%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE167+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.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 01:52:34 PM UTC 2026
% Result : Theorem 4.73s 22.55s
% Output : CNFRefutation 4.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 70 ( 39 unt; 3 def)
% Number of atoms : 175 ( 67 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 99 ( 48 ~; 42 |; 5 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 81 !; 2 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
fof(f11,axiom,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
fof(f14,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X2,X0),X1),X2)
=> leq(multiplication(X1,star(X0)),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_induction2) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(f19,conjecture,
! [X0,X1] :
( leq(X0,multiplication(X0,star(X1)))
& ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,star(X1)),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( leq(X0,multiplication(X0,star(X1)))
& ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,star(X1)),X0) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X2,X0),X1),X2)
| leq(multiplication(X1,star(X0)),X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f24,plain,
? [X0,X1] :
( ~ leq(X0,multiplication(X0,star(X1)))
| ( multiplication(X0,X1) = zero
& ~ leq(multiplication(X0,star(X1)),X0) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
& ( addition(X0,X1) != X1
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f26,plain,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| ( zero = multiplication(sK0,sK1)
& ~ leq(multiplication(sK0,star(sK1)),sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f24]) ).
fof(f27,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f28,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f29,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f30,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f32,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f37,plain,
! [X0] : star(X0) = addition(one,multiplication(X0,star(X0))),
inference(cnf_transformation,[],[f11]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X2,X0),X1),X2)
| leq(multiplication(X1,star(X0)),X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| zero = multiplication(sK0,sK1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f47,plain,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| ~ leq(multiplication(sK0,star(sK1)),sK0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f27]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f29]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f30]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f32]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_59,plain,
! [X0: $i] : addition(one,multiplication(X0,star(X0))) = star(X0),
inference(cnf_transformation,[],[f37]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_68,negated_conjecture,
( ~ leq(sK0,multiplication(sK0,star(sK1)))
| ~ leq(multiplication(sK0,star(sK1)),sK0) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_69,negated_conjecture,
( ( multiplication(sK0,sK1) = zero )
| ~ leq(sK0,multiplication(sK0,star(sK1))) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_73,plain,
addition(sK0,sK0) = sK0,
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_76,plain,
( leq(sK0,sK0)
| ( addition(sK0,sK0) != sK0 ) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_232,definition,
iPr_def_10 = star(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_233,definition,
iPr_def_11 = multiplication(sK0,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_234,definition,
iPr_def_12 = multiplication(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_235,negated_conjecture,
( ( iPr_def_12 = zero )
| ~ leq(sK0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_69,c_234,c_232,c_233]) ).
tcf(c_236,negated_conjecture,
( ~ leq(iPr_def_11,sK0)
| ~ leq(sK0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_237,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_243,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( leq(X0,X2)
| ~ leq(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_246,plain,
sK0 = sK0,
inference(instantiation,[status(thm)],[c_237]) ).
tcf(c_598,plain,
addition(one,multiplication(sK1,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_232,c_59]) ).
tcf(c_725,plain,
! [X0: $i,X1: $i] :
( leq(sK0,iPr_def_11)
| ~ leq(X0,X1)
| ( iPr_def_11 != X1 )
| ( sK0 != X0 ) ),
inference(instantiation,[status(thm)],[c_243]) ).
tcf(c_730,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_760,plain,
! [X0: $i] :
( leq(sK0,iPr_def_11)
| ~ leq(X0,multiplication(sK0,iPr_def_10))
| ( iPr_def_11 != multiplication(sK0,iPr_def_10) )
| ( sK0 != X0 ) ),
inference(instantiation,[status(thm)],[c_725]) ).
tcf(c_761,plain,
( leq(sK0,iPr_def_11)
| ~ leq(sK0,multiplication(sK0,iPr_def_10))
| ( iPr_def_11 != multiplication(sK0,iPr_def_10) )
| ( sK0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_760]) ).
tcf(c_872,plain,
addition(one,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_598,c_730]) ).
tcf(c_881,plain,
addition(iPr_def_10,one) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_872,c_50,c_49]) ).
tcf(c_1100,plain,
! [X0: $i] :
( leq(X0,multiplication(sK0,iPr_def_10))
| ( addition(X0,multiplication(sK0,iPr_def_10)) != multiplication(sK0,iPr_def_10) ) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_1101,plain,
( leq(sK0,multiplication(sK0,iPr_def_10))
| ( addition(sK0,multiplication(sK0,iPr_def_10)) != multiplication(sK0,iPr_def_10) ) ),
inference(instantiation,[status(thm)],[c_1100]) ).
tcf(c_1488,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,one)) = multiplication(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_881,c_56]) ).
tcf(c_1496,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),X0) = multiplication(X0,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_1488,c_54]) ).
tcf(c_1497,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_10)) = multiplication(X0,iPr_def_10),
inference(theory_normalisation,[status(thm)],[c_1496,c_50,c_49]) ).
tcf(c_1498,plain,
addition(sK0,multiplication(sK0,iPr_def_10)) = multiplication(sK0,iPr_def_10),
inference(instantiation,[status(thm)],[c_1497]) ).
tcf(c_1891,plain,
! [X0: $i,X1: $i] :
( leq(iPr_def_11,sK0)
| ~ leq(X1,X0)
| ( iPr_def_11 != X1 )
| ( sK0 != X0 ) ),
inference(instantiation,[status(thm)],[c_243]) ).
tcf(c_7588,plain,
! [X0: $i] :
( leq(iPr_def_11,sK0)
| ~ leq(multiplication(sK0,iPr_def_10),X0)
| ( iPr_def_11 != multiplication(sK0,iPr_def_10) )
| ( sK0 != X0 ) ),
inference(instantiation,[status(thm)],[c_1891]) ).
tcf(c_7589,plain,
( leq(iPr_def_11,sK0)
| ~ leq(multiplication(sK0,iPr_def_10),sK0)
| ( iPr_def_11 != multiplication(sK0,iPr_def_10) )
| ( sK0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_7588]) ).
tcf(c_11789,negated_conjecture,
iPr_def_12 = zero,
inference(global_subsumption_just,[status(thm)],[c_235,c_246,c_233,c_235,c_761,c_1101,c_1498]) ).
tcf(c_11793,plain,
! [X0: $i] : addition(X0,iPr_def_12) = X0,
inference(light_normalisation,[status(thm)],[c_51,c_11789]) ).
tcf(c_11797,plain,
! [X0: $i] : addition(iPr_def_12,X0) = X0,
inference(superposition,[status(thm)],[c_11793,c_49]) ).
tcf(c_12539,plain,
! [X0: $i] :
( leq(multiplication(X0,star(sK1)),sK0)
| ~ leq(addition(iPr_def_12,X0),sK0) ),
inference(superposition,[status(thm)],[c_234,c_62]) ).
tcf(c_12548,plain,
! [X0: $i] :
( leq(multiplication(X0,iPr_def_10),sK0)
| ~ leq(X0,sK0) ),
inference(light_normalisation,[status(thm)],[c_12539,c_232,c_11797]) ).
tcf(c_12576,plain,
( leq(multiplication(sK0,iPr_def_10),sK0)
| ~ leq(sK0,sK0) ),
inference(instantiation,[status(thm)],[c_12548]) ).
tcf(c_12577,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_12576,c_7589,c_1498,c_1101,c_761,c_236,c_233,c_246,c_76,c_73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE167+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/20.61 % Computer : n006.cluster.edu
% 0.11/20.61 % Model : x86_64 x86_64
% 0.11/20.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/20.61 % Memory : 8046.5625MB
% 0.11/20.61 % OS : Linux 6.8.0-71-generic
% 0.11/20.61 % CPULimit : 300
% 0.11/20.61 % WCLimit : 300
% 0.11/20.61 % DateTime : Wed Sep 23 19:11:50 UTC 2026
% 0.11/20.61 % CPUTime :
% 0.11/20.61 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/20.65 Running first-order theorem proving
% 0.11/20.65 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
% 0.11/20.67
% 0.11/20.67 % ======== iProver multi-core TPTP/SMT =========
% 0.11/20.67
% 0.11/20.67 % Detected problem language: tptp
% 0.11/20.68 % Proving...
% 4.73/22.55 % SZS status Started for theBenchmark.p
% 4.73/22.55 % SZS status Theorem for theBenchmark.p
% 4.73/22.55
% 4.73/22.55 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.73/22.55
% 4.73/22.55 % ------ iProver source info
% 4.73/22.55
% 4.73/22.55 % git: date: 2026-07-19 20:42:38 +0200
% 4.73/22.55 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.73/22.55 % git: non_committed_changes: false
% 4.73/22.55
% 4.73/22.55 % ------ Parsing...
% 4.73/22.55 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.73/22.55
% 4.73/22.55 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.73/22.55
% 4.73/22.55 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.73/22.55
% 4.73/22.55 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.73/22.55 % ------ Proving...
% 4.73/22.55 % ------ Problem Properties
% 4.73/22.55
% 4.73/22.55 %
% 4.73/22.55 % clauses 24
% 4.73/22.55 % conjectures 2
% 4.73/22.55 % EPR 2
% 4.73/22.55 % Horn 24
% 4.73/22.55 % unary 17
% 4.73/22.55 % binary 7
% 4.73/22.55 % lits 31
% 4.73/22.55 % lits eq 20
% 4.73/22.55 % fd_pure 0
% 4.73/22.55 % fd_pseudo 0
% 4.73/22.55 % fd_cond 0
% 4.73/22.55 % fd_pseudo_cond 0
% 4.73/22.55 % AC symbols 1
% 4.73/22.55
% 4.73/22.55 % ------ Schedule dynamic 5 is on
% 4.73/22.55
% 4.73/22.55 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.73/22.55
% 4.73/22.55
% 4.73/22.55 % ------
% 4.73/22.55 % Current options:
% 4.73/22.55 % ------
% 4.73/22.55
% 4.73/22.55
% 4.73/22.55 %
% 4.73/22.55
% 4.73/22.55 % ------ Proving...
% 4.73/22.55 %
% 4.73/22.55
% 4.73/22.55 % SZS status Theorem for theBenchmark.p
% 4.73/22.55
% 4.73/22.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.73/22.55
% 4.73/22.55
%------------------------------------------------------------------------------