%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD069-1 : 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 : n004.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 01:15:53 PM UTC 2026
% Result : Unsatisfiable 4.13s 11.51s
% Output : CNFRefutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 13
% Syntax : Number of formulae : 40 ( 14 unt; 0 def)
% Number of atoms : 88 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 96 ( 48 ~; 48 |; 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 : 38 ( 0 sgn 38 !; 0 ?; 22 :)
% 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(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(f29,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_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,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_4) ).
fof(f32,negated_conjecture,
~ equalish(b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_not_equal_to_additive_identity_5) ).
fof(f33,negated_conjecture,
equalish(add(a,b),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_equals_additive_identity_6) ).
tcf(c_83,plain,
defined(b),
inference(cnf_transformation,[],[f29]) ).
tcf(c_84,negated_conjecture,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[],[f30]) ).
tcf(c_85,negated_conjecture,
less_or_equal(additive_identity,b),
inference(cnf_transformation,[],[f31]) ).
tcf(c_86,negated_conjecture,
~ equalish(b,additive_identity),
inference(cnf_transformation,[],[f32]) ).
tcf(c_87,negated_conjecture,
equalish(add(a,b),additive_identity),
inference(cnf_transformation,[],[f33]) ).
tcf(c_90,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f11]) ).
tcf(c_91,plain,
! [X0: $i] :
( equalish(add(additive_identity,X0),X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_92,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_93,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_94,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_95,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_96,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_113,plain,
( less_or_equal(additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_254,plain,
( equalish(b,additive_identity)
| ~ less_or_equal(additive_identity,b)
| ~ less_or_equal(b,additive_identity) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_261,plain,
! [X0: $i] :
( less_or_equal(b,additive_identity)
| ~ equalish(X0,b)
| ~ less_or_equal(X0,additive_identity) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_271,plain,
( equalish(add(additive_identity,b),b)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_302,plain,
( less_or_equal(b,additive_identity)
| ~ equalish(add(additive_identity,b),b)
| ~ less_or_equal(add(additive_identity,b),additive_identity) ),
inference(instantiation,[status(thm)],[c_261]) ).
tcf(c_337,plain,
! [X0: $i] :
( less_or_equal(add(additive_identity,b),additive_identity)
| ~ less_or_equal(X0,additive_identity)
| ~ less_or_equal(add(additive_identity,b),X0) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_384,plain,
! [X0: $i] :
( less_or_equal(add(additive_identity,b),add(X0,b))
| ~ defined(b)
| ~ less_or_equal(additive_identity,X0) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_496,plain,
! [X0: $i] :
( less_or_equal(add(additive_identity,b),additive_identity)
| ~ less_or_equal(add(X0,b),additive_identity)
| ~ less_or_equal(add(additive_identity,b),add(X0,b)) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_554,plain,
! [X0: $i,X1: $i] :
( less_or_equal(add(X1,b),additive_identity)
| ~ less_or_equal(X0,additive_identity)
| ~ equalish(X0,add(X1,b)) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_606,plain,
equalish(additive_identity,add(a,b)),
inference(superposition,[status(thm)],[c_87,c_98]) ).
tcf(c_1420,plain,
( less_or_equal(add(a,b),additive_identity)
| ~ less_or_equal(additive_identity,additive_identity)
| ~ equalish(additive_identity,add(a,b)) ),
inference(instantiation,[status(thm)],[c_554]) ).
tcf(c_2513,plain,
( less_or_equal(add(additive_identity,b),additive_identity)
| ~ less_or_equal(add(a,b),additive_identity)
| ~ less_or_equal(add(additive_identity,b),add(a,b)) ),
inference(instantiation,[status(thm)],[c_496]) ).
tcf(c_6036,plain,
( less_or_equal(add(additive_identity,b),add(a,b))
| ~ defined(b)
| ~ less_or_equal(additive_identity,a) ),
inference(instantiation,[status(thm)],[c_384]) ).
tcf(c_6037,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6036,c_2513,c_1420,c_606,c_302,c_271,c_254,c_113,c_86,c_84,c_85,c_83,c_90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD069-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/10.58 % Computer : n004.cluster.edu
% 0.09/10.58 % Model : x86_64 x86_64
% 0.09/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.58 % Memory : 8046.5625MB
% 0.09/10.58 % OS : Linux 6.8.0-71-generic
% 0.09/10.59 % CPULimit : 300
% 0.09/10.59 % WCLimit : 300
% 0.09/10.59 % DateTime : Fri Sep 25 11:03:19 UTC 2026
% 0.09/10.59 % CPUTime :
% 0.09/10.59 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/10.63 Running first-order theorem proving
% 0.14/10.63 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
% 0.14/10.64
% 0.14/10.64 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.64
% 0.14/10.64 % Detected problem language: tptp
% 0.14/10.65 % Proving...
% 4.13/11.51 % SZS status Started for theBenchmark.p
% 4.13/11.51 % SZS status Unsatisfiable for theBenchmark.p
% 4.13/11.51
% 4.13/11.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.13/11.51
% 4.13/11.51 % ------ iProver source info
% 4.13/11.51
% 4.13/11.51 % git: date: 2026-07-19 20:42:38 +0200
% 4.13/11.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.13/11.51 % git: non_committed_changes: false
% 4.13/11.51
% 4.13/11.51 % ------ Parsing...% successful
% 4.13/11.51
% 4.13/11.51
% 4.13/11.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.13/11.51
% 4.13/11.51 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.13/11.51
% 4.13/11.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.13/11.51 % ------ Proving...
% 4.13/11.51 % ------ Problem Properties
% 4.13/11.51
% 4.13/11.51 %
% 4.13/11.51 % clauses 26
% 4.13/11.51 % conjectures 4
% 4.13/11.51 % EPR 13
% 4.13/11.51 % Horn 25
% 4.13/11.51 % unary 7
% 4.13/11.51 % binary 3
% 4.13/11.51 % lits 65
% 4.13/11.51 % lits eq 0
% 4.13/11.51 % fd_pure 0
% 4.13/11.51 % fd_pseudo 0
% 4.13/11.51 % fd_cond 0
% 4.13/11.51 % fd_pseudo_cond 0
% 4.13/11.51 % AC symbols 0
% 4.13/11.51
% 4.13/11.51 % ------ Schedule dynamic 5 is on
% 4.13/11.51
% 4.13/11.51 % ------ no equalities: superposition off
% 4.13/11.51
% 4.13/11.51 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.13/11.51
% 4.13/11.51
% 4.13/11.51 % ------
% 4.13/11.51 % Current options:
% 4.13/11.51 % ------
% 4.13/11.51
% 4.13/11.51
% 4.13/11.51 %
% 4.13/11.51
% 4.13/11.51 % ------ Proving...
% 4.13/11.51 %
% 4.13/11.51
% 4.13/11.51 % SZS status Unsatisfiable for theBenchmark.p
% 4.13/11.51
% 4.13/11.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.13/11.51
% 4.13/11.51
%------------------------------------------------------------------------------