%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD021-1 : 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 : n007.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 01:15:39 PM UTC 2026
% Result : Unsatisfiable 2.04s 1.29s
% Output : CNFRefutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 47 ( 16 unt; 1 def)
% Number of atoms : 113 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 101 ( 50 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( ~ defined(X0)
| equalish(add(additive_identity,X0),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
fof(f16,axiom,
! [X0,X1] :
( ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1)
| equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',antisymmetry_of_order_relation) ).
fof(f18,axiom,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',totality_of_order_relation) ).
fof(f19,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X0,X2)
| ~ defined(X1)
| less_or_equal(add(X0,X1),add(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_order_relation_and_addition) ).
fof(f22,axiom,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
fof(f23,axiom,
! [X2,X0,X1] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
fof(f26,axiom,
! [X2,X0,X1] :
( ~ equalish(X2,X0)
| ~ less_or_equal(X2,X1)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_order_relation) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,axiom,
defined(m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_is_defined) ).
fof(f30,negated_conjecture,
equalish(m,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_equals_additive_identity_3) ).
fof(f31,negated_conjecture,
~ equalish(add(m,a),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_not_equal_to_a_4) ).
tcf(c_81,plain,
! [X0: $i] :
( equalish(add(additive_identity,X0),X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_90,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f11]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,X0)
| less_or_equal(X0,X1)
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(add(X0,X2),add(X1,X2))
| ~ defined(X2)
| ~ less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(X1,X2)
| ~ less_or_equal(X0,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_107,plain,
defined(a),
inference(cnf_transformation,[],[f28]) ).
tcf(c_108,plain,
defined(m),
inference(cnf_transformation,[],[f29]) ).
tcf(c_109,negated_conjecture,
equalish(m,additive_identity),
inference(cnf_transformation,[],[f30]) ).
tcf(c_110,negated_conjecture,
~ equalish(add(m,a),a),
inference(cnf_transformation,[],[f31]) ).
tcf(c_119,plain,
( less_or_equal(additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_283,definition,
iPr_def_10 = add(m,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_284,negated_conjecture,
~ equalish(iPr_def_10,a),
inference(demodulation,[status(thm)],[c_110,c_283]) ).
tcf(c_285,negated_conjecture,
equalish(m,additive_identity),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_706,plain,
equalish(additive_identity,m),
inference(superposition,[status(thm)],[c_285,c_101]) ).
tcf(c_881,plain,
! [X0: $i] :
( less_or_equal(additive_identity,X0)
| ~ less_or_equal(m,X0) ),
inference(superposition,[status(thm)],[c_285,c_105]) ).
tcf(c_888,plain,
! [X0: $i] :
( less_or_equal(m,X0)
| ~ less_or_equal(additive_identity,X0) ),
inference(superposition,[status(thm)],[c_706,c_105]) ).
tcf(c_928,plain,
( less_or_equal(m,additive_identity)
| ~ less_or_equal(additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_888]) ).
tcf(c_981,plain,
! [X0: $i] :
( equalish(iPr_def_10,a)
| ~ equalish(iPr_def_10,X0)
| ~ equalish(X0,a) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_1090,plain,
( equalish(iPr_def_10,a)
| ~ equalish(iPr_def_10,add(additive_identity,a))
| ~ equalish(add(additive_identity,a),a) ),
inference(instantiation,[status(thm)],[c_981]) ).
tcf(c_1091,plain,
( equalish(add(additive_identity,a),a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_1139,plain,
! [X0: $i] :
( less_or_equal(additive_identity,X0)
| less_or_equal(X0,m)
| ~ defined(m)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_97,c_881]) ).
tcf(c_1144,plain,
! [X0: $i] :
( less_or_equal(additive_identity,X0)
| less_or_equal(X0,m)
| ~ defined(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1139,c_108]) ).
tcf(c_1401,plain,
( less_or_equal(additive_identity,m)
| ~ defined(m) ),
inference(superposition,[status(thm)],[c_1144,c_881]) ).
tcf(c_1402,plain,
less_or_equal(additive_identity,m),
inference(forward_subsumption_resolution,[status(thm)],[c_1401,c_108]) ).
tcf(c_1429,plain,
( equalish(iPr_def_10,add(additive_identity,a))
| ~ less_or_equal(iPr_def_10,add(additive_identity,a))
| ~ less_or_equal(add(additive_identity,a),iPr_def_10) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1497,plain,
! [X0: $i] :
( less_or_equal(iPr_def_10,add(X0,a))
| ~ defined(a)
| ~ less_or_equal(m,X0) ),
inference(superposition,[status(thm)],[c_283,c_98]) ).
tcf(c_1498,plain,
! [X0: $i] :
( less_or_equal(add(X0,a),iPr_def_10)
| ~ defined(a)
| ~ less_or_equal(X0,m) ),
inference(superposition,[status(thm)],[c_283,c_98]) ).
tcf(c_1501,plain,
! [X0: $i] :
( less_or_equal(add(X0,a),iPr_def_10)
| ~ less_or_equal(X0,m) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1498,c_107]) ).
tcf(c_1504,plain,
! [X0: $i] :
( less_or_equal(iPr_def_10,add(X0,a))
| ~ less_or_equal(m,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1497,c_107]) ).
tcf(c_1515,plain,
( less_or_equal(iPr_def_10,add(additive_identity,a))
| ~ less_or_equal(m,additive_identity) ),
inference(instantiation,[status(thm)],[c_1504]) ).
tcf(c_1516,plain,
( less_or_equal(add(additive_identity,a),iPr_def_10)
| ~ less_or_equal(additive_identity,m) ),
inference(instantiation,[status(thm)],[c_1501]) ).
tcf(c_1517,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1516,c_1515,c_1429,c_1402,c_1091,c_1090,c_928,c_284,c_119,c_90,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD021-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 10:38:23 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 2.04/1.29 % SZS status Started for theBenchmark.p
% 2.04/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.04/1.29
% 2.04/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.04/1.29
% 2.04/1.29 % ------ iProver source info
% 2.04/1.29
% 2.04/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.04/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.04/1.29 % git: non_committed_changes: false
% 2.04/1.29
% 2.04/1.29 % ------ Parsing...% successful
% 2.04/1.29
% 2.04/1.29
% 2.04/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.04/1.29
% 2.04/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.04/1.29
% 2.04/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.04/1.29
% 2.04/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.04/1.29 % ------ Proving...
% 2.04/1.29 % ------ Problem Properties
% 2.04/1.29
% 2.04/1.29 %
% 2.04/1.29 % clauses 32
% 2.04/1.29 % conjectures 2
% 2.04/1.29 % EPR 14
% 2.04/1.29 % Horn 29
% 2.04/1.29 % unary 8
% 2.04/1.29 % binary 6
% 2.04/1.29 % lits 78
% 2.04/1.29 % lits eq 1
% 2.04/1.29 % fd_pure 0
% 2.04/1.29 % fd_pseudo 0
% 2.04/1.29 % fd_cond 0
% 2.04/1.29 % fd_pseudo_cond 0
% 2.04/1.29 % AC symbols 0
% 2.04/1.29
% 2.04/1.29 % ------ Schedule dynamic 5 is on
% 2.04/1.29
% 2.04/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.04/1.29
% 2.04/1.29
% 2.04/1.29 % ------
% 2.04/1.29 % Current options:
% 2.04/1.29 % ------
% 2.04/1.29
% 2.04/1.29
% 2.04/1.29 %
% 2.04/1.29
% 2.04/1.29 % ------ Proving...
% 2.04/1.29 %
% 2.04/1.29
% 2.04/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.04/1.29
% 2.04/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.04/1.29
% 2.04/1.29
%------------------------------------------------------------------------------