%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD055-3 : 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 : n020.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 01:15:49 PM UTC 2026
% Result : Unsatisfiable 1.55s 1.30s
% Output : CNFRefutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 11 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 66 ( 33 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
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(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
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(f23,axiom,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_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(f28,axiom,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
fof(f30,negated_conjecture,
less_or_equal(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_4) ).
fof(f31,negated_conjecture,
sum(additive_identity,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_5) ).
fof(f32,negated_conjecture,
~ less_or_equal(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_or_equal_6) ).
tcf(c_83,plain,
! [X0: $i] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_94,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f14]) ).
tcf(c_102,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_103,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,X0)
| less_or_equal(X0,X1)
| ~ defined(X1)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_104,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_108,plain,
defined(b),
inference(cnf_transformation,[],[f28]) ).
tcf(c_110,negated_conjecture,
less_or_equal(a,b),
inference(cnf_transformation,[],[f30]) ).
tcf(c_111,negated_conjecture,
sum(additive_identity,b,c),
inference(cnf_transformation,[],[f31]) ).
tcf(c_112,negated_conjecture,
~ less_or_equal(a,c),
inference(cnf_transformation,[],[f32]) ).
tcf(c_119,plain,
( less_or_equal(additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_294,plain,
! [X0: $i] :
( less_or_equal(a,c)
| ~ less_or_equal(a,X0)
| ~ less_or_equal(X0,c) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less_or_equal(X2,c)
| ~ less_or_equal(X0,X3)
| ~ sum(X3,X1,c)
| ~ sum(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_430,plain,
( less_or_equal(a,c)
| ~ less_or_equal(b,c)
| ~ less_or_equal(a,b) ),
inference(instantiation,[status(thm)],[c_294]) ).
tcf(c_540,plain,
! [X0: $i,X1: $i] :
( less_or_equal(X1,c)
| ~ less_or_equal(X0,additive_identity)
| ~ sum(additive_identity,b,c)
| ~ sum(X0,b,X1) ),
inference(instantiation,[status(thm)],[c_316]) ).
tcf(c_1819,plain,
( less_or_equal(b,c)
| ~ less_or_equal(additive_identity,additive_identity)
| ~ sum(additive_identity,b,c)
| ~ sum(additive_identity,b,b) ),
inference(instantiation,[status(thm)],[c_540]) ).
tcf(c_1820,plain,
( sum(additive_identity,b,b)
| ~ defined(b) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_1821,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1820,c_1819,c_430,c_119,c_111,c_112,c_110,c_94,c_108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD055-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 10:58:19 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 1.55/1.30 % SZS status Started for theBenchmark.p
% 1.55/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 1.55/1.30
% 1.55/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.55/1.30
% 1.55/1.30 % ------ iProver source info
% 1.55/1.30
% 1.55/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 1.55/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.55/1.30 % git: non_committed_changes: false
% 1.55/1.30
% 1.55/1.30 % ------ Parsing...% successful
% 1.55/1.30
% 1.55/1.30
% 1.55/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.55/1.30
% 1.55/1.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.55/1.30
% 1.55/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.55/1.30 % ------ Proving...
% 1.55/1.30 % ------ Problem Properties
% 1.55/1.30
% 1.55/1.30 %
% 1.55/1.30 % clauses 32
% 1.55/1.30 % conjectures 3
% 1.55/1.30 % EPR 24
% 1.55/1.30 % Horn 29
% 1.55/1.30 % unary 9
% 1.55/1.30 % binary 6
% 1.55/1.30 % lits 83
% 1.55/1.30 % lits eq 0
% 1.55/1.30 % fd_pure 0
% 1.55/1.30 % fd_pseudo 0
% 3.38/1.30 % fd_cond 0
% 3.38/1.30 % fd_pseudo_cond 0
% 3.38/1.30 % AC symbols 0
% 3.38/1.30
% 3.38/1.30 % ------ Schedule dynamic 5 is on
% 3.38/1.30
% 3.38/1.30 % ------ no equalities: superposition off
% 3.38/1.30
% 3.38/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.38/1.30
% 3.38/1.30
% 3.38/1.30 % ------
% 3.38/1.30 % Current options:
% 3.38/1.30 % ------
% 3.38/1.30
% 3.38/1.30
% 3.38/1.30 %
% 3.38/1.30
% 3.38/1.30 % ------ Proving...
% 3.38/1.30 %
% 3.38/1.30
% 3.38/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.38/1.30
% 3.38/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.38/1.30
% 3.38/1.30
%------------------------------------------------------------------------------