%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD070-2 : 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 : n015.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 01:15:54 PM UTC 2026
% Result : Unsatisfiable 0.88s 6.21s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 83 ( 25 unt; 0 def)
% Number of atoms : 184 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 199 ( 98 ~; 101 |; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 67 !; 0 ?; 49 :)
% 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(f10,axiom,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| defined(add(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_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(f28,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f29,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f30,axiom,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
fof(f31,negated_conjecture,
equalish(add(a,b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_equals_c_4) ).
fof(f32,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_5) ).
fof(f33,negated_conjecture,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_6) ).
fof(f34,negated_conjecture,
~ less_or_equal(additive_identity,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_7) ).
tcf(c_84,plain,
! [X0: $i] :
( equalish(add(additive_identity,X0),X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( defined(add(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_93,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f11]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_99,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_100,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_101,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_104,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_108,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_110,plain,
defined(a),
inference(cnf_transformation,[],[f28]) ).
tcf(c_111,plain,
defined(b),
inference(cnf_transformation,[],[f29]) ).
tcf(c_112,plain,
defined(c),
inference(cnf_transformation,[],[f30]) ).
tcf(c_113,negated_conjecture,
equalish(add(a,b),c),
inference(cnf_transformation,[],[f31]) ).
tcf(c_114,negated_conjecture,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[],[f32]) ).
tcf(c_115,negated_conjecture,
less_or_equal(additive_identity,b),
inference(cnf_transformation,[],[f33]) ).
tcf(c_116,negated_conjecture,
~ less_or_equal(additive_identity,c),
inference(cnf_transformation,[],[f34]) ).
tcf(c_295,plain,
( less_or_equal(additive_identity,c)
| less_or_equal(c,additive_identity)
| ~ defined(additive_identity)
| ~ defined(c) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_296,plain,
! [X0: $i] :
( less_or_equal(additive_identity,c)
| ~ less_or_equal(additive_identity,X0)
| ~ less_or_equal(X0,c) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_298,plain,
! [X0: $i] :
( less_or_equal(c,X0)
| less_or_equal(X0,c)
| ~ defined(c)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,c)
| ~ less_or_equal(X0,c)
| ~ equalish(X0,X1) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_310,plain,
( less_or_equal(c,c)
| ~ defined(c) ),
inference(instantiation,[status(thm)],[c_298]) ).
tcf(c_312,plain,
! [X0: $i] :
( less_or_equal(X0,c)
| ~ less_or_equal(c,c)
| ~ equalish(c,X0) ),
inference(instantiation,[status(thm)],[c_300]) ).
tcf(c_324,plain,
! [X0: $i] :
( equalish(c,X0)
| ~ equalish(X0,c) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_334,plain,
( equalish(c,add(a,b))
| ~ equalish(add(a,b),c) ),
inference(instantiation,[status(thm)],[c_324]) ).
tcf(c_353,plain,
( less_or_equal(add(a,b),c)
| ~ less_or_equal(c,c)
| ~ equalish(c,add(a,b)) ),
inference(instantiation,[status(thm)],[c_312]) ).
tcf(c_416,plain,
( less_or_equal(additive_identity,c)
| ~ less_or_equal(additive_identity,add(a,b))
| ~ less_or_equal(add(a,b),c) ),
inference(instantiation,[status(thm)],[c_296]) ).
tcf(c_507,plain,
( defined(add(a,b))
| ~ defined(b)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_511,plain,
! [X0: $i] :
( less_or_equal(additive_identity,add(a,b))
| ~ less_or_equal(additive_identity,X0)
| ~ less_or_equal(X0,add(a,b)) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_520,plain,
! [X0: $i] :
( less_or_equal(c,add(a,b))
| ~ equalish(X0,c)
| ~ less_or_equal(X0,add(a,b)) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_559,plain,
! [X0: $i] :
( less_or_equal(X0,add(a,b))
| less_or_equal(add(a,b),X0)
| ~ defined(X0)
| ~ defined(add(a,b)) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_692,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,add(a,b))
| ~ equalish(X0,X1)
| ~ less_or_equal(X0,add(a,b)) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_750,plain,
! [X0: $i] :
( less_or_equal(additive_identity,X0)
| ~ less_or_equal(b,X0) ),
inference(superposition,[status(thm)],[c_115,c_99]) ).
tcf(c_954,plain,
( less_or_equal(add(a,b),add(a,b))
| ~ defined(add(a,b)) ),
inference(instantiation,[status(thm)],[c_559]) ).
tcf(c_1520,plain,
( less_or_equal(c,add(a,b))
| ~ equalish(add(a,b),c)
| ~ less_or_equal(add(a,b),add(a,b)) ),
inference(instantiation,[status(thm)],[c_520]) ).
tcf(c_1707,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,add(a,b))
| ~ equalish(add(X0,b),X1)
| ~ less_or_equal(add(X0,b),add(a,b)) ),
inference(instantiation,[status(thm)],[c_692]) ).
tcf(c_1784,plain,
! [X0: $i] :
( less_or_equal(add(X0,b),add(a,b))
| ~ defined(b)
| ~ less_or_equal(X0,a) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_1785,plain,
( less_or_equal(add(additive_identity,b),add(a,b))
| ~ defined(b)
| ~ less_or_equal(additive_identity,a) ),
inference(instantiation,[status(thm)],[c_1784]) ).
tcf(c_2272,plain,
! [X0: $i] :
( less_or_equal(c,X0)
| ~ less_or_equal(add(a,b),X0) ),
inference(superposition,[status(thm)],[c_113,c_108]) ).
tcf(c_2575,plain,
( less_or_equal(c,additive_identity)
| ~ defined(additive_identity)
| ~ defined(c) ),
inference(superposition,[status(thm)],[c_100,c_116]) ).
tcf(c_2578,plain,
! [X0: $i] :
( less_or_equal(c,X0)
| less_or_equal(X0,add(a,b))
| ~ defined(X0)
| ~ defined(add(a,b)) ),
inference(superposition,[status(thm)],[c_100,c_2272]) ).
tcf(c_2979,plain,
less_or_equal(c,additive_identity),
inference(global_subsumption_just,[status(thm)],[c_2575,c_112,c_93,c_116,c_295]) ).
tcf(c_2981,plain,
! [X0: $i] :
( less_or_equal(c,X0)
| ~ less_or_equal(additive_identity,X0) ),
inference(superposition,[status(thm)],[c_2979,c_99]) ).
tcf(c_3036,plain,
less_or_equal(c,b),
inference(superposition,[status(thm)],[c_115,c_2981]) ).
tcf(c_4590,plain,
equalish(c,add(a,b)),
inference(superposition,[status(thm)],[c_113,c_104]) ).
tcf(c_4681,plain,
! [X0: $i] :
( less_or_equal(add(a,b),X0)
| ~ less_or_equal(c,X0) ),
inference(superposition,[status(thm)],[c_4590,c_108]) ).
tcf(c_4726,plain,
! [X0: $i,X1: $i] :
( less_or_equal(add(a,b),X1)
| ~ less_or_equal(c,X0)
| ~ less_or_equal(X0,X1) ),
inference(superposition,[status(thm)],[c_4681,c_99]) ).
tcf(c_4972,plain,
( less_or_equal(add(a,b),b)
| ~ less_or_equal(c,c) ),
inference(superposition,[status(thm)],[c_3036,c_4726]) ).
tcf(c_6213,plain,
( less_or_equal(b,add(a,b))
| ~ equalish(add(additive_identity,b),b)
| ~ less_or_equal(add(additive_identity,b),add(a,b)) ),
inference(instantiation,[status(thm)],[c_1707]) ).
tcf(c_10179,plain,
equalish(c,add(a,b)),
inference(superposition,[status(thm)],[c_113,c_104]) ).
tcf(c_10285,plain,
! [X0: $i] :
( less_or_equal(c,X0)
| ~ less_or_equal(add(a,b),X0) ),
inference(superposition,[status(thm)],[c_113,c_108]) ).
tcf(c_10292,plain,
! [X0: $i] :
( less_or_equal(add(a,b),X0)
| ~ less_or_equal(c,X0) ),
inference(superposition,[status(thm)],[c_10179,c_108]) ).
tcf(c_10314,plain,
! [X0: $i,X1: $i] :
( less_or_equal(add(a,b),X1)
| ~ less_or_equal(c,X0)
| ~ less_or_equal(X0,X1) ),
inference(superposition,[status(thm)],[c_10292,c_99]) ).
tcf(c_10353,plain,
! [X0: $i] :
( less_or_equal(c,X0)
| less_or_equal(X0,add(a,b))
| ~ defined(X0)
| ~ defined(add(a,b)) ),
inference(superposition,[status(thm)],[c_100,c_10285]) ).
tcf(c_10418,plain,
! [X0: $i] :
( less_or_equal(c,X0)
| less_or_equal(X0,add(a,b))
| ~ defined(X0) ),
inference(global_subsumption_just,[status(thm)],[c_10353,c_111,c_110,c_507,c_2578]) ).
tcf(c_10423,plain,
( less_or_equal(c,add(a,b))
| ~ defined(add(a,b)) ),
inference(superposition,[status(thm)],[c_10418,c_10285]) ).
tcf(c_10428,plain,
less_or_equal(c,add(a,b)),
inference(global_subsumption_just,[status(thm)],[c_10423,c_111,c_110,c_113,c_507,c_954,c_1520]) ).
tcf(c_10596,plain,
( less_or_equal(add(a,b),b)
| ~ less_or_equal(c,additive_identity) ),
inference(superposition,[status(thm)],[c_115,c_10314]) ).
tcf(c_10607,plain,
( less_or_equal(add(a,b),add(a,b))
| ~ less_or_equal(c,c) ),
inference(superposition,[status(thm)],[c_10428,c_10314]) ).
tcf(c_10628,plain,
less_or_equal(add(a,b),b),
inference(global_subsumption_just,[status(thm)],[c_10596,c_112,c_310,c_4972]) ).
tcf(c_10631,plain,
! [X0: $i] :
( less_or_equal(add(a,b),X0)
| ~ less_or_equal(b,X0) ),
inference(superposition,[status(thm)],[c_10628,c_99]) ).
tcf(c_10650,plain,
! [X0: $i] :
( equalish(add(a,b),X0)
| ~ less_or_equal(b,X0)
| ~ less_or_equal(X0,add(a,b)) ),
inference(superposition,[status(thm)],[c_10631,c_98]) ).
tcf(c_10782,plain,
less_or_equal(add(a,b),add(a,b)),
inference(global_subsumption_just,[status(thm)],[c_10607,c_111,c_110,c_507,c_954]) ).
tcf(c_12398,plain,
! [X0: $i] :
( ~ less_or_equal(X0,add(a,b))
| ~ less_or_equal(b,X0) ),
inference(global_subsumption_just,[status(thm)],[c_10650,c_112,c_116,c_113,c_310,c_334,c_353,c_416,c_511,c_750]) ).
tcf(c_12399,plain,
! [X0: $i] :
( ~ less_or_equal(b,X0)
| ~ less_or_equal(X0,add(a,b)) ),
inference(renaming,[status(thm)],[c_12398]) ).
tcf(c_12423,plain,
~ less_or_equal(b,add(a,b)),
inference(superposition,[status(thm)],[c_10782,c_12399]) ).
tcf(c_13058,plain,
( equalish(add(additive_identity,b),b)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_13059,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_13058,c_12423,c_6213,c_1785,c_114,c_111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD070-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/5.38 % Computer : n015.cluster.edu
% 0.08/5.38 % Model : x86_64 x86_64
% 0.08/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.38 % Memory : 8046.5625MB
% 0.08/5.38 % OS : Linux 6.8.0-71-generic
% 0.08/5.38 % CPULimit : 300
% 0.08/5.38 % WCLimit : 300
% 0.08/5.38 % DateTime : Fri Sep 25 11:07:17 UTC 2026
% 0.08/5.38 % CPUTime :
% 0.08/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 0.88/6.21 % SZS status Started for theBenchmark.p
% 0.88/6.21 % SZS status Unsatisfiable for theBenchmark.p
% 0.88/6.21
% 0.88/6.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.88/6.21
% 0.88/6.21 % ------ iProver source info
% 0.88/6.21
% 0.88/6.21 % git: date: 2026-07-19 20:42:38 +0200
% 0.88/6.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.88/6.21 % git: non_committed_changes: false
% 0.88/6.21
% 0.88/6.21 % ------ Parsing...% successful
% 0.88/6.21
% 0.88/6.21
% 0.88/6.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.88/6.21
% 0.88/6.21 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.88/6.21
% 0.88/6.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.88/6.21 % ------ Proving...
% 0.88/6.21 % ------ Problem Properties
% 0.88/6.21
% 0.88/6.21 %
% 0.88/6.21 % clauses 34
% 0.88/6.21 % conjectures 4
% 0.88/6.21 % EPR 16
% 0.88/6.21 % Horn 31
% 0.88/6.21 % unary 10
% 0.88/6.21 % binary 6
% 0.88/6.21 % lits 80
% 0.88/6.21 % lits eq 0
% 0.88/6.21 % fd_pure 0
% 0.88/6.21 % fd_pseudo 0
% 0.88/6.21 % fd_cond 0
% 0.88/6.21 % fd_pseudo_cond 0
% 0.88/6.21 % AC symbols 0
% 0.88/6.21
% 0.88/6.21 % ------ Input Options Time Limit: Unbounded
% 0.88/6.21
% 0.88/6.21
% 0.88/6.21 % ------
% 0.88/6.21 % Current options:
% 0.88/6.21 % ------
% 0.88/6.21
% 0.88/6.21
% 0.88/6.21 %
% 0.88/6.21
% 0.88/6.21 % ------ Proving...
% 0.88/6.21 %
% 0.88/6.21
% 0.88/6.21 % SZS status Unsatisfiable for theBenchmark.p
% 0.88/6.21
% 0.88/6.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.88/6.21
% 0.88/6.21
%------------------------------------------------------------------------------