%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE021+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 01:52:10 PM UTC 2026
% Result : Theorem 0.93s 1.28s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 30 unt; 3 def)
% Number of atoms : 123 ( 50 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 88 ( 38 ~; 29 |; 13 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 66 !; 2 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f17,conjecture,
! [X0,X1] :
( test(X1)
=> ( leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0)
& leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> ( leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0)
& leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0))) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
? [X0,X1] :
( test(X1)
& ( ~ leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0)
| ~ leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0))) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f27,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) )
& ( addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1)
| complement(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) )
& ( addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1)
| complement(X1,X0) ) ),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f30,plain,
( test(sK2)
& ( ~ leq(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),sK1)
| ~ leq(sK1,addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f23]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f34,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f39,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f42,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f45,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
test(sK2),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
( ~ leq(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),sK1)
| ~ leq(sK1,addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1))) ),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f49]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f34]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f37]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f39]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_68,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_70,negated_conjecture,
( ~ leq(sK1,addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)))
| ~ leq(addition(multiplication(sK2,sK1),multiplication(c(sK2),sK1)),sK1) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_71,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f52]) ).
tcf(c_199,plain,
( ~ leq(sK1,multiplication(addition(c(sK2),sK2),sK1))
| ~ leq(multiplication(addition(c(sK2),sK2),sK1),sK1) ),
inference(ac_demodulation,[status(thm)],[c_70,c_57,c_57,c_50,c_49]) ).
tcf(c_200,plain,
( ~ leq(sK1,multiplication(addition(sK2,c(sK2)),sK1))
| ~ leq(multiplication(addition(sK2,c(sK2)),sK1),sK1) ),
inference(theory_normalisation,[status(thm)],[c_199,c_50,c_49]) ).
tcf(c_464,definition,
iPr_def_10 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_465,definition,
iPr_def_11 = addition(sK2,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_466,definition,
iPr_def_12 = multiplication(iPr_def_11,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_467,plain,
( ~ leq(iPr_def_12,sK1)
| ~ leq(sK1,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_200,c_464,c_465,c_466]) ).
tcf(c_468,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_749,plain,
addition(iPr_def_10,sK2) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_465,c_50,c_49]) ).
tcf(c_763,plain,
( complement(sK2,iPr_def_10)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_464,c_68]) ).
tcf(c_767,plain,
complement(sK2,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_763,c_468]) ).
tcf(c_785,plain,
! [X0: $i] : leq(X0,X0),
inference(superposition,[status(thm)],[c_52,c_60]) ).
tcf(c_847,plain,
addition(iPr_def_10,sK2) = one,
inference(superposition,[status(thm)],[c_767,c_66]) ).
tcf(c_848,plain,
one = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_847,c_749]) ).
tcf(c_855,plain,
! [X0: $i] : multiplication(iPr_def_11,X0) = X0,
inference(demodulation,[status(thm)],[c_55,c_848]) ).
tcf(c_857,plain,
sK1 = iPr_def_12,
inference(demodulation,[status(thm)],[c_466,c_855]) ).
tcf(c_858,plain,
~ leq(iPr_def_12,iPr_def_12),
inference(demodulation,[status(thm)],[c_467,c_857]) ).
tcf(c_859,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_858,c_785]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE021+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/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 : Wed Sep 23 18:39:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 0.93/1.28 % SZS status Started for theBenchmark.p
% 0.93/1.28 % SZS status Theorem for theBenchmark.p
% 0.93/1.28
% 0.93/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.93/1.28
% 0.93/1.28 % ------ iProver source info
% 0.93/1.28
% 0.93/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.93/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.93/1.28 % git: non_committed_changes: false
% 0.93/1.28
% 0.93/1.28 % ------ Parsing...
% 0.93/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.93/1.28
% 0.93/1.28 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.93/1.28
% 0.93/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.93/1.28
% 0.93/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.93/1.28 % ------ Proving...
% 0.93/1.28 % ------ Problem Properties
% 0.93/1.28
% 0.93/1.28 %
% 0.93/1.28 % clauses 26
% 0.93/1.28 % conjectures 1
% 0.93/1.28 % EPR 3
% 0.93/1.28 % Horn 25
% 0.93/1.28 % unary 15
% 0.93/1.28 % binary 9
% 0.93/1.28 % lits 40
% 0.93/1.28 % lits eq 23
% 0.93/1.28 % fd_pure 0
% 0.93/1.28 % fd_pseudo 0
% 0.93/1.28 % fd_cond 0
% 0.93/1.28 % fd_pseudo_cond 1
% 0.93/1.28 % AC symbols 1
% 0.93/1.28
% 0.93/1.28 % ------ Schedule dynamic 5 is on
% 0.93/1.28
% 0.93/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.93/1.28
% 0.93/1.28
% 0.93/1.28 % ------
% 0.93/1.28 % Current options:
% 0.93/1.28 % ------
% 0.93/1.28
% 0.93/1.28
% 0.93/1.28 %
% 0.93/1.28
% 0.93/1.28 % ------ Proving...
% 0.93/1.28 %
% 0.93/1.28
% 0.93/1.28 % SZS status Theorem for theBenchmark.p
% 0.93/1.28
% 0.93/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.93/1.28
% 0.93/1.28
%------------------------------------------------------------------------------