%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD062-3 : 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 : n003.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 01:15:51 PM UTC 2026
% Result : Unsatisfiable 22.45s 9.17s
% Output : CNFRefutation 22.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 74 ( 22 unt; 2 def)
% Number of atoms : 222 ( 2 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 198 ( 103 ~; 95 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 94 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
fof(f3,axiom,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
fof(f4,axiom,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
fof(f13,axiom,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| defined(add(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_addition) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
fof(f15,axiom,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_inverse) ).
fof(f19,axiom,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| sum(X0,X1,add(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',transitivity_of_order_relation) ).
fof(f24,axiom,
! [X2,X3,X0,X1,X4] :
( ~ sum(X3,X4,X1)
| ~ sum(X2,X4,X0)
| ~ less_or_equal(X2,X3)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
fof(f30,negated_conjecture,
~ less_or_equal(additive_inverse(b),additive_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_4) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_81,plain,
! [X0: $i] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_82,plain,
! [X0: $i] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( defined(add(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_92,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f14]) ).
tcf(c_93,plain,
! [X0: $i] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( sum(X0,X1,add(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_100,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,[],[f22]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( less_or_equal(X2,X4)
| ~ less_or_equal(X0,X3)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_105,plain,
defined(a),
inference(cnf_transformation,[],[f27]) ).
tcf(c_106,plain,
defined(b),
inference(cnf_transformation,[],[f28]) ).
tcf(c_107,negated_conjecture,
less_or_equal(a,b),
inference(cnf_transformation,[],[f29]) ).
tcf(c_108,negated_conjecture,
~ less_or_equal(additive_inverse(b),additive_inverse(a)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_281,definition,
iPr_def_10 = additive_inverse(b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_282,definition,
iPr_def_11 = additive_inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_283,negated_conjecture,
~ less_or_equal(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_108,c_282,c_281]) ).
tcf(c_284,negated_conjecture,
less_or_equal(a,b),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_720,plain,
( defined(iPr_def_10)
| ~ defined(b) ),
inference(superposition,[status(thm)],[c_281,c_93]) ).
tcf(c_721,plain,
( defined(iPr_def_11)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_282,c_93]) ).
tcf(c_722,plain,
defined(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_721,c_105]) ).
tcf(c_723,plain,
defined(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_720,c_106]) ).
tcf(c_736,plain,
( sum(iPr_def_10,b,additive_identity)
| ~ defined(b) ),
inference(superposition,[status(thm)],[c_281,c_82]) ).
tcf(c_737,plain,
( sum(iPr_def_11,a,additive_identity)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_282,c_82]) ).
tcf(c_738,plain,
sum(iPr_def_11,a,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_737,c_105]) ).
tcf(c_739,plain,
sum(iPr_def_10,b,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_736,c_106]) ).
tcf(c_746,plain,
sum(b,iPr_def_10,additive_identity),
inference(superposition,[status(thm)],[c_739,c_83]) ).
tcf(c_747,plain,
sum(a,iPr_def_11,additive_identity),
inference(superposition,[status(thm)],[c_738,c_83]) ).
tcf(c_1092,plain,
! [X0: $i,X1: $i] :
( sum(X1,X0,add(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_97,c_83]) ).
tcf(c_1145,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(iPr_def_10,iPr_def_11)
| ~ less_or_equal(X0,X2)
| ~ sum(X2,X1,iPr_def_11)
| ~ sum(X0,X1,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_1586,plain,
! [X0: $i,X1: $i] :
( less_or_equal(additive_identity,X1)
| ~ less_or_equal(a,X0)
| ~ sum(X0,iPr_def_11,X1) ),
inference(superposition,[status(thm)],[c_747,c_102]) ).
tcf(c_1649,plain,
! [X0: $i] :
( less_or_equal(iPr_def_10,iPr_def_11)
| ~ less_or_equal(additive_identity,X0)
| ~ sum(additive_identity,iPr_def_10,iPr_def_10)
| ~ sum(X0,iPr_def_10,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_1145]) ).
tcf(c_1650,plain,
( sum(additive_identity,iPr_def_10,iPr_def_10)
| ~ defined(iPr_def_10) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_1674,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(iPr_def_10,X1,X2)
| ~ sum(additive_identity,X0,X2)
| ~ sum(b,X0,X1) ),
inference(superposition,[status(thm)],[c_739,c_79]) ).
tcf(c_1678,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(b,X2,X1)
| ~ sum(iPr_def_10,X0,X2)
| ~ sum(additive_identity,X0,X1) ),
inference(superposition,[status(thm)],[c_746,c_79]) ).
tcf(c_3293,plain,
! [X0: $i] :
( sum(X0,iPr_def_10,iPr_def_11)
| ~ sum(iPr_def_10,X0,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_33482,plain,
! [X0: $i] :
( sum(X0,additive_identity,X0)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_81,c_83]) ).
tcf(c_33730,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(X1,X2)
| ~ defined(X1)
| ~ less_or_equal(additive_identity,X0)
| ~ sum(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_81,c_102]) ).
tcf(c_33805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sum(X0,X3,X2)
| ~ defined(X0)
| ~ sum(additive_identity,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_33482,c_79]) ).
tcf(c_42387,plain,
! [X0: $i,X1: $i] :
( sum(iPr_def_10,X1,X0)
| ~ defined(X0)
| ~ sum(b,X0,X1) ),
inference(superposition,[status(thm)],[c_81,c_1674]) ).
tcf(c_42476,plain,
! [X0: $i] :
( sum(iPr_def_10,add(X0,b),X0)
| ~ defined(b)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_1092,c_42387]) ).
tcf(c_42479,plain,
! [X0: $i] :
( sum(iPr_def_10,add(X0,b),X0)
| ~ defined(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42476,c_106]) ).
tcf(c_111149,plain,
! [X0: $i,X1: $i] :
( sum(b,X1,add(additive_identity,X0))
| ~ defined(additive_identity)
| ~ defined(X0)
| ~ sum(iPr_def_10,X0,X1) ),
inference(superposition,[status(thm)],[c_97,c_1678]) ).
tcf(c_111188,plain,
! [X0: $i,X1: $i] :
( sum(b,X1,add(additive_identity,X0))
| ~ defined(X0)
| ~ sum(iPr_def_10,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_111149,c_92]) ).
tcf(c_135545,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,X1,X0)
| ~ defined(additive_identity)
| ~ defined(X0)
| ~ sum(additive_identity,X0,X1) ),
inference(superposition,[status(thm)],[c_81,c_33805]) ).
tcf(c_135599,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,X1,X0)
| ~ defined(X0)
| ~ sum(additive_identity,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_135545,c_92]) ).
tcf(c_152737,plain,
! [X0: $i] :
( less_or_equal(additive_identity,add(additive_identity,X0))
| ~ defined(X0)
| ~ less_or_equal(a,b)
| ~ sum(iPr_def_10,X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_111188,c_1586]) ).
tcf(c_152762,plain,
! [X0: $i] :
( less_or_equal(additive_identity,add(additive_identity,X0))
| ~ defined(X0)
| ~ sum(iPr_def_10,X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_152737,c_284]) ).
tcf(c_153366,plain,
! [X0: $i,X1: $i] :
( less_or_equal(additive_identity,X1)
| ~ defined(X0)
| ~ sum(iPr_def_10,X0,iPr_def_11)
| ~ less_or_equal(add(additive_identity,X0),X1) ),
inference(superposition,[status(thm)],[c_152762,c_100]) ).
tcf(c_156008,plain,
! [X0: $i] :
( sum(additive_identity,add(additive_identity,X0),X0)
| ~ defined(additive_identity)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_97,c_135599]) ).
tcf(c_156025,plain,
! [X0: $i] :
( sum(additive_identity,add(additive_identity,X0),X0)
| ~ defined(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_156008,c_92]) ).
tcf(c_156785,plain,
! [X0: $i] :
( sum(add(additive_identity,X0),additive_identity,X0)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_156025,c_83]) ).
tcf(c_158254,plain,
! [X0: $i] :
( less_or_equal(additive_identity,X0)
| ~ defined(additive_identity)
| ~ defined(X0)
| ~ less_or_equal(additive_identity,add(additive_identity,X0)) ),
inference(superposition,[status(thm)],[c_156785,c_33730]) ).
tcf(c_158278,plain,
! [X0: $i] :
( less_or_equal(additive_identity,X0)
| ~ defined(X0)
| ~ less_or_equal(additive_identity,add(additive_identity,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_158254,c_92]) ).
tcf(c_158400,plain,
! [X0: $i] :
( ~ sum(iPr_def_10,X0,iPr_def_11)
| ~ defined(X0) ),
inference(global_subsumption_just,[status(thm)],[c_153366,c_283,c_723,c_1649,c_1650,c_3293,c_152762,c_158278]) ).
tcf(c_158401,plain,
! [X0: $i] :
( ~ defined(X0)
| ~ sum(iPr_def_10,X0,iPr_def_11) ),
inference(renaming,[status(thm)],[c_158400]) ).
tcf(c_158409,plain,
( ~ defined(iPr_def_11)
| ~ defined(add(iPr_def_11,b)) ),
inference(superposition,[status(thm)],[c_42479,c_158401]) ).
tcf(c_158410,plain,
~ defined(add(iPr_def_11,b)),
inference(forward_subsumption_resolution,[status(thm)],[c_158409,c_722]) ).
tcf(c_159075,plain,
( ~ defined(iPr_def_11)
| ~ defined(b) ),
inference(superposition,[status(thm)],[c_91,c_158410]) ).
tcf(c_159076,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_159075,c_722,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD062-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.38 % Computer : n003.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Fri Sep 25 11:02:15 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 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...
% 22.45/9.17 % SZS status Started for theBenchmark.p
% 22.45/9.17 % SZS status Unsatisfiable for theBenchmark.p
% 22.45/9.17
% 22.45/9.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.45/9.17
% 22.45/9.17 % ------ iProver source info
% 22.45/9.17
% 22.45/9.17 % git: date: 2026-07-19 20:42:38 +0200
% 22.45/9.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.45/9.17 % git: non_committed_changes: false
% 22.45/9.17
% 22.45/9.17 % ------ Parsing...% successful
% 22.45/9.17
% 22.45/9.17
% 22.45/9.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.45/9.17
% 22.45/9.17 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 22.45/9.17
% 22.45/9.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 22.45/9.17
% 22.45/9.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 22.45/9.17 % ------ Proving...
% 22.45/9.17 % ------ Problem Properties
% 22.45/9.17
% 22.45/9.17 %
% 22.45/9.17 % clauses 32
% 22.45/9.17 % conjectures 2
% 22.45/9.17 % EPR 22
% 22.45/9.17 % Horn 29
% 22.45/9.17 % unary 9
% 22.45/9.17 % binary 6
% 22.45/9.17 % lits 83
% 22.45/9.17 % lits eq 2
% 22.45/9.17 % fd_pure 0
% 22.45/9.17 % fd_pseudo 0
% 22.45/9.17 % fd_cond 0
% 22.45/9.17 % fd_pseudo_cond 0
% 22.45/9.17 % AC symbols 0
% 22.45/9.17
% 22.45/9.17 % ------ Schedule dynamic 5 is on
% 22.45/9.17
% 22.45/9.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 22.45/9.17
% 22.45/9.17
% 22.45/9.17 % ------
% 22.45/9.17 % Current options:
% 22.45/9.17 % ------
% 22.45/9.17
% 22.45/9.17
% 22.45/9.17 %
% 22.45/9.17
% 22.45/9.17 % ------ Proving...
% 22.45/9.17 %
% 22.45/9.17
% 22.45/9.17 % SZS status Unsatisfiable for theBenchmark.p
% 22.45/9.17
% 22.45/9.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.45/9.17
% 22.45/9.17
%------------------------------------------------------------------------------