%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE148+2 : 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 : n019.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 01:52:31 PM UTC 2026
% Result : Theorem 8.91s 8.01s
% Output : CNFRefutation 8.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 72 ( 57 unt; 3 def)
% Number of atoms : 140 ( 66 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 21 ~; 13 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 76 ( 0 sgn 74 !; 2 ?; 32 :)
% 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(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
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(f10,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
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,strong_iteration(X1)))
& ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,strong_iteration(X1)),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( leq(X0,multiplication(X0,strong_iteration(X1)))
& ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,strong_iteration(X1)),X0) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f24,plain,
? [X0,X1] :
( ~ leq(X0,multiplication(X0,strong_iteration(X1)))
| ( multiplication(X0,X1) = zero
& ~ leq(multiplication(X0,strong_iteration(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,strong_iteration(sK1)))
| ( zero = multiplication(sK0,sK1)
& ~ leq(multiplication(sK0,strong_iteration(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(f31,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
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(f36,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f41,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| zero = multiplication(sK0,sK1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f47,plain,
( ~ leq(sK0,multiplication(sK0,strong_iteration(sK1)))
| ~ leq(multiplication(sK0,strong_iteration(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_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f31]) ).
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_58,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f36]) ).
tcf(c_63,plain,
! [X0: $i] : addition(multiplication(X0,strong_iteration(X0)),one) = strong_iteration(X0),
inference(cnf_transformation,[],[f41]) ).
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,strong_iteration(sK1)))
| ~ leq(multiplication(sK0,strong_iteration(sK1)),sK0) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_69,negated_conjecture,
( ( multiplication(sK0,sK1) = zero )
| ~ leq(sK0,multiplication(sK0,strong_iteration(sK1))) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_88,plain,
! [X0: $i] : addition(one,multiplication(X0,strong_iteration(X0))) = strong_iteration(X0),
inference(theory_normalisation,[status(thm)],[c_63,c_50,c_49]) ).
tcf(c_232,definition,
iPr_def_10 = strong_iteration(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_590,plain,
addition(one,multiplication(sK1,iPr_def_10)) = iPr_def_10,
inference(superposition,[status(thm)],[c_232,c_88]) ).
tcf(c_592,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_716,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_754,plain,
! [X0: $i] : multiplication(sK0,multiplication(sK1,X0)) = multiplication(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_234,c_53]) ).
tcf(c_861,plain,
addition(one,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_590,c_716]) ).
tcf(c_869,plain,
addition(iPr_def_10,one) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_861,c_50,c_49]) ).
tcf(c_1006,plain,
! [X0: $i] : addition(multiplication(X0,one),multiplication(X0,multiplication(sK1,iPr_def_10))) = multiplication(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_590,c_56]) ).
tcf(c_1018,plain,
! [X0: $i] : addition(X0,multiplication(X0,multiplication(sK1,iPr_def_10))) = multiplication(X0,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_1006,c_54]) ).
tcf(c_1479,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,one)) = multiplication(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_869,c_56]) ).
tcf(c_1487,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),X0) = multiplication(X0,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_1479,c_54]) ).
tcf(c_1488,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_10)) = multiplication(X0,iPr_def_10),
inference(theory_normalisation,[status(thm)],[c_1487,c_50,c_49]) ).
tcf(c_10848,plain,
addition(sK0,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_233,c_1488]) ).
tcf(c_10861,plain,
! [X0: $i] : leq(X0,multiplication(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_1488,c_66]) ).
tcf(c_10954,plain,
addition(iPr_def_11,sK0) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_10848,c_50,c_49]) ).
tcf(c_12076,plain,
leq(sK0,iPr_def_11),
inference(superposition,[status(thm)],[c_233,c_10861]) ).
tcf(c_12078,plain,
~ leq(iPr_def_11,sK0),
inference(backward_subsumption_resolution,[status(thm)],[c_236,c_12076]) ).
tcf(c_12079,plain,
zero = iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_235,c_12076]) ).
tcf(c_12110,plain,
! [X0: $i] : addition(iPr_def_12,X0) = X0,
inference(demodulation,[status(thm)],[c_592,c_12079]) ).
tcf(c_12111,plain,
! [X0: $i] : multiplication(iPr_def_12,X0) = iPr_def_12,
inference(demodulation,[status(thm)],[c_58,c_12079]) ).
tcf(c_12113,plain,
! [X0: $i] : multiplication(sK0,multiplication(sK1,X0)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_754,c_12111]) ).
tcf(c_13164,plain,
( leq(iPr_def_11,sK0)
| ( sK0 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_10954,c_66]) ).
tcf(c_13202,plain,
sK0 != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_13164,c_12078]) ).
tcf(c_28258,plain,
addition(sK0,iPr_def_12) = multiplication(sK0,iPr_def_10),
inference(superposition,[status(thm)],[c_12113,c_1018]) ).
tcf(c_28417,plain,
addition(iPr_def_12,sK0) = multiplication(sK0,iPr_def_10),
inference(theory_normalisation,[status(thm)],[c_28258,c_50,c_49]) ).
tcf(c_28418,plain,
addition(iPr_def_12,sK0) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_28417,c_233]) ).
tcf(c_29182,plain,
sK0 = iPr_def_11,
inference(demodulation,[status(thm)],[c_28418,c_12110]) ).
tcf(c_29183,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_29182,c_13202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE148+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.43 % Computer : n019.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Wed Sep 23 19:06:24 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.48 Running first-order theorem proving
% 0.16/5.48 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
% 0.16/5.49
% 0.16/5.50 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.50
% 0.16/5.50 % Detected problem language: tptp
% 0.21/5.51 % Proving...
% 8.91/8.01 % SZS status Started for theBenchmark.p
% 8.91/8.01 % SZS status Theorem for theBenchmark.p
% 8.91/8.01
% 8.91/8.01 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.91/8.01
% 8.91/8.01 % ------ iProver source info
% 8.91/8.01
% 8.91/8.01 % git: date: 2026-07-19 20:42:38 +0200
% 8.91/8.01 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.91/8.01 % git: non_committed_changes: false
% 8.91/8.01
% 8.91/8.01 % ------ Parsing...
% 8.91/8.01 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.91/8.01
% 8.91/8.01 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 8.91/8.01
% 8.91/8.01 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.91/8.01
% 8.91/8.01 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.91/8.01 % ------ Proving...
% 8.91/8.01 % ------ Problem Properties
% 8.91/8.01
% 8.91/8.01 %
% 8.91/8.01 % clauses 24
% 8.91/8.01 % conjectures 2
% 8.91/8.01 % EPR 2
% 8.91/8.01 % Horn 24
% 8.91/8.01 % unary 17
% 8.91/8.01 % binary 7
% 8.91/8.01 % lits 31
% 8.91/8.01 % lits eq 20
% 8.91/8.01 % fd_pure 0
% 8.91/8.01 % fd_pseudo 0
% 8.91/8.01 % fd_cond 0
% 8.91/8.01 % fd_pseudo_cond 0
% 8.91/8.01 % AC symbols 1
% 8.91/8.01
% 8.91/8.01 % ------ Schedule dynamic 5 is on
% 8.91/8.01
% 8.91/8.01 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.91/8.01
% 8.91/8.01
% 8.91/8.01 % ------
% 8.91/8.01 % Current options:
% 8.91/8.01 % ------
% 8.91/8.01
% 8.91/8.01
% 8.91/8.01 %
% 8.91/8.01
% 8.91/8.01 % ------ Proving...
% 8.91/8.01 %
% 8.91/8.01
% 8.91/8.01 % SZS status Theorem for theBenchmark.p
% 8.91/8.01
% 8.91/8.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.91/8.01
% 8.91/8.01
%------------------------------------------------------------------------------