%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE009+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 : n004.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 3.72s 1.27s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 66 ( 48 unt; 5 def)
% Number of atoms : 140 ( 66 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 76 ( 33 ~; 20 |; 17 &)
% ( 3 <=>; 3 =>; 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 : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 61 !; 4 ?; 16 :)
% 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(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/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/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(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(f19,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> 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(f20,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> 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] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f27,plain,
? [X0,X1] :
( test(X0)
& test(X1)
& 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(f28,plain,
? [X0,X1] :
( test(X0)
& test(X1)
& one != addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
inference(flattening,[],[f27]) ).
fof(f32,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(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(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f35,plain,
( test(sK1)
& test(sK2)
& 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)],[f28]) ).
fof(f36,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f37,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f42,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f43,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f44,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] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f33]) ).
fof(f53,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f58,plain,
test(sK1),
inference(cnf_transformation,[],[f35]) ).
fof(f59,plain,
test(sK2),
inference(cnf_transformation,[],[f35]) ).
fof(f60,plain,
one != addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))),
inference(cnf_transformation,[],[f35]) ).
fof(f61,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f53]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f36]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f42]) ).
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,[],[f43]) ).
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,[],[f44]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_67,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_71,negated_conjecture,
addition(addition(addition(multiplication(sK1,sK2),multiplication(sK1,c(sK2))),multiplication(c(sK1),sK2)),multiplication(c(sK1),c(sK2))) != one,
inference(cnf_transformation,[],[f60]) ).
tcf(c_72,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f59]) ).
tcf(c_73,negated_conjecture,
test(sK1),
inference(cnf_transformation,[],[f58]) ).
tcf(c_92,negated_conjecture,
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_71,c_50,c_49]) ).
tcf(c_219,plain,
addition(multiplication(sK1,sK2),addition(multiplication(sK1,c(sK2)),multiplication(c(sK1),addition(c(sK2),sK2)))) != one,
inference(ac_demodulation,[status(thm)],[c_92,c_56,c_50,c_49]) ).
tcf(c_220,plain,
addition(multiplication(c(sK1),addition(c(sK2),sK2)),multiplication(sK1,addition(c(sK2),sK2))) != one,
inference(ac_demodulation,[status(thm)],[c_219,c_56,c_50,c_49]) ).
tcf(c_221,plain,
multiplication(addition(c(sK1),sK1),addition(c(sK2),sK2)) != one,
inference(ac_demodulation,[status(thm)],[c_220,c_57,c_50,c_49]) ).
tcf(c_222,plain,
multiplication(addition(sK1,c(sK1)),addition(sK2,c(sK2))) != one,
inference(theory_normalisation,[status(thm)],[c_221,c_50,c_49]) ).
tcf(c_383,definition,
iPr_def_10 = c(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_384,definition,
iPr_def_11 = addition(sK1,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_385,definition,
iPr_def_12 = c(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_386,definition,
iPr_def_13 = addition(sK2,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_387,definition,
iPr_def_14 = multiplication(iPr_def_11,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_388,plain,
iPr_def_14 != one,
inference(demodulation,[status(thm)],[c_222,c_385,c_386,c_383,c_384,c_387]) ).
tcf(c_389,negated_conjecture,
test(sK1),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_390,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_668,plain,
addition(iPr_def_10,sK1) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_384,c_50,c_49]) ).
tcf(c_671,plain,
addition(iPr_def_12,sK2) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_386,c_50,c_49]) ).
tcf(c_681,plain,
( complement(sK2,iPr_def_12)
| ~ test(sK2) ),
inference(superposition,[status(thm)],[c_385,c_67]) ).
tcf(c_682,plain,
( complement(sK1,iPr_def_10)
| ~ test(sK1) ),
inference(superposition,[status(thm)],[c_383,c_67]) ).
tcf(c_686,plain,
complement(sK1,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_682,c_389]) ).
tcf(c_687,plain,
complement(sK2,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_681,c_390]) ).
tcf(c_764,plain,
addition(iPr_def_12,sK2) = one,
inference(superposition,[status(thm)],[c_687,c_65]) ).
tcf(c_765,plain,
addition(iPr_def_10,sK1) = one,
inference(superposition,[status(thm)],[c_686,c_65]) ).
tcf(c_766,plain,
one = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_765,c_668]) ).
tcf(c_767,plain,
one = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_764,c_671]) ).
tcf(c_774,plain,
! [X0: $i] : multiplication(iPr_def_11,X0) = X0,
inference(demodulation,[status(thm)],[c_55,c_766]) ).
tcf(c_776,plain,
iPr_def_11 != iPr_def_14,
inference(demodulation,[status(thm)],[c_388,c_766]) ).
tcf(c_777,plain,
iPr_def_13 = iPr_def_14,
inference(demodulation,[status(thm)],[c_387,c_774]) ).
tcf(c_795,plain,
iPr_def_11 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_767,c_766]) ).
tcf(c_797,plain,
iPr_def_11 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_777,c_795]) ).
tcf(c_798,plain,
$false,
inference(ground_joinability,[status(thm)],[c_776,c_797]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 18:34:35 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 3.72/1.27 % SZS status Started for theBenchmark.p
% 3.72/1.27 % SZS status Theorem for theBenchmark.p
% 3.72/1.27
% 3.72/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.72/1.27
% 3.72/1.27 % ------ iProver source info
% 3.72/1.27
% 3.72/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.72/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.72/1.27 % git: non_committed_changes: false
% 3.72/1.27
% 3.72/1.27 % ------ Parsing...
% 3.72/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.72/1.27
% 3.72/1.27 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.72/1.27
% 3.72/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.72/1.27
% 3.72/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.72/1.27 % ------ Proving...
% 3.72/1.27 % ------ Problem Properties
% 3.72/1.27
% 3.72/1.27 %
% 3.72/1.27 % clauses 30
% 3.72/1.27 % conjectures 2
% 3.72/1.27 % EPR 4
% 3.72/1.27 % Horn 29
% 3.72/1.27 % unary 19
% 3.72/1.27 % binary 7
% 3.72/1.27 % lits 46
% 3.72/1.27 % lits eq 27
% 3.72/1.27 % fd_pure 0
% 3.72/1.27 % fd_pseudo 0
% 3.72/1.27 % fd_cond 0
% 3.72/1.27 % fd_pseudo_cond 1
% 3.72/1.27 % AC symbols 1
% 3.72/1.27
% 3.72/1.27 % ------ Schedule dynamic 5 is on
% 3.72/1.27
% 3.72/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.72/1.27
% 3.72/1.27
% 3.72/1.27 % ------
% 3.72/1.27 % Current options:
% 3.72/1.27 % ------
% 3.72/1.27
% 3.72/1.27
% 3.72/1.27 %
% 3.72/1.27
% 3.72/1.27 % ------ Proving...
% 3.72/1.27 %
% 3.72/1.27
% 3.72/1.27 % SZS status Theorem for theBenchmark.p
% 3.72/1.27
% 3.72/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.72/1.28
% 3.72/1.28
%------------------------------------------------------------------------------