%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE009+4 : 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 : n018.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 3.73s 6.28s
% Output : CNFRefutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 43 unt; 5 def)
% Number of atoms : 171 ( 59 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 111 ( 49 ~; 35 |; 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/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(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/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/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(f19,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/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,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)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f22,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f29,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,[],[f20]) ).
fof(f30,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,[],[f29]) ).
fof(f34,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(f35,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,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f37,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)],[f30]) ).
fof(f38,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f39,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f41,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f44,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f45,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f46,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f49,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f52,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f35]) ).
fof(f56,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f61,plain,
test(sK1),
inference(cnf_transformation,[],[f37]) ).
fof(f62,plain,
test(sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f63,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,[],[f37]) ).
fof(f64,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f56]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f38]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f39]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f41]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f44]) ).
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,[],[f45]) ).
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,[],[f46]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_68,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_72,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,[],[f63]) ).
tcf(c_73,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f62]) ).
tcf(c_74,negated_conjecture,
test(sK1),
inference(cnf_transformation,[],[f61]) ).
tcf(c_94,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_72,c_50,c_49]) ).
tcf(c_239,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_94,c_56,c_56,c_50,c_49]) ).
tcf(c_240,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_239,c_56,c_56,c_50,c_49]) ).
tcf(c_241,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_240,c_57,c_57,c_50,c_49]) ).
tcf(c_242,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_241,c_50,c_49]) ).
tcf(c_402,definition,
iPr_def_10 = c(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_403,definition,
iPr_def_11 = addition(sK1,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_404,definition,
iPr_def_12 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_405,definition,
iPr_def_13 = addition(sK2,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_406,definition,
iPr_def_14 = multiplication(iPr_def_11,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_407,plain,
( ~ leq(iPr_def_14,one)
| ~ leq(one,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_242,c_404,c_405,c_402,c_403,c_406]) ).
tcf(c_408,negated_conjecture,
test(sK1),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_409,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_726,plain,
addition(iPr_def_10,sK1) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_403,c_50,c_49]) ).
tcf(c_727,plain,
addition(iPr_def_12,sK2) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_405,c_50,c_49]) ).
tcf(c_741,plain,
( complement(sK2,iPr_def_12)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_404,c_68]) ).
tcf(c_742,plain,
( complement(sK1,iPr_def_10)
| ~ test(sK1) ),
inference(superposition,[status(thm)],[c_402,c_68]) ).
tcf(c_746,plain,
complement(sK1,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_742,c_408]) ).
tcf(c_747,plain,
complement(sK2,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_741,c_409]) ).
tcf(c_781,plain,
! [X0: $i] : leq(X0,X0),
inference(superposition,[status(thm)],[c_52,c_60]) ).
tcf(c_827,plain,
addition(iPr_def_12,sK2) = one,
inference(superposition,[status(thm)],[c_747,c_66]) ).
tcf(c_828,plain,
addition(iPr_def_10,sK1) = one,
inference(superposition,[status(thm)],[c_746,c_66]) ).
tcf(c_829,plain,
one = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_828,c_726]) ).
tcf(c_830,plain,
one = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_827,c_727]) ).
tcf(c_837,plain,
! [X0: $i] : multiplication(iPr_def_11,X0) = X0,
inference(demodulation,[status(thm)],[c_55,c_829]) ).
tcf(c_839,plain,
( ~ leq(iPr_def_14,iPr_def_11)
| ~ leq(iPr_def_11,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_407,c_829]) ).
tcf(c_842,plain,
iPr_def_13 = iPr_def_14,
inference(demodulation,[status(thm)],[c_406,c_837]) ).
tcf(c_849,plain,
iPr_def_11 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_830,c_829]) ).
tcf(c_851,plain,
~ leq(iPr_def_11,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_839,c_842,c_849]) ).
tcf(c_852,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_851,c_781]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n018.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Wed Sep 23 18:37:38 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.42
% 0.14/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42
% 0.14/5.42 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 3.73/6.28 % SZS status Started for theBenchmark.p
% 3.73/6.28 % SZS status Theorem for theBenchmark.p
% 3.73/6.28
% 3.73/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.73/6.28
% 3.73/6.28 % ------ iProver source info
% 3.73/6.28
% 3.73/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.73/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.73/6.28 % git: non_committed_changes: false
% 3.73/6.28
% 3.73/6.28 % ------ Parsing...
% 3.73/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.73/6.28
% 3.73/6.28 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.73/6.28
% 3.73/6.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.73/6.28
% 3.73/6.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.73/6.28 % ------ Proving...
% 3.73/6.28 % ------ Problem Properties
% 3.73/6.28
% 3.73/6.28 %
% 3.73/6.28 % clauses 31
% 3.73/6.28 % conjectures 2
% 3.73/6.28 % EPR 4
% 3.73/6.28 % Horn 30
% 3.73/6.28 % unary 18
% 3.73/6.28 % binary 9
% 3.73/6.28 % lits 49
% 3.73/6.28 % lits eq 27
% 3.73/6.28 % fd_pure 0
% 3.73/6.28 % fd_pseudo 0
% 3.73/6.28 % fd_cond 0
% 3.73/6.28 % fd_pseudo_cond 1
% 3.73/6.28 % AC symbols 1
% 3.73/6.28
% 3.73/6.28 % ------ Schedule dynamic 5 is on
% 3.73/6.28
% 3.73/6.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.73/6.28
% 3.73/6.28
% 3.73/6.28 % ------
% 3.73/6.28 % Current options:
% 3.73/6.28 % ------
% 3.73/6.28
% 3.73/6.28
% 3.73/6.28 %
% 3.73/6.28
% 3.73/6.28 % ------ Proving...
% 3.73/6.28 %
% 3.73/6.28
% 3.73/6.28 % SZS status Theorem for theBenchmark.p
% 3.73/6.28
% 3.73/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.73/6.29
% 3.73/6.29
%------------------------------------------------------------------------------