum(X0,X3,multiplicative_identity)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(X2,X3,multiplicative_identity)
| ~ product(X1,a,X3)
| ~ product(X0,a,X2)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ sum(X0,X1,multiplicative_inverse(a)) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(a,additive_identity,additive_identity)
| ~ sum(a,X0,X2)
| ~ sum(X2,X1,additive_identity)
| ~ sum(X0,X1,additive_identity) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_219,plain,
( sum(additive_inverse(a),a,additive_identity)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,X1,X1)
| ~ sum(X0,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,X1,X1)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_709,plain,
! [X0: $i] :
( sum(X0,additive_inverse(a),additive_identity)
| ~ sum(additive_inverse(a),X0,additive_identity) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_731,plain,
( product(multiplicative_identity,a,a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_832,plain,
! [X0: $i] :
( sum(X0,additive_identity,X0)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_80,c_82]) ).
tcf(c_901,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(additive_identity,X2,X1)
| ~ sum(additive_identity,X0,X2)
| ~ sum(multiplicative_inverse(a),X0,X1) ),
inference(superposition,[status(thm)],[c_106,c_78]) ).
tcf(c_935,plain,
! [X0: $i] :
( sum(additive_identity,X0,multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(a))
| ~ sum(additive_identity,additive_identity,X0) ),
inference(superposition,[status(thm)],[c_832,c_901]) ).
tcf(c_1171,plain,
! [X0: $i,X1: $i] :
( sum(X1,multiplicative_identity,multiplicative_identity)
| ~ product(X0,a,X1)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ sum(X0,multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(instantiation,[status(thm)],[c_147]) ).
tcf(c_1523,plain,
! [X0: $i] :
( sum(X0,X0,X0)
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_identity,X0,X0) ),
inference(instantiation,[status(thm)],[c_389]) ).
tcf(c_1926,plain,
! [X0: $i] :
( sum(X0,additive_identity,X0)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_80,c_82]) ).
tcf(c_2016,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(additive_identity,X2,X1)
| ~ sum(additive_identity,X0,X2)
| ~ sum(multiplicative_inverse(a),X0,X1) ),
inference(superposition,[status(thm)],[c_106,c_78]) ).
tcf(c_2027,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,X1,multiplicative_inverse(a))
| ~ sum(additive_identity,X0,X2)
| ~ sum(X0,X1,additive_identity) ),
inference(superposition,[status(thm)],[c_106,c_79]) ).
tcf(c_2033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(X2,X3,X0)
| ~ defined(X0)
| ~ sum(X1,X3,additive_identity)
| ~ sum(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_1926,c_79]) ).
tcf(c_2061,plain,
! [X0: $i] :
( sum(multiplicative_inverse(a),X0,additive_identity)
| ~ defined(additive_identity)
| ~ sum(additive_identity,X0,additive_identity) ),
inference(superposition,[status(thm)],[c_106,c_2033]) ).
tcf(c_2096,plain,
! [X0: $i] :
( sum(multiplicative_inverse(a),X0,additive_identity)
| ~ sum(additive_identity,X0,additive_identity) ),
inference(global_subsumption_just,[status(thm)],[c_2061,c_91,c_2061]) ).
tcf(c_2102,plain,
! [X0: $i] :
( sum(X0,multiplicative_inverse(a),additive_identity)
| ~ sum(additive_identity,X0,additive_identity) ),
inference(superposition,[status(thm)],[c_2096,c_82]) ).
tcf(c_2107,plain,
! [X0: $i] :
( sum(additive_identity,X0,multiplicative_inverse(a))
| ~ defined(multiplicative_inverse(a))
| ~ sum(additive_identity,additive_identity,X0) ),
inference(superposition,[status(thm)],[c_1926,c_2016]) ).
tcf(c_2198,plain,
! [X0: $i] :
( sum(additive_identity,X0,multiplicative_inverse(a))
| ~ sum(additive_identity,additive_identity,X0) ),
inference(global_subsumption_just,[status(thm)],[c_2107,c_104,c_105,c_117,c_935]) ).
tcf(c_2208,plain,
! [X0: $i,X1: $i] :
( sum(multiplicative_inverse(a),X1,multiplicative_inverse(a))
| ~ sum(additive_identity,additive_identity,X0)
| ~ sum(X0,X1,additive_identity) ),
inference(superposition,[status(thm)],[c_2198,c_2027]) ).
tcf(c_2999,plain,
( sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ product(multiplicative_inverse(a),a,multiplicative_identity)
| ~ sum(multiplicative_inverse(a),multiplicative_inverse(a),multiplicative_inverse(a)) ),
inference(instantiation,[status(thm)],[c_1171]) ).
tcf(c_3535,plain,
! [X0: $i] :
( sum(multiplicative_inverse(a),multiplicative_inverse(a),multiplicative_inverse(a))
| ~ sum(additive_identity,additive_identity,X0)
| ~ sum(additive_identity,X0,additive_identity) ),
inference(superposition,[status(thm)],[c_2102,c_2208]) ).
tcf(c_3541,plain,
( sum(multiplicative_inverse(a),multiplicative_inverse(a),multiplicative_inverse(a))
| ~ sum(additive_identity,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_3535]) ).
tcf(c_4141,plain,
( sum(a,additive_inverse(a),additive_identity)
| ~ sum(additive_inverse(a),a,additive_identity) ),
inference(instantiation,[status(thm)],[c_709]) ).
tcf(c_16128,plain,
! [X0: $i] :
( sum(a,additive_identity,additive_identity)
| ~ sum(a,a,a)
| ~ sum(a,X0,additive_identity) ),
inference(instantiation,[status(thm)],[c_159]) ).
tcf(c_17525,plain,
( sum(a,a,a)
| ~ product(multiplicative_identity,a,a)
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
inference(instantiation,[status(thm)],[c_1523]) ).
tcf(c_27174,plain,
( sum(a,additive_identity,additive_identity)
| ~ sum(a,a,a)
| ~ sum(a,additive_inverse(a),additive_identity) ),
inference(instantiation,[status(thm)],[c_16128]) ).
tcf(c_27175,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_27174,c_17525,c_4141,c_3541,c_2999,c_731,c_219,c_119,c_118,c_109,c_105,c_91,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD040-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 10:52:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 25.78/4.32 % SZS status Started for theBenchmark.p
% 25.78/4.32 % SZS status Unsatisfiable for theBenchmark.p
% 25.78/4.32
% 25.78/4.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 25.78/4.32
% 25.78/4.32 % ------ iProver source info
% 25.78/4.32
% 25.78/4.32 % git: date: 2026-07-19 20:42:38 +0200
% 25.78/4.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 25.78/4.32 % git: non_committed_changes: false
% 25.78/4.32
% 25.78/4.32 % ------ Parsing...% successful
% 25.78/4.32
% 25.78/4.32
% 25.78/4.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 25.78/4.32
% 25.78/4.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e %
% 25.78/4.32
% 25.78/4.32 % ------ Preprocessing...
% 25.78/4.32 % ------ Proving...
% 25.78/4.32 % ------ Problem Properties
% 25.78/4.32
% 25.78/4.32 %
% 25.78/4.32 % clauses 29
% 25.78/4.32 % conjectures 3
% 25.78/4.32 % EPR 20
% 25.78/4.32 % Horn 26
% 25.78/4.32 % unary 6
% 25.78/4.32 % binary 6
% 25.78/4.32 % lits 80
% 25.78/4.32 % lits eq 0
% 25.78/4.32 % fd_pure 0
% 25.78/4.32 % fd_pseudo 0
% 25.78/4.32 % fd_cond 0
% 25.78/4.32 % fd_pseudo_cond 0
% 25.78/4.32 % AC symbols 0
% 25.78/4.32
% 25.78/4.32 % ------ Input Options Time Limit: Unbounded
% 25.78/4.32
% 25.78/4.32
% 25.78/4.32 % ------
% 25.78/4.32 % Current options:
% 25.78/4.32 % ------
% 25.78/4.32
% 25.78/4.32
% 25.78/4.32 %
% 25.78/4.32
% 25.78/4.32 % ------ Proving...
% 25.78/4.32 %
% 25.78/4.32
% 25.78/4.32 % SZS status Unsatisfiable for theBenchmark.p
% 25.78/4.32
% 25.78/4.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.78/4.32
% 25.78/4.32
%------------------------------------------------------------------------------