%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD068-4 : 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 : n018.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 4.28s 1.30s
% Output : CNFRefutation 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 90 ( 46 ~; 44 |; 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 : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 47 ( 0 sgn 47 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
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(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/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_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(f30,negated_conjecture,
sum(b,additive_inverse(a),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_4) ).
fof(f31,negated_conjecture,
less_or_equal(additive_identity,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_5) ).
fof(f32,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_6) ).
tcf(c_81,plain,
defined(a),
inference(cnf_transformation,[],[f27]) ).
tcf(c_82,plain,
defined(b),
inference(cnf_transformation,[],[f28]) ).
tcf(c_84,negated_conjecture,
sum(b,additive_inverse(a),u),
inference(cnf_transformation,[],[f30]) ).
tcf(c_85,negated_conjecture,
less_or_equal(additive_identity,u),
inference(cnf_transformation,[],[f31]) ).
tcf(c_86,negated_conjecture,
~ less_or_equal(a,b),
inference(cnf_transformation,[],[f32]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_88,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_91,plain,
! [X0: $i] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_95,plain,
! [X0: $i] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_96,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_308,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(a,b)
| ~ less_or_equal(X0,X2)
| ~ sum(X2,X1,b)
| ~ sum(X0,X1,a) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_316,plain,
! [X0: $i] :
( less_or_equal(a,b)
| ~ less_or_equal(additive_identity,X0)
| ~ sum(additive_identity,a,a)
| ~ sum(X0,a,b) ),
inference(instantiation,[status(thm)],[c_308]) ).
tcf(c_317,plain,
( sum(additive_identity,a,a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_367,plain,
( sum(additive_identity,b,b)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i] :
( sum(X1,X0,b)
| ~ sum(X0,X1,b) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sum(X2,X3,b)
| ~ sum(X0,X4,b)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_457,plain,
( sum(b,additive_identity,b)
| ~ sum(additive_identity,b,b) ),
inference(instantiation,[status(thm)],[c_369]) ).
tcf(c_469,plain,
( sum(additive_inverse(a),a,additive_identity)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_715,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,X1,b)
| ~ sum(b,additive_identity,b)
| ~ sum(b,X0,X2)
| ~ sum(X0,X1,additive_identity) ),
inference(instantiation,[status(thm)],[c_373]) ).
tcf(c_1773,plain,
! [X0: $i] :
( sum(u,X0,b)
| ~ sum(b,additive_identity,b)
| ~ sum(b,additive_inverse(a),u)
| ~ sum(additive_inverse(a),X0,additive_identity) ),
inference(instantiation,[status(thm)],[c_715]) ).
tcf(c_2259,plain,
( sum(u,a,b)
| ~ sum(b,additive_identity,b)
| ~ sum(b,additive_inverse(a),u)
| ~ sum(additive_inverse(a),a,additive_identity) ),
inference(instantiation,[status(thm)],[c_1773]) ).
tcf(c_2261,plain,
( less_or_equal(a,b)
| ~ less_or_equal(additive_identity,u)
| ~ sum(additive_identity,a,a)
| ~ sum(u,a,b) ),
inference(instantiation,[status(thm)],[c_316]) ).
tcf(c_2262,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2261,c_2259,c_469,c_457,c_367,c_317,c_84,c_86,c_85,c_81,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD068-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 11:05:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 4.28/1.30 % SZS status Started for theBenchmark.p
% 4.28/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 4.28/1.30
% 4.28/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.28/1.30
% 4.28/1.30 % ------ iProver source info
% 4.28/1.30
% 4.28/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 4.28/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.28/1.30 % git: non_committed_changes: false
% 4.28/1.30
% 4.28/1.30 % ------ Parsing...% successful
% 4.28/1.30
% 4.28/1.30
% 4.28/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.28/1.30
% 4.28/1.30 % ------ Preprocessing... sf_s rm: 6 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.28/1.30
% 4.28/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.28/1.30 % ------ Proving...
% 4.28/1.30 % ------ Problem Properties
% 4.28/1.30
% 4.28/1.30 %
% 4.28/1.30 % clauses 17
% 4.28/1.30 % conjectures 3
% 4.28/1.30 % EPR 14
% 4.28/1.30 % Horn 16
% 4.28/1.30 % unary 7
% 4.28/1.30 % binary 4
% 4.28/1.30 % lits 37
% 4.28/1.30 % lits eq 0
% 4.28/1.30 % fd_pure 0
% 4.28/1.30 % fd_pseudo 0
% 4.28/1.30 % fd_cond 0
% 4.28/1.30 % fd_pseudo_cond 0
% 4.28/1.30 % AC symbols 0
% 4.28/1.30
% 4.28/1.30 % ------ Schedule dynamic 5 is on
% 4.28/1.30
% 4.28/1.30 % ------ no equalities: superposition off
% 4.28/1.30
% 4.28/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.28/1.30
% 4.28/1.30
% 4.28/1.30 % ------
% 4.28/1.30 % Current options:
% 4.28/1.30 % ------
% 4.28/1.30
% 4.28/1.30
% 4.28/1.30 %
% 4.28/1.30
% 4.28/1.30 % ------ Proving...
% 4.28/1.30 %
% 4.28/1.30
% 4.28/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 4.28/1.30
% 4.28/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.28/1.30
% 4.28/1.30
%------------------------------------------------------------------------------