%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD063-3 : 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 : n010.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 83.04s 23.62s
% Output : CNFRefutation 83.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 47 ( 9 unt; 0 def)
% Number of atoms : 121 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 150 ( 76 ~; 74 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 68 !; 0 ?; 49 :)
% 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(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(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(f29,negated_conjecture,
less_or_equal(additive_inverse(b),additive_inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_or_equal_3) ).
fof(f30,negated_conjecture,
~ less_or_equal(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_or_equal_4) ).
tcf(c_80,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_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_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(additive_inverse(b),additive_inverse(a)),
inference(cnf_transformation,[],[f29]) ).
tcf(c_108,negated_conjecture,
~ less_or_equal(a,b),
inference(cnf_transformation,[],[f30]) ).
tcf(c_284,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_102]) ).
tcf(c_308,plain,
( sum(additive_identity,b,b)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_310,plain,
! [X0: $i,X1: $i] :
( sum(X1,X0,b)
| ~ sum(X0,X1,b) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_316,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_80]) ).
tcf(c_857,plain,
( sum(b,additive_identity,b)
| ~ sum(additive_identity,b,b) ),
inference(instantiation,[status(thm)],[c_310]) ).
tcf(c_880,plain,
( sum(additive_identity,a,a)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_2839,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_316]) ).
tcf(c_3021,plain,
( sum(additive_inverse(b),b,additive_identity)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_13832,plain,
( sum(additive_inverse(a),a,additive_identity)
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_14054,plain,
! [X0: $i,X1: $i] :
( sum(add(b,X0),X1,b)
| ~ sum(b,additive_identity,b)
| ~ sum(X0,X1,additive_identity)
| ~ sum(b,X0,add(b,X0)) ),
inference(instantiation,[status(thm)],[c_2839]) ).
tcf(c_14055,plain,
! [X0: $i] :
( sum(b,X0,add(b,X0))
| ~ defined(b)
| ~ defined(X0) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_30638,plain,
! [X0: $i,X1: $i] :
( less_or_equal(a,b)
| ~ less_or_equal(X0,X1)
| ~ sum(X1,a,b)
| ~ sum(X0,a,a) ),
inference(instantiation,[status(thm)],[c_284]) ).
tcf(c_39883,plain,
! [X0: $i] :
( sum(add(b,X0),a,b)
| ~ sum(b,additive_identity,b)
| ~ sum(X0,a,additive_identity)
| ~ sum(b,X0,add(b,X0)) ),
inference(instantiation,[status(thm)],[c_14054]) ).
tcf(c_46372,plain,
( sum(add(b,additive_inverse(a)),a,b)
| ~ sum(b,additive_identity,b)
| ~ sum(additive_inverse(a),a,additive_identity)
| ~ sum(b,additive_inverse(a),add(b,additive_inverse(a))) ),
inference(instantiation,[status(thm)],[c_39883]) ).
tcf(c_58758,plain,
( sum(b,additive_inverse(a),add(b,additive_inverse(a)))
| ~ defined(b)
| ~ defined(additive_inverse(a)) ),
inference(instantiation,[status(thm)],[c_14055]) ).
tcf(c_97346,plain,
( defined(additive_inverse(a))
| ~ defined(a) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_121387,plain,
! [X0: $i] :
( less_or_equal(a,b)
| ~ sum(X0,a,a)
| ~ less_or_equal(X0,add(b,additive_inverse(a)))
| ~ sum(add(b,additive_inverse(a)),a,b) ),
inference(instantiation,[status(thm)],[c_30638]) ).
tcf(c_121390,plain,
( less_or_equal(a,b)
| ~ sum(additive_identity,a,a)
| ~ less_or_equal(additive_identity,add(b,additive_inverse(a)))
| ~ sum(add(b,additive_inverse(a)),a,b) ),
inference(instantiation,[status(thm)],[c_121387]) ).
tcf(c_158096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( less_or_equal(X4,add(b,X2))
| ~ less_or_equal(X3,X0)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,add(b,X2)) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_173574,plain,
! [X0: $i,X1: $i] :
( sum(additive_inverse(a),X0,X1)
| ~ sum(X0,additive_inverse(a),X1) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_182362,plain,
! [X0: $i] :
( sum(additive_inverse(a),X0,add(X0,additive_inverse(a)))
| ~ sum(X0,additive_inverse(a),add(X0,additive_inverse(a))) ),
inference(instantiation,[status(thm)],[c_173574]) ).
tcf(c_201043,plain,
( sum(additive_inverse(a),b,add(b,additive_inverse(a)))
| ~ sum(b,additive_inverse(a),add(b,additive_inverse(a))) ),
inference(instantiation,[status(thm)],[c_182362]) ).
tcf(c_206729,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,add(b,additive_inverse(a)))
| ~ less_or_equal(X0,additive_inverse(a))
| ~ sum(X0,b,X1)
| ~ sum(additive_inverse(a),b,add(b,additive_inverse(a))) ),
inference(instantiation,[status(thm)],[c_158096]) ).
tcf(c_221029,plain,
( less_or_equal(additive_identity,add(b,additive_inverse(a)))
| ~ sum(additive_inverse(b),b,additive_identity)
| ~ less_or_equal(additive_inverse(b),additive_inverse(a))
| ~ sum(additive_inverse(a),b,add(b,additive_inverse(a))) ),
inference(instantiation,[status(thm)],[c_206729]) ).
tcf(c_221030,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_221029,c_201043,c_121390,c_97346,c_58758,c_46372,c_13832,c_3021,c_880,c_857,c_308,c_107,c_108,c_105,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD063-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n010.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 11:01:29 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 83.04/23.62 % SZS status Started for theBenchmark.p
% 83.04/23.62 % SZS status Unsatisfiable for theBenchmark.p
% 83.04/23.62
% 83.04/23.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 83.04/23.62
% 83.04/23.62 % ------ iProver source info
% 83.04/23.62
% 83.04/23.62 % git: date: 2026-07-19 20:42:38 +0200
% 83.04/23.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 83.04/23.62 % git: non_committed_changes: false
% 83.04/23.62
% 83.04/23.62 % ------ Parsing...% successful
% 83.04/23.62
% 83.04/23.62
% 83.04/23.62 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 83.04/23.62
% 83.04/23.62 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 83.04/23.62
% 83.04/23.62 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 83.04/23.62 % ------ Proving...
% 83.04/23.62 % ------ Problem Properties
% 83.04/23.62
% 83.04/23.62 %
% 83.04/23.62 % clauses 30
% 83.04/23.62 % conjectures 2
% 83.04/23.62 % EPR 21
% 83.04/23.62 % Horn 27
% 83.04/23.62 % unary 7
% 83.04/23.62 % binary 6
% 83.04/23.62 % lits 81
% 83.04/23.62 % lits eq 0
% 83.04/23.62 % fd_pure 0
% 83.04/23.62 % fd_pseudo 0
% 83.04/23.62 % fd_cond 0
% 83.04/23.62 % fd_pseudo_cond 0
% 83.04/23.62 % AC symbols 0
% 83.04/23.62
% 83.04/23.62 % ------ Input Options Time Limit: Unbounded
% 83.04/23.62
% 83.04/23.62
% 83.04/23.62 % ------
% 83.04/23.62 % Current options:
% 83.04/23.62 % ------
% 83.04/23.62
% 83.04/23.62
% 83.04/23.62 %
% 83.04/23.62
% 83.04/23.62 % ------ Proving...
% 83.04/23.62 %
% 83.04/23.62
% 83.04/23.62 % SZS status Unsatisfiable for theBenchmark.p
% 83.04/23.62
% 83.04/23.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 83.04/23.62
% 83.04/23.62
%------------------------------------------------------------------------------