%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD059-2 : 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 : n026.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 01:15:50 PM UTC 2026
% Result : Unsatisfiable 4.22s 6.28s
% Output : CNFRefutation 4.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 61 ( 18 unt; 0 def)
% Number of atoms : 134 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 145 ( 72 ~; 73 |; 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 55 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( ~ defined(X0)
| equalish(add(additive_identity,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/FLD001-0.ax',antisymmetry_of_order_relation) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',transitivity_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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_order_relation) ).
fof(f28,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,axiom,
defined(u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
fof(f30,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_3) ).
fof(f31,negated_conjecture,
equalish(add(a,a),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_equals_u_4) ).
fof(f32,negated_conjecture,
~ less_or_equal(additive_identity,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_5) ).
tcf(c_81,plain,
defined(a),
inference(cnf_transformation,[],[f28]) ).
tcf(c_82,plain,
defined(u),
inference(cnf_transformation,[],[f29]) ).
tcf(c_83,negated_conjecture,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[],[f30]) ).
tcf(c_84,negated_conjecture,
equalish(add(a,a),u),
inference(cnf_transformation,[],[f31]) ).
tcf(c_85,negated_conjecture,
~ less_or_equal(additive_identity,u),
inference(cnf_transformation,[],[f32]) ).
tcf(c_88,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f11]) ).
tcf(c_89,plain,
! [X0: $i] :
( equalish(add(additive_identity,X0),X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(X2,X1)
| ~ equalish(X0,X2)
| ~ less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_91,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_92,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_93,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(X0,X2)
| ~ less_or_equal(X1,X2)
| ~ less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_249,plain,
! [X0: $i] :
( less_or_equal(additive_identity,u)
| ~ equalish(X0,additive_identity)
| ~ less_or_equal(X0,u) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_252,plain,
! [X0: $i] :
( less_or_equal(u,X0)
| less_or_equal(X0,u)
| ~ defined(u)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X0,u)
| ~ less_or_equal(X1,u)
| ~ less_or_equal(X0,X1) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,u)
| ~ less_or_equal(X0,u)
| ~ equalish(X0,X1) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_258,plain,
( less_or_equal(u,u)
| ~ defined(u) ),
inference(instantiation,[status(thm)],[c_252]) ).
tcf(c_260,plain,
( less_or_equal(additive_identity,u)
| ~ equalish(u,additive_identity)
| ~ less_or_equal(u,u) ),
inference(instantiation,[status(thm)],[c_249]) ).
tcf(c_270,plain,
! [X0: $i] :
( less_or_equal(X0,u)
| ~ less_or_equal(u,u)
| ~ equalish(u,X0) ),
inference(instantiation,[status(thm)],[c_254]) ).
tcf(c_282,plain,
! [X0: $i] :
( equalish(u,X0)
| ~ equalish(X0,u) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_298,plain,
( equalish(u,add(a,a))
| ~ equalish(add(a,a),u) ),
inference(instantiation,[status(thm)],[c_282]) ).
tcf(c_320,plain,
( less_or_equal(add(a,a),u)
| ~ less_or_equal(u,u)
| ~ equalish(u,add(a,a)) ),
inference(instantiation,[status(thm)],[c_270]) ).
tcf(c_385,plain,
! [X0: $i] :
( less_or_equal(X0,u)
| ~ less_or_equal(add(a,a),u)
| ~ less_or_equal(X0,add(a,a)) ),
inference(instantiation,[status(thm)],[c_253]) ).
tcf(c_469,plain,
( equalish(add(additive_identity,a),a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_565,plain,
! [X0: $i] :
( less_or_equal(add(X0,a),u)
| ~ less_or_equal(add(a,a),u)
| ~ less_or_equal(add(X0,a),add(a,a)) ),
inference(instantiation,[status(thm)],[c_385]) ).
tcf(c_566,plain,
! [X0: $i] :
( less_or_equal(add(X0,a),add(a,a))
| ~ defined(a)
| ~ less_or_equal(X0,a) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_567,plain,
( less_or_equal(add(additive_identity,a),u)
| ~ less_or_equal(add(a,a),u)
| ~ less_or_equal(add(additive_identity,a),add(a,a)) ),
inference(instantiation,[status(thm)],[c_565]) ).
tcf(c_568,plain,
( less_or_equal(add(additive_identity,a),add(a,a))
| ~ defined(a)
| ~ less_or_equal(additive_identity,a) ),
inference(instantiation,[status(thm)],[c_566]) ).
tcf(c_608,plain,
! [X0: $i] :
( equalish(a,X0)
| ~ equalish(X0,a) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_609,plain,
( equalish(a,additive_identity)
| ~ equalish(additive_identity,a) ),
inference(instantiation,[status(thm)],[c_608]) ).
tcf(c_1314,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,u)
| ~ less_or_equal(add(X0,a),u)
| ~ equalish(add(X0,a),X1) ),
inference(instantiation,[status(thm)],[c_254]) ).
tcf(c_1418,plain,
( equalish(additive_identity,a)
| ~ less_or_equal(a,additive_identity) ),
inference(superposition,[status(thm)],[c_83,c_94]) ).
tcf(c_1656,plain,
( less_or_equal(u,additive_identity)
| ~ defined(additive_identity)
| ~ defined(u) ),
inference(superposition,[status(thm)],[c_92,c_85]) ).
tcf(c_1664,plain,
less_or_equal(u,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_1656,c_88,c_82]) ).
tcf(c_1758,plain,
! [X0: $i] :
( less_or_equal(u,X0)
| ~ less_or_equal(additive_identity,X0) ),
inference(superposition,[status(thm)],[c_1664,c_93]) ).
tcf(c_1759,plain,
! [X0: $i] :
( less_or_equal(X0,additive_identity)
| ~ equalish(u,X0) ),
inference(superposition,[status(thm)],[c_1664,c_90]) ).
tcf(c_2227,plain,
less_or_equal(u,a),
inference(superposition,[status(thm)],[c_83,c_1758]) ).
tcf(c_2383,plain,
( less_or_equal(a,u)
| ~ equalish(add(additive_identity,a),a)
| ~ less_or_equal(add(additive_identity,a),u) ),
inference(instantiation,[status(thm)],[c_1314]) ).
tcf(c_3280,plain,
( equalish(u,a)
| ~ less_or_equal(a,u) ),
inference(superposition,[status(thm)],[c_2227,c_94]) ).
tcf(c_3494,plain,
equalish(u,a),
inference(global_subsumption_just,[status(thm)],[c_3280,c_82,c_81,c_83,c_84,c_258,c_298,c_320,c_469,c_567,c_568,c_2383,c_3280]) ).
tcf(c_3497,plain,
! [X0: $i] :
( equalish(u,X0)
| ~ equalish(a,X0) ),
inference(superposition,[status(thm)],[c_3494,c_100]) ).
tcf(c_3499,plain,
less_or_equal(a,additive_identity),
inference(superposition,[status(thm)],[c_3494,c_1759]) ).
tcf(c_3503,plain,
equalish(additive_identity,a),
inference(backward_subsumption_resolution,[status(thm)],[c_1418,c_3499]) ).
tcf(c_3504,plain,
( equalish(u,additive_identity)
| ~ equalish(a,additive_identity) ),
inference(instantiation,[status(thm)],[c_3497]) ).
tcf(c_3505,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3504,c_3503,c_609,c_260,c_258,c_85,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD059-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.36 % Computer : n026.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Fri Sep 25 11:01:30 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.40 Running first-order theorem proving
% 0.13/5.40 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
% 0.13/5.41
% 0.13/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.41
% 0.13/5.41 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 4.22/6.28 % SZS status Started for theBenchmark.p
% 4.22/6.28 % SZS status Unsatisfiable for theBenchmark.p
% 4.22/6.28
% 4.22/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.22/6.28
% 4.22/6.28 % ------ iProver source info
% 4.22/6.28
% 4.22/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.22/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.22/6.28 % git: non_committed_changes: false
% 4.22/6.28
% 4.22/6.28 % ------ Parsing...% successful
% 4.22/6.28
% 4.22/6.28
% 4.22/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.22/6.28
% 4.22/6.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.22/6.28
% 4.22/6.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.22/6.28 % ------ Proving...
% 4.22/6.28 % ------ Problem Properties
% 4.22/6.28
% 4.22/6.28 %
% 4.22/6.28 % clauses 25
% 4.22/6.28 % conjectures 3
% 4.22/6.28 % EPR 12
% 4.22/6.28 % Horn 24
% 4.22/6.28 % unary 6
% 4.22/6.28 % binary 3
% 4.22/6.28 % lits 64
% 4.22/6.28 % lits eq 0
% 4.22/6.28 % fd_pure 0
% 4.22/6.28 % fd_pseudo 0
% 4.22/6.28 % fd_cond 0
% 4.22/6.28 % fd_pseudo_cond 0
% 4.22/6.28 % AC symbols 0
% 4.22/6.28
% 4.22/6.28 % ------ Schedule dynamic 5 is on
% 4.22/6.28
% 4.22/6.28 % ------ no equalities: superposition off
% 4.22/6.28
% 4.22/6.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.22/6.28
% 4.22/6.28
% 4.22/6.28 % ------
% 4.22/6.28 % Current options:
% 4.22/6.28 % ------
% 4.22/6.28
% 4.22/6.28
% 4.22/6.28 %
% 4.22/6.28
% 4.22/6.28 % ------ Proving...
% 4.22/6.28 %
% 4.22/6.28
% 4.22/6.28 % SZS status Unsatisfiable for theBenchmark.p
% 4.22/6.28
% 4.22/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.22/6.28
% 4.22/6.28
%------------------------------------------------------------------------------