%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE026+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 : n011.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 01:52:12 PM UTC 2026
% Result : Theorem 3.79s 1.23s
% Output : CNFRefutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 38 unt; 0 def)
% Number of atoms : 115 ( 64 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 86 ( 32 ~; 24 |; 22 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 85 !; 9 ?; 29 :)
% 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(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/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/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(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+1.ax',test_1) ).
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(f19,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
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,X2] :
( test(X2)
& test(X1)
& multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
& ~ leq(multiplication(X1,X0),multiplication(X0,X2)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f23,plain,
? [X0,X1,X2] :
( test(X2)
& test(X1)
& multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
& ~ leq(multiplication(X1,X0),multiplication(X0,X2)) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f31,plain,
( test(sK2)
& test(sK1)
& multiplication(sK1,sK0) = multiplication(multiplication(sK1,sK0),sK2)
& ~ leq(multiplication(sK1,sK0),multiplication(sK0,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f23]) ).
fof(f33,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(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(flattening,[],[f33]) ).
fof(f35,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f36,plain,
! [X0] :
( ( ~ test(X0)
| ? [X2] : complement(X2,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(rectify,[],[f35]) ).
fof(f37,plain,
! [X0] :
( ( ~ test(X0)
| complement(sK3(X0),X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0))],[f36]) ).
fof(f39,plain,
test(sK1),
inference(cnf_transformation,[],[f31]) ).
fof(f40,plain,
multiplication(sK1,sK0) = multiplication(multiplication(sK1,sK0),sK2),
inference(cnf_transformation,[],[f31]) ).
fof(f41,plain,
~ leq(multiplication(sK1,sK0),multiplication(sK0,sK2)),
inference(cnf_transformation,[],[f31]) ).
fof(f42,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f46,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f48,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f50,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f51,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f57,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f34]) ).
fof(f61,plain,
! [X0] :
( ~ test(X0)
| complement(sK3(X0),X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f63,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
~ leq(multiplication(sK1,sK0),multiplication(sK0,sK2)),
inference(cnf_transformation,[],[f41]) ).
tcf(c_50,negated_conjecture,
multiplication(multiplication(sK1,sK0),sK2) = multiplication(sK1,sK0),
inference(cnf_transformation,[],[f40]) ).
tcf(c_51,negated_conjecture,
test(sK1),
inference(cnf_transformation,[],[f39]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f42]) ).
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_59,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f48]) ).
tcf(c_60,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f49]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f51]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_73,plain,
! [X0: $i] :
( complement(sK3(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_74,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f63]) ).
tcf(c_219,plain,
multiplication(sK1,multiplication(sK0,sK2)) = multiplication(sK1,sK0),
inference(demodulation,[status(thm)],[c_50,c_59]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] :
( ( multiplication(sK0,sK2) != X1 )
| ( multiplication(sK1,sK0) != X0 )
| ( addition(X0,X1) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_53]) ).
tcf(c_250,plain,
addition(multiplication(sK1,sK0),multiplication(sK0,sK2)) != multiplication(sK0,sK2),
inference(unflattening,[status(thm)],[c_249]) ).
tcf(c_935,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_61,c_62]) ).
tcf(c_942,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(superposition,[status(thm)],[c_60,c_935]) ).
tcf(c_1012,plain,
! [X0: $i] :
( ( addition(X0,sK3(X0)) = one )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_73,c_71]) ).
tcf(c_2176,plain,
addition(sK1,sK3(sK1)) = one,
inference(superposition,[status(thm)],[c_51,c_1012]) ).
tcf(c_2214,plain,
! [X0: $i] : addition(sK1,addition(sK3(sK1),X0)) = addition(one,X0),
inference(superposition,[status(thm)],[c_2176,c_61]) ).
tcf(c_2298,plain,
addition(sK3(sK1),sK1) = addition(one,sK1),
inference(superposition,[status(thm)],[c_2214,c_942]) ).
tcf(c_2299,plain,
addition(sK1,sK3(sK1)) = addition(one,sK1),
inference(theory_normalisation,[status(thm)],[c_2298,c_61,c_62]) ).
tcf(c_2300,plain,
addition(one,sK1) = one,
inference(light_normalisation,[status(thm)],[c_2299,c_2176]) ).
tcf(c_2346,plain,
! [X0: $i] : addition(multiplication(one,X0),multiplication(sK1,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_2300,c_57]) ).
tcf(c_2353,plain,
! [X0: $i] : addition(X0,multiplication(sK1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2346,c_74]) ).
tcf(c_2781,plain,
addition(multiplication(sK0,sK2),multiplication(sK1,sK0)) = multiplication(sK0,sK2),
inference(superposition,[status(thm)],[c_219,c_2353]) ).
tcf(c_2809,plain,
addition(multiplication(sK1,sK0),multiplication(sK0,sK2)) = multiplication(sK0,sK2),
inference(theory_normalisation,[status(thm)],[c_2781,c_61,c_62]) ).
tcf(c_2810,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2809,c_250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE026+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 % Computer : n011.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Wed Sep 23 18:39:57 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 0.14/0.45
% 0.14/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.45
% 0.14/0.45 % Detected problem language: tptp
% 0.19/0.46 % Proving...
% 3.79/1.23 % SZS status Started for theBenchmark.p
% 3.79/1.23 % SZS status Theorem for theBenchmark.p
% 3.79/1.23
% 3.79/1.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.79/1.23
% 3.79/1.23 % ------ iProver source info
% 3.79/1.23
% 3.79/1.23 % git: date: 2026-07-19 20:42:38 +0200
% 3.79/1.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.79/1.23 % git: non_committed_changes: false
% 3.79/1.23
% 3.79/1.23 % ------ Parsing...
% 3.79/1.23 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.79/1.23
% 3.79/1.23 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.79/1.23
% 3.79/1.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.79/1.23
% 3.79/1.23 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.79/1.23 % ------ Proving...
% 3.79/1.23 % ------ Problem Properties
% 3.79/1.23
% 3.79/1.23 %
% 3.79/1.23 % clauses 26
% 3.79/1.23 % conjectures 2
% 3.79/1.23 % EPR 3
% 3.79/1.23 % Horn 25
% 3.79/1.23 % unary 15
% 3.79/1.23 % binary 7
% 3.79/1.23 % lits 42
% 3.79/1.23 % lits eq 23
% 3.79/1.23 % fd_pure 0
% 3.79/1.23 % fd_pseudo 0
% 3.79/1.23 % fd_cond 0
% 3.79/1.23 % fd_pseudo_cond 1
% 3.79/1.23 % AC symbols 1
% 3.79/1.23
% 3.79/1.23 % ------ Schedule dynamic 5 is on
% 3.79/1.23
% 3.79/1.23 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.79/1.23
% 3.79/1.23
% 3.79/1.23 % ------
% 3.79/1.23 % Current options:
% 3.79/1.23 % ------
% 3.79/1.23
% 3.79/1.23
% 3.79/1.23 %
% 3.79/1.23
% 3.79/1.23 % ------ Proving...
% 3.79/1.23 %
% 3.79/1.23
% 3.79/1.23 % SZS status Theorem for theBenchmark.p
% 3.79/1.23
% 3.79/1.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.79/1.23
% 3.79/1.23
%------------------------------------------------------------------------------