%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD067-3 : 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 : n016.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 3.82s 1.32s
% Output : CNFRefutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 32 ( 17 unt; 2 def)
% Number of atoms : 71 ( 2 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 49 ( 26 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
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(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(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_identity,add(b,additive_inverse(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_4) ).
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_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_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_identity,add(b,additive_inverse(a))),
inference(cnf_transformation,[],[f30]) ).
tcf(c_281,definition,
iPr_def_10 = additive_inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_282,definition,
iPr_def_11 = add(b,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_283,negated_conjecture,
~ less_or_equal(additive_identity,iPr_def_11),
inference(demodulation,[status(thm)],[c_108,c_281,c_282]) ).
tcf(c_284,negated_conjecture,
less_or_equal(a,b),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_734,plain,
( defined(iPr_def_10)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_281,c_93]) ).
tcf(c_735,plain,
defined(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_734,c_105]) ).
tcf(c_748,plain,
( sum(iPr_def_10,a,additive_identity)
| ~ defined(a) ),
inference(superposition,[status(thm)],[c_281,c_82]) ).
tcf(c_749,plain,
sum(iPr_def_10,a,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_748,c_105]) ).
tcf(c_756,plain,
sum(a,iPr_def_10,additive_identity),
inference(superposition,[status(thm)],[c_749,c_83]) ).
tcf(c_817,plain,
( sum(b,iPr_def_10,iPr_def_11)
| ~ defined(iPr_def_10)
| ~ defined(b) ),
inference(superposition,[status(thm)],[c_282,c_97]) ).
tcf(c_819,plain,
sum(b,iPr_def_10,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_817,c_735,c_106]) ).
tcf(c_1047,plain,
! [X0: $i,X1: $i] :
( less_or_equal(additive_identity,X1)
| ~ less_or_equal(a,X0)
| ~ sum(X0,iPr_def_10,X1) ),
inference(superposition,[status(thm)],[c_756,c_102]) ).
tcf(c_4782,plain,
( less_or_equal(additive_identity,iPr_def_11)
| ~ less_or_equal(a,b) ),
inference(superposition,[status(thm)],[c_819,c_1047]) ).
tcf(c_4784,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4782,c_283,c_284]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD067-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Fri Sep 25 11:07:00 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.12/0.45
% 0.12/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.45
% 0.12/0.45 % Detected problem language: tptp
% 0.12/0.46 % Proving...
% 3.82/1.32 % SZS status Started for theBenchmark.p
% 3.82/1.32 % SZS status Unsatisfiable for theBenchmark.p
% 3.82/1.32
% 3.82/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.82/1.32
% 3.82/1.32 % ------ iProver source info
% 3.82/1.32
% 3.82/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 3.82/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.82/1.32 % git: non_committed_changes: false
% 3.82/1.32
% 3.82/1.32 % ------ Parsing...% successful
% 3.82/1.32
% 3.82/1.32
% 3.82/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.82/1.32
% 3.82/1.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.82/1.32
% 3.82/1.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.82/1.32
% 3.82/1.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.82/1.32 % ------ Proving...
% 3.82/1.32 % ------ Problem Properties
% 3.82/1.32
% 3.82/1.32 %
% 3.82/1.32 % clauses 32
% 3.82/1.32 % conjectures 2
% 3.82/1.32 % EPR 22
% 3.82/1.32 % Horn 29
% 3.82/1.32 % unary 9
% 3.82/1.32 % binary 6
% 3.82/1.32 % lits 83
% 3.82/1.32 % lits eq 2
% 3.82/1.32 % fd_pure 0
% 3.82/1.32 % fd_pseudo 0
% 3.82/1.32 % fd_cond 0
% 3.82/1.32 % fd_pseudo_cond 0
% 3.82/1.32 % AC symbols 0
% 3.82/1.32
% 3.82/1.32 % ------ Schedule dynamic 5 is on
% 3.82/1.32
% 3.82/1.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.82/1.32
% 3.82/1.32
% 3.82/1.32 % ------
% 3.82/1.32 % Current options:
% 3.82/1.32 % ------
% 3.82/1.32
% 3.82/1.32
% 3.82/1.32 %
% 3.82/1.32
% 3.82/1.32 % ------ Proving...
% 3.82/1.32 %
% 3.82/1.32
% 3.82/1.32 % SZS status Unsatisfiable for theBenchmark.p
% 3.82/1.32
% 3.82/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.82/1.32
% 3.82/1.32
%------------------------------------------------------------------------------