%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD008-3 : 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 : n014.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 01:15:35 PM UTC 2026
% Result : Unsatisfiable 7.68s 1.75s
% Output : CNFRefutation 7.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 79 ( 33 unt; 5 def)
% Number of atoms : 248 ( 5 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 153 ( 79 ~; 74 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 9 ( 7 usr; 6 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 76 !; 0 ?; 54 :)
% 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/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
fof(f3,axiom,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_addition) ).
fof(f13,axiom,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| defined(add(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_addition) ).
fof(f15,axiom,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_addition) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f28,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
fof(f29,negated_conjecture,
~ sum(additive_identity,additive_inverse(add(a,b)),add(additive_inverse(a),additive_inverse(b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
tcf(c_78,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_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X2,X5,X4)
| ~ sum(X1,X5,X3)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_80,plain,
! [X0: $i] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_81,plain,
! [X0: $i] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] :
( defined(add(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_92,plain,
! [X0: $i] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( sum(X0,X1,add(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_104,plain,
defined(a),
inference(cnf_transformation,[],[f27]) ).
tcf(c_105,plain,
defined(b),
inference(cnf_transformation,[],[f28]) ).
tcf(c_106,negated_conjecture,
~ sum(additive_identity,additive_inverse(add(a,b)),add(additive_inverse(a),additive_inverse(b))),
inference(cnf_transformation,[],[f29]) ).
tcf(c_277,definition,
iPr_def_10 = add(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_278,definition,
iPr_def_11 = additive_inverse(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_279,definition,
iPr_def_12 = additive_inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_280,definition,
iPr_def_13 = additive_inverse(b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_281,definition,
iPr_def_14 = add(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_282,negated_conjecture,
~ sum(additive_identity,iPr_def_11,iPr_def_14),
inference(demodulation,[status(thm)],[c_106,c_280,c_279,c_281,c_277,c_278]) ).
tcf(c_736,plain,
( defined(iPr_def_12)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_279,c_92]) ).
tcf(c_737,plain,
( defined(iPr_def_13)
| ~ defined(b) ),
inference(superposition,[status(thm)],[c_280,c_92]) ).
tcf(c_738,plain,
( defined(iPr_def_11)
| ~ defined(iPr_def_10) ),
inference(superposition,[status(thm)],[c_278,c_92]) ).
tcf(c_741,plain,
defined(iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_737,c_105]) ).
tcf(c_742,plain,
defined(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_736,c_104]) ).
tcf(c_759,plain,
( sum(iPr_def_12,a,additive_identity)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_279,c_81]) ).
tcf(c_760,plain,
( sum(iPr_def_13,b,additive_identity)
| ~ defined(b) ),
inference(superposition,[status(thm)],[c_280,c_81]) ).
tcf(c_761,plain,
( sum(iPr_def_11,iPr_def_10,additive_identity)
| ~ defined(iPr_def_10) ),
inference(superposition,[status(thm)],[c_278,c_81]) ).
tcf(c_764,plain,
sum(iPr_def_13,b,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_760,c_105]) ).
tcf(c_765,plain,
sum(iPr_def_12,a,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_759,c_104]) ).
tcf(c_774,plain,
! [X0: $i] :
( sum(X0,additive_identity,X0)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_80,c_82]) ).
tcf(c_776,plain,
sum(a,iPr_def_12,additive_identity),
inference(superposition,[status(thm)],[c_765,c_82]) ).
tcf(c_799,plain,
( defined(iPr_def_10)
| ~ defined(b)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_277,c_90]) ).
tcf(c_800,plain,
( defined(iPr_def_14)
| ~ defined(iPr_def_13)
| ~ defined(iPr_def_12) ),
inference(superposition,[status(thm)],[c_281,c_90]) ).
tcf(c_801,plain,
defined(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_800,c_741,c_742]) ).
tcf(c_802,plain,
defined(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_799,c_105,c_104]) ).
tcf(c_803,plain,
sum(iPr_def_11,iPr_def_10,additive_identity),
inference(backward_subsumption_resolution,[status(thm)],[c_761,c_802]) ).
tcf(c_804,plain,
defined(iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_738,c_802]) ).
tcf(c_835,plain,
sum(iPr_def_10,iPr_def_11,additive_identity),
inference(superposition,[status(thm)],[c_803,c_82]) ).
tcf(c_875,plain,
( sum(a,b,iPr_def_10)
| ~ defined(b)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_277,c_96]) ).
tcf(c_876,plain,
( sum(iPr_def_12,iPr_def_13,iPr_def_14)
| ~ defined(iPr_def_13)
| ~ defined(iPr_def_12) ),
inference(superposition,[status(thm)],[c_281,c_96]) ).
tcf(c_878,plain,
sum(iPr_def_12,iPr_def_13,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_876,c_741,c_742]) ).
tcf(c_879,plain,
sum(a,b,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_875,c_105,c_104]) ).
tcf(c_883,plain,
sum(iPr_def_13,iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_878,c_82]) ).
tcf(c_884,plain,
sum(b,a,iPr_def_10),
inference(superposition,[status(thm)],[c_879,c_82]) ).
tcf(c_1156,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(additive_identity,iPr_def_11,iPr_def_14)
| ~ sum(X1,iPr_def_11,X2)
| ~ sum(X0,X2,iPr_def_14)
| ~ sum(X0,X1,additive_identity) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_1247,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(iPr_def_12,X1,X2)
| ~ sum(additive_identity,X0,X2)
| ~ sum(a,X0,X1) ),
inference(superposition,[status(thm)],[c_765,c_78]) ).
tcf(c_1256,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(a,X1,X2)
| ~ sum(iPr_def_10,X0,X2)
| ~ sum(b,X0,X1) ),
inference(superposition,[status(thm)],[c_879,c_78]) ).
tcf(c_1260,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(b,X1,X2)
| ~ sum(iPr_def_10,X0,X2)
| ~ sum(a,X0,X1) ),
inference(superposition,[status(thm)],[c_884,c_78]) ).
tcf(c_1384,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,X1,additive_identity)
| ~ sum(iPr_def_13,X0,X2)
| ~ sum(X0,X1,b) ),
inference(superposition,[status(thm)],[c_764,c_79]) ).
tcf(c_1390,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,X1,additive_identity)
| ~ sum(iPr_def_10,X0,X2)
| ~ sum(X0,X1,iPr_def_11) ),
inference(superposition,[status(thm)],[c_835,c_79]) ).
tcf(c_1499,plain,
( sum(additive_identity,iPr_def_14,iPr_def_14)
| ~ defined(iPr_def_14) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_1500,plain,
! [X0: $i,X1: $i] :
( sum(X1,X0,iPr_def_14)
| ~ sum(X0,X1,iPr_def_14) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_1835,plain,
! [X0: $i,X1: $i] :
( sum(iPr_def_12,X1,X0)
| ~ defined(X0)
| ~ sum(a,X0,X1) ),
inference(superposition,[status(thm)],[c_80,c_1247]) ).
tcf(c_3138,plain,
( sum(iPr_def_14,additive_identity,iPr_def_14)
| ~ sum(additive_identity,iPr_def_14,iPr_def_14) ),
inference(instantiation,[status(thm)],[c_1500]) ).
tcf(c_7177,plain,
! [X0: $i] :
( sum(additive_identity,iPr_def_11,iPr_def_14)
| ~ sum(iPr_def_14,additive_identity,iPr_def_14)
| ~ sum(iPr_def_14,X0,additive_identity)
| ~ sum(X0,iPr_def_11,additive_identity) ),
inference(instantiation,[status(thm)],[c_1156]) ).
tcf(c_7202,plain,
! [X0: $i] :
( sum(a,b,X0)
| ~ defined(b)
| ~ sum(iPr_def_10,additive_identity,X0) ),
inference(superposition,[status(thm)],[c_774,c_1256]) ).
tcf(c_7227,plain,
! [X0: $i] :
( sum(a,b,X0)
| ~ sum(iPr_def_10,additive_identity,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7202,c_105]) ).
tcf(c_9682,plain,
! [X0: $i] :
( sum(b,additive_identity,X0)
| ~ sum(iPr_def_10,iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_776,c_1260]) ).
tcf(c_11600,plain,
! [X0: $i] :
( sum(iPr_def_14,X0,additive_identity)
| ~ sum(iPr_def_12,X0,b) ),
inference(superposition,[status(thm)],[c_883,c_1384]) ).
tcf(c_14797,plain,
( sum(iPr_def_12,iPr_def_10,b)
| ~ defined(b) ),
inference(superposition,[status(thm)],[c_879,c_1835]) ).
tcf(c_14813,plain,
sum(iPr_def_12,iPr_def_10,b),
inference(forward_subsumption_resolution,[status(thm)],[c_14797,c_105]) ).
tcf(c_14862,plain,
sum(iPr_def_10,iPr_def_12,b),
inference(superposition,[status(thm)],[c_14813,c_82]) ).
tcf(c_14958,plain,
sum(b,additive_identity,b),
inference(superposition,[status(thm)],[c_14862,c_9682]) ).
tcf(c_15120,plain,
sum(additive_identity,b,b),
inference(superposition,[status(thm)],[c_14958,c_82]) ).
tcf(c_15164,plain,
! [X0: $i] :
( sum(iPr_def_12,X0,b)
| ~ sum(a,b,X0) ),
inference(superposition,[status(thm)],[c_15120,c_1247]) ).
tcf(c_15579,plain,
! [X0: $i] :
( sum(X0,iPr_def_11,additive_identity)
| ~ defined(iPr_def_11)
| ~ sum(iPr_def_10,additive_identity,X0) ),
inference(superposition,[status(thm)],[c_80,c_1390]) ).
tcf(c_15586,plain,
! [X0: $i] :
( sum(X0,iPr_def_11,additive_identity)
| ~ sum(iPr_def_10,additive_identity,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15579,c_804]) ).
tcf(c_15679,plain,
! [X0: $i] : ~ sum(iPr_def_10,additive_identity,X0),
inference(global_subsumption_just,[status(thm)],[c_15586,c_282,c_801,c_1499,c_3138,c_7177,c_7227,c_11600,c_15164,c_15586]) ).
tcf(c_15683,plain,
~ defined(iPr_def_10),
inference(superposition,[status(thm)],[c_774,c_15679]) ).
tcf(c_15687,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_15683,c_802]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD008-3 : 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 : n014.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 10:35:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 7.68/1.75 % SZS status Started for theBenchmark.p
% 7.68/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 7.68/1.75
% 7.68/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.68/1.75
% 7.68/1.75 % ------ iProver source info
% 7.68/1.75
% 7.68/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 7.68/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.68/1.75 % git: non_committed_changes: false
% 7.68/1.75
% 7.68/1.75 % ------ Parsing...% successful
% 7.68/1.75
% 7.68/1.75
% 7.68/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.68/1.75
% 7.68/1.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.68/1.75
% 7.68/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.68/1.75
% 7.68/1.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.68/1.75 % ------ Proving...
% 7.68/1.75 % ------ Problem Properties
% 7.68/1.75
% 7.68/1.75 %
% 7.68/1.75 % clauses 34
% 7.68/1.75 % conjectures 1
% 7.68/1.75 % EPR 21
% 7.68/1.75 % Horn 31
% 7.68/1.75 % unary 11
% 7.68/1.75 % binary 6
% 7.68/1.75 % lits 85
% 7.68/1.75 % lits eq 5
% 7.68/1.75 % fd_pure 0
% 7.68/1.75 % fd_pseudo 0
% 7.68/1.75 % fd_cond 0
% 7.68/1.75 % fd_pseudo_cond 0
% 7.68/1.75 % AC symbols 0
% 7.68/1.75
% 7.68/1.75 % ------ Schedule dynamic 5 is on
% 7.68/1.75
% 7.68/1.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.68/1.75
% 7.68/1.75
% 7.68/1.75 % ------
% 7.68/1.75 % Current options:
% 7.68/1.75 % ------
% 7.68/1.75
% 7.68/1.75
% 7.68/1.75 %
% 7.68/1.75
% 7.68/1.75 % ------ Proving...
% 7.68/1.75 %
% 7.68/1.75
% 7.68/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 7.68/1.75
% 7.68/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.68/1.75
% 7.68/1.75
%------------------------------------------------------------------------------