%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : FLD058-3 : 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 : n003.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 3.44s 1.28s
% Output : CNFRefutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 17 unt; 0 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 120 ( 60 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 70 ( 0 sgn 70 !; 0 ?; 42 :)
% 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/sandbox/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/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_2) ).
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(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(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
fof(f21,axiom,
! [X0,X1] :
( ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1)
| sum(additive_identity,X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
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(f29,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_3) ).
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,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_5) ).
fof(f32,negated_conjecture,
sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_6) ).
tcf(c_81,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_82,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_83,plain,
! [X0: $i] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_94,plain,
defined(additive_identity),
inference(cnf_transformation,[],[f14]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,X0,X1)
| ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
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_109,negated_conjecture,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[],[f29]) ).
tcf(c_110,negated_conjecture,
less_or_equal(a,b),
inference(cnf_transformation,[],[f30]) ).
tcf(c_111,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[],[f31]) ).
tcf(c_112,negated_conjecture,
sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[],[f32]) ).
tcf(c_115,plain,
( sum(additive_identity,additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_119,plain,
( less_or_equal(additive_identity,additive_identity)
| ~ defined(additive_identity) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_289,negated_conjecture,
sum(additive_identity,b,additive_identity),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_297,plain,
( sum(additive_identity,a,additive_identity)
| ~ less_or_equal(additive_identity,a)
| ~ less_or_equal(a,additive_identity) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_331,plain,
! [X0: $i] :
( less_or_equal(a,additive_identity)
| ~ less_or_equal(a,X0)
| ~ less_or_equal(X0,additive_identity) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_492,plain,
( less_or_equal(a,additive_identity)
| ~ less_or_equal(b,additive_identity)
| ~ less_or_equal(a,b) ),
inference(instantiation,[status(thm)],[c_331]) ).
tcf(c_617,plain,
sum(b,additive_identity,additive_identity),
inference(superposition,[status(thm)],[c_289,c_85]) ).
tcf(c_618,plain,
! [X0: $i] :
( sum(X0,additive_identity,X0)
| ~ defined(X0) ),
inference(superposition,[status(thm)],[c_83,c_85]) ).
tcf(c_2270,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(additive_identity,X1,X2)
| ~ sum(additive_identity,X0,X2)
| ~ sum(b,X0,X1) ),
inference(superposition,[status(thm)],[c_289,c_81]) ).
tcf(c_2555,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X2,X1,additive_identity)
| ~ sum(b,X0,X2)
| ~ sum(X0,X1,additive_identity) ),
inference(superposition,[status(thm)],[c_617,c_82]) ).
tcf(c_2652,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(b,additive_identity)
| ~ less_or_equal(X0,X2)
| ~ sum(X2,X1,additive_identity)
| ~ sum(X0,X1,b) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_2653,plain,
( less_or_equal(b,additive_identity)
| ~ less_or_equal(additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,b) ),
inference(instantiation,[status(thm)],[c_2652]) ).
tcf(c_3018,plain,
! [X0: $i,X1: $i] :
( sum(additive_identity,X1,X0)
| ~ defined(X0)
| ~ sum(b,X0,X1) ),
inference(superposition,[status(thm)],[c_83,c_2270]) ).
tcf(c_6579,plain,
! [X0: $i] :
( sum(X0,b,additive_identity)
| ~ sum(b,additive_identity,X0) ),
inference(superposition,[status(thm)],[c_289,c_2555]) ).
tcf(c_7409,plain,
( sum(b,b,additive_identity)
| ~ defined(b) ),
inference(superposition,[status(thm)],[c_618,c_6579]) ).
tcf(c_7410,plain,
sum(b,b,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[c_7409,c_108]) ).
tcf(c_7525,plain,
( sum(additive_identity,additive_identity,b)
| ~ defined(b) ),
inference(superposition,[status(thm)],[c_7410,c_3018]) ).
tcf(c_7527,plain,
sum(additive_identity,additive_identity,b),
inference(forward_subsumption_resolution,[status(thm)],[c_7525,c_108]) ).
tcf(c_7550,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7527,c_2653,c_492,c_297,c_119,c_115,c_111,c_109,c_110,c_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD058-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n003.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 11:00:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 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...
% 3.44/1.28 % SZS status Started for theBenchmark.p
% 3.44/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 3.44/1.28
% 3.44/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.44/1.28
% 3.44/1.28 % ------ iProver source info
% 3.44/1.28
% 3.44/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.44/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.44/1.28 % git: non_committed_changes: false
% 3.44/1.28
% 3.44/1.28 % ------ Parsing...% successful
% 3.44/1.28
% 3.44/1.28
% 3.44/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.44/1.28
% 3.44/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.44/1.28
% 3.44/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.44/1.28 % ------ Proving...
% 3.44/1.28 % ------ Problem Properties
% 3.44/1.28
% 3.44/1.28 %
% 3.44/1.28 % clauses 32
% 3.44/1.28 % conjectures 4
% 3.44/1.28 % EPR 24
% 3.44/1.28 % Horn 29
% 3.44/1.28 % unary 9
% 3.44/1.28 % binary 6
% 3.44/1.28 % lits 83
% 3.44/1.28 % lits eq 0
% 3.44/1.28 % fd_pure 0
% 3.44/1.28 % fd_pseudo 0
% 3.44/1.28 % fd_cond 0
% 3.44/1.28 % fd_pseudo_cond 0
% 3.44/1.28 % AC symbols 0
% 3.44/1.28
% 3.44/1.28 % ------ Schedule dynamic 5 is on
% 3.44/1.28
% 3.44/1.28 % ------ no equalities: superposition off
% 3.44/1.28
% 3.44/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.44/1.28
% 3.44/1.28
% 3.44/1.28 % ------
% 3.44/1.28 % Current options:
% 3.44/1.28 % ------
% 3.44/1.28
% 3.44/1.28
% 3.44/1.28 %
% 3.44/1.28
% 3.44/1.28 % ------ Proving...
% 3.44/1.28 %
% 3.44/1.28
% 3.44/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 3.44/1.28
% 3.44/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.44/1.28
% 3.44/1.28
%------------------------------------------------------------------------------