%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE009+3 : 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 : n007.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 01:52:07 PM UTC 2026
% Result : Theorem 2.26s 1.29s
% Output : CNFRefutation 2.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 45 unt; 5 def)
% Number of atoms : 167 ( 59 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 107 ( 47 ~; 33 |; 19 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 75 !; 4 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+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/KLE001+0.ax',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+1.ax',test_2) ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_3) ).
fof(f17,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
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(X0)
& test(X1)
& ( ~ leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f24,plain,
? [X0,X1] :
( test(X0)
& test(X1)
& ( ~ leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
inference(flattening,[],[f23]) ).
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(nnf_transformation,[],[f14]) ).
fof(f29,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,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f31,plain,
( test(sK1)
& test(sK2)
& ( ~ leq(addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f24]) ).
fof(f32,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f33,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f35,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f39,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f40,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f43,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f46,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f29]) ).
fof(f50,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
test(sK1),
inference(cnf_transformation,[],[f31]) ).
fof(f54,plain,
test(sK2),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
( ~ leq(addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),one)
| ~ leq(one,addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2)))) ),
inference(cnf_transformation,[],[f31]) ).
fof(f56,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f50]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f32]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f35]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f37]) ).
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,[],[f39]) ).
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,[],[f40]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_68,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_70,negated_conjecture,
( ~ leq(one,addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))))
| ~ leq(addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),one) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_71,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f54]) ).
tcf(c_72,negated_conjecture,
test(sK1),
inference(cnf_transformation,[],[f53]) ).
tcf(c_90,negated_conjecture,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(sK1,c(sK2)),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),c(sK2))))))
| ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(sK1,c(sK2)),addition(multiplication(c(sK1),sK2),multiplication(c(sK1),c(sK2))))),one) ),
inference(theory_normalisation,[status(thm)],[c_70,c_50,c_49]) ).
tcf(c_211,plain,
( ~ leq(one,addition(multiplication(sK1,sK2),addition(multiplication(sK1,c(sK2)),multiplication(c(sK1),addition(c(sK2),sK2)))))
| ~ leq(addition(multiplication(sK1,sK2),addition(multiplication(sK1,c(sK2)),multiplication(c(sK1),addition(c(sK2),sK2)))),one) ),
inference(ac_demodulation,[status(thm)],[c_90,c_56,c_56,c_50,c_49]) ).
tcf(c_212,plain,
( ~ leq(one,addition(multiplication(c(sK1),addition(c(sK2),sK2)),multiplication(sK1,addition(c(sK2),sK2))))
| ~ leq(addition(multiplication(c(sK1),addition(c(sK2),sK2)),multiplication(sK1,addition(c(sK2),sK2))),one) ),
inference(ac_demodulation,[status(thm)],[c_211,c_56,c_56,c_50,c_49]) ).
tcf(c_213,plain,
( ~ leq(one,multiplication(addition(c(sK1),sK1),addition(c(sK2),sK2)))
| ~ leq(multiplication(addition(c(sK1),sK1),addition(c(sK2),sK2)),one) ),
inference(ac_demodulation,[status(thm)],[c_212,c_57,c_57,c_50,c_49]) ).
tcf(c_214,plain,
( ~ leq(one,multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))))
| ~ leq(multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))),one) ),
inference(theory_normalisation,[status(thm)],[c_213,c_50,c_49]) ).
tcf(c_493,definition,
iPr_def_10 = c(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_494,definition,
iPr_def_11 = addition(sK1,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_495,definition,
iPr_def_12 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_496,definition,
iPr_def_13 = addition(sK2,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_497,definition,
iPr_def_14 = multiplication(iPr_def_11,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_498,plain,
( ~ leq(iPr_def_14,one)
| ~ leq(one,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_214,c_495,c_496,c_493,c_494,c_497]) ).
tcf(c_499,negated_conjecture,
test(sK1),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_500,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_793,plain,
addition(iPr_def_10,sK1) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_494,c_50,c_49]) ).
tcf(c_794,plain,
addition(iPr_def_12,sK2) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_496,c_50,c_49]) ).
tcf(c_808,plain,
complement(sK2,c(sK2)),
inference(superposition,[status(thm)],[c_500,c_68]) ).
tcf(c_809,plain,
complement(sK1,c(sK1)),
inference(superposition,[status(thm)],[c_499,c_68]) ).
tcf(c_810,plain,
complement(sK1,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_809,c_493]) ).
tcf(c_811,plain,
complement(sK2,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_808,c_495]) ).
tcf(c_833,plain,
! [X0: $i] : leq(X0,X0),
inference(superposition,[status(thm)],[c_52,c_60]) ).
tcf(c_878,plain,
addition(iPr_def_10,sK1) = one,
inference(superposition,[status(thm)],[c_810,c_66]) ).
tcf(c_879,plain,
addition(iPr_def_12,sK2) = one,
inference(superposition,[status(thm)],[c_811,c_66]) ).
tcf(c_883,plain,
one = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_879,c_794]) ).
tcf(c_884,plain,
one = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_878,c_793]) ).
tcf(c_892,plain,
! [X0: $i] : multiplication(X0,iPr_def_13) = X0,
inference(demodulation,[status(thm)],[c_54,c_883]) ).
tcf(c_893,plain,
( ~ leq(iPr_def_14,iPr_def_13)
| ~ leq(iPr_def_13,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_498,c_883]) ).
tcf(c_896,plain,
iPr_def_11 = iPr_def_14,
inference(demodulation,[status(thm)],[c_497,c_892]) ).
tcf(c_991,plain,
iPr_def_11 = iPr_def_13,
inference(demodulation,[status(thm)],[c_883,c_884]) ).
tcf(c_1005,plain,
~ leq(iPr_def_11,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_893,c_896,c_991]) ).
tcf(c_1006,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1005,c_833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 18:33:22 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 2.26/1.29 % SZS status Started for theBenchmark.p
% 2.26/1.29 % SZS status Theorem for theBenchmark.p
% 2.26/1.29
% 2.26/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.26/1.29
% 2.26/1.29 % ------ iProver source info
% 2.26/1.29
% 2.26/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.26/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.26/1.29 % git: non_committed_changes: false
% 2.26/1.29
% 2.26/1.29 % ------ Parsing...
% 2.26/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.26/1.29
% 2.26/1.29 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.26/1.29
% 2.26/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.26/1.29
% 2.26/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.26/1.29 % ------ Proving...
% 2.26/1.29 % ------ Problem Properties
% 2.26/1.29
% 2.26/1.29 %
% 2.26/1.29 % clauses 29
% 2.26/1.29 % conjectures 2
% 2.26/1.29 % EPR 4
% 2.26/1.29 % Horn 28
% 2.26/1.29 % unary 18
% 2.26/1.29 % binary 9
% 2.26/1.29 % lits 43
% 2.26/1.29 % lits eq 25
% 2.26/1.29 % fd_pure 0
% 2.26/1.29 % fd_pseudo 0
% 2.26/1.29 % fd_cond 0
% 2.26/1.29 % fd_pseudo_cond 1
% 2.26/1.29 % AC symbols 1
% 2.26/1.29
% 2.26/1.29 % ------ Schedule dynamic 5 is on
% 2.26/1.29
% 2.26/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.26/1.29
% 2.26/1.29
% 2.26/1.29 % ------
% 2.26/1.29 % Current options:
% 2.26/1.29 % ------
% 2.26/1.29
% 2.26/1.29
% 2.26/1.29 %
% 2.26/1.29
% 2.26/1.29 % ------ Proving...
% 2.26/1.29 %
% 2.26/1.29
% 2.26/1.29 % SZS status Theorem for theBenchmark.p
% 2.26/1.29
% 2.26/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.26/1.30
% 2.26/1.30
%------------------------------------------------------------------------------