%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD065-1 : 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 : n019.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 01:15:52 PM UTC 2026
% Result : Unsatisfiable 11.82s 2.71s
% Output : CNFRefutation 11.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 19 unt; 1 def)
% Number of atoms : 142 ( 1 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 134 ( 67 ~; 67 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 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; 2 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?; 32 :)
% 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(f3,axiom,
! [X0] :
( ~ defined(X0)
| equalish(add(X0,additive_inverse(X0)),additive_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_addition) ).
fof(f4,axiom,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| equalish(add(X0,X1),add(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_identity) ).
fof(f12,axiom,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_inverse) ).
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(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,negated_conjecture,
less_or_equal(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_2) ).
fof(f30,negated_conjecture,
~ less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_3) ).
tcf(c_80,plain,
! [X0: $i] :
( equalish(add(additive_identity,X0),X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_81,plain,
! [X0: $i] :
( equalish(add(X0,additive_inverse(X0)),additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( equalish(add(X0,X1),add(X1,X0))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_89,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f11]) ).
tcf(c_90,plain,
! [X0: $i] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
inference(cnf_transformation,[],[f12]) ).
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_96,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_97,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_100,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_104,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_106,plain,
defined(a),
inference(cnf_transformation,[],[f28]) ).
tcf(c_107,negated_conjecture,
less_or_equal(additive_inverse(a),additive_identity),
inference(cnf_transformation,[],[f29]) ).
tcf(c_108,negated_conjecture,
~ less_or_equal(additive_identity,a),
inference(cnf_transformation,[],[f30]) ).
tcf(c_279,definition,
iPr_def_10 = additive_inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_280,negated_conjecture,
~ less_or_equal(additive_identity,a),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_281,negated_conjecture,
less_or_equal(iPr_def_10,additive_identity),
inference(demodulation,[status(thm)],[c_107,c_279]) ).
tcf(c_714,plain,
! [X0: $i] :
( equalish(X0,add(additive_identity,X0))
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_80,c_100]) ).
tcf(c_892,plain,
( less_or_equal(a,additive_identity)
| ~ defined(additive_identity)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_96,c_280]) ).
tcf(c_900,plain,
less_or_equal(a,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_892,c_89,c_106]) ).
tcf(c_912,plain,
! [X0: $i] :
( less_or_equal(X0,additive_identity)
| ~ equalish(a,X0) ),
inference(superposition,[status(thm)],[c_900,c_104]) ).
tcf(c_983,plain,
! [X0: $i] :
( less_or_equal(additive_identity,a)
| ~ equalish(X0,additive_identity)
| ~ less_or_equal(X0,a) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_1001,plain,
( less_or_equal(add(additive_identity,a),additive_identity)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_714,c_912]) ).
tcf(c_1004,plain,
less_or_equal(add(additive_identity,a),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_1001,c_106]) ).
tcf(c_1059,plain,
! [X0: $i] :
( less_or_equal(a,X0)
| less_or_equal(X0,a)
| ~ defined(a)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_1342,plain,
( less_or_equal(a,a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_1059]) ).
tcf(c_1344,plain,
( less_or_equal(additive_identity,a)
| ~ equalish(a,additive_identity)
| ~ less_or_equal(a,a) ),
inference(instantiation,[status(thm)],[c_983]) ).
tcf(c_1411,plain,
( defined(iPr_def_10)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_279,c_90]) ).
tcf(c_1412,plain,
defined(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1411,c_106]) ).
tcf(c_2079,plain,
( equalish(a,additive_identity)
| ~ equalish(additive_identity,a) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_3798,plain,
! [X0: $i] :
( equalish(additive_identity,a)
| ~ equalish(additive_identity,X0)
| ~ equalish(X0,a) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_9032,plain,
( equalish(additive_identity,a)
| ~ equalish(additive_identity,add(additive_identity,a))
| ~ equalish(add(additive_identity,a),a) ),
inference(instantiation,[status(thm)],[c_3798]) ).
tcf(c_9033,plain,
( equalish(add(additive_identity,a),a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_18415,plain,
( equalish(add(a,iPr_def_10),additive_identity)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_279,c_81]) ).
tcf(c_18417,plain,
equalish(add(a,iPr_def_10),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_18415,c_106]) ).
tcf(c_18420,plain,
equalish(additive_identity,add(a,iPr_def_10)),
inference(superposition,[status(thm)],[c_18417,c_100]) ).
tcf(c_18518,plain,
! [X0: $i] :
( equalish(additive_identity,X0)
| ~ equalish(add(a,iPr_def_10),X0) ),
inference(superposition,[status(thm)],[c_18420,c_101]) ).
tcf(c_18805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less_or_equal(X2,add(X3,X1))
| ~ defined(X1)
| ~ less_or_equal(X0,X3)
| ~ equalish(add(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_97,c_104]) ).
tcf(c_28411,plain,
( equalish(additive_identity,add(additive_identity,a))
| ~ less_or_equal(additive_identity,add(additive_identity,a))
| ~ less_or_equal(add(additive_identity,a),additive_identity) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_29431,plain,
( equalish(additive_identity,add(iPr_def_10,a))
| ~ defined(iPr_def_10)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_82,c_18518]) ).
tcf(c_29445,plain,
equalish(additive_identity,add(iPr_def_10,a)),
inference(forward_subsumption_resolution,[status(thm)],[c_29431,c_1412,c_106]) ).
tcf(c_33498,plain,
equalish(add(iPr_def_10,a),additive_identity),
inference(superposition,[status(thm)],[c_29445,c_100]) ).
tcf(c_39290,plain,
! [X0: $i] :
( less_or_equal(additive_identity,add(X0,a))
| ~ defined(a)
| ~ less_or_equal(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_33498,c_18805]) ).
tcf(c_39296,plain,
! [X0: $i] :
( less_or_equal(additive_identity,add(X0,a))
| ~ less_or_equal(iPr_def_10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39290,c_106]) ).
tcf(c_39380,plain,
( less_or_equal(additive_identity,add(additive_identity,a))
| ~ less_or_equal(iPr_def_10,additive_identity) ),
inference(instantiation,[status(thm)],[c_39296]) ).
tcf(c_39381,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_39380,c_28411,c_9033,c_9032,c_2079,c_1344,c_1342,c_1004,c_281,c_108,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD065-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 11:01:48 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 11.82/2.71 % SZS status Started for theBenchmark.p
% 11.82/2.71 % SZS status Unsatisfiable for theBenchmark.p
% 11.82/2.71
% 11.82/2.71 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 11.82/2.71
% 11.82/2.71 % ------ iProver source info
% 11.82/2.71
% 11.82/2.71 % git: date: 2026-07-19 20:42:38 +0200
% 11.82/2.71 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 11.82/2.71 % git: non_committed_changes: false
% 11.82/2.71
% 11.82/2.71 % ------ Parsing...% successful
% 11.82/2.71
% 11.82/2.71
% 11.82/2.71 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 11.82/2.71
% 11.82/2.71 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 11.82/2.71
% 11.82/2.71 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 11.82/2.71
% 11.82/2.71 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 11.82/2.71 % ------ Proving...
% 11.82/2.71 % ------ Problem Properties
% 11.82/2.71
% 11.82/2.71 %
% 11.82/2.71 % clauses 31
% 11.82/2.71 % conjectures 2
% 11.82/2.71 % EPR 13
% 11.82/2.71 % Horn 28
% 11.82/2.71 % unary 7
% 11.82/2.71 % binary 6
% 11.82/2.71 % lits 77
% 11.82/2.71 % lits eq 1
% 11.82/2.71 % fd_pure 0
% 11.82/2.71 % fd_pseudo 0
% 11.82/2.71 % fd_cond 0
% 11.82/2.71 % fd_pseudo_cond 0
% 11.82/2.71 % AC symbols 0
% 11.82/2.71
% 11.82/2.71 % ------ Schedule dynamic 5 is on
% 11.82/2.71
% 11.82/2.71 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 11.82/2.71
% 11.82/2.71
% 11.82/2.71 % ------
% 11.82/2.71 % Current options:
% 11.82/2.71 % ------
% 11.82/2.71
% 11.82/2.71
% 11.82/2.71 %
% 11.82/2.71
% 11.82/2.71 % ------ Proving...
% 11.82/2.71 %
% 11.82/2.71
% 11.82/2.71 % SZS status Unsatisfiable for theBenchmark.p
% 11.82/2.71
% 11.82/2.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 11.82/2.71
% 11.82/2.71
%------------------------------------------------------------------------------