%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE020+1 : 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 : 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 01:52:10 PM UTC 2026
% Result : Theorem 6.76s 6.97s
% Output : CNFRefutation 6.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 78 ( 58 unt; 0 def)
% Number of atoms : 128 ( 77 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 80 ( 30 ~; 22 |; 24 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 103 ( 0 sgn 94 !; 9 ?; 40 :)
% 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(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
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(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(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(f17,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1)
& test(X0) )
=> addition(X0,multiplication(X1,X2)) = multiplication(addition(X0,X1),addition(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1)
& test(X0) )
=> addition(X0,multiplication(X1,X2)) = multiplication(addition(X0,X1),addition(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] :
( test(X2)
& test(X1)
& test(X0)
& addition(X0,multiplication(X1,X2)) != multiplication(addition(X0,X1),addition(X0,X2)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
? [X0,X1,X2] :
( test(X2)
& test(X1)
& test(X0)
& addition(X0,multiplication(X1,X2)) != multiplication(addition(X0,X1),addition(X0,X2)) ),
inference(flattening,[],[f19]) ).
fof(f23,plain,
( test(sK2)
& test(sK1)
& test(sK0)
& addition(sK0,multiplication(sK1,sK2)) != multiplication(addition(sK0,sK1),addition(sK0,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f20]) ).
fof(f24,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X0] :
( ( ~ test(X0)
| ? [X2] : complement(X2,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f26,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))],[f25]) ).
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,
test(sK2),
inference(cnf_transformation,[],[f23]) ).
fof(f31,plain,
test(sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f32,plain,
test(sK0),
inference(cnf_transformation,[],[f23]) ).
fof(f33,plain,
addition(sK0,multiplication(sK1,sK2)) != multiplication(addition(sK0,sK1),addition(sK0,sK2)),
inference(cnf_transformation,[],[f23]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f35,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f36,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f38,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f39,plain,
! [X0] :
( ~ test(X0)
| complement(sK3(X0),X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f44,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f29]) ).
fof(f46,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f51,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f52,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f53,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
tcf(c_49,negated_conjecture,
multiplication(addition(sK0,sK1),addition(sK0,sK2)) != addition(sK0,multiplication(sK1,sK2)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_50,negated_conjecture,
test(sK0),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,negated_conjecture,
test(sK1),
inference(cnf_transformation,[],[f31]) ).
tcf(c_52,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f30]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f34]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_55,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f36]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f38]) ).
tcf(c_59,plain,
! [X0: $i] :
( complement(sK3(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( multiplication(X1,X0) = zero )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_70,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f51]) ).
tcf(c_71,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f52]) ).
tcf(c_72,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f53]) ).
tcf(c_718,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_56,c_57]) ).
tcf(c_721,plain,
addition(multiplication(sK0,sK0),addition(multiplication(sK1,sK0),addition(multiplication(sK0,sK2),multiplication(sK1,sK2)))) != addition(sK0,multiplication(sK1,sK2)),
inference(demodulation,[status(thm)],[c_49,c_53,c_54,c_56,c_718]) ).
tcf(c_727,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(superposition,[status(thm)],[c_55,c_718]) ).
tcf(c_757,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_70,c_57]) ).
tcf(c_775,plain,
! [X0: $i] :
( ( multiplication(X0,sK3(X0)) = zero )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_59,c_64]) ).
tcf(c_795,plain,
! [X0: $i] :
( ( addition(X0,sK3(X0)) = one )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_59,c_66]) ).
tcf(c_805,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_57,c_727]) ).
tcf(c_828,plain,
multiplication(sK0,sK3(sK0)) = zero,
inference(superposition,[status(thm)],[c_50,c_775]) ).
tcf(c_1351,plain,
addition(sK0,sK3(sK0)) = one,
inference(superposition,[status(thm)],[c_50,c_795]) ).
tcf(c_1352,plain,
addition(sK1,sK3(sK1)) = one,
inference(superposition,[status(thm)],[c_51,c_795]) ).
tcf(c_1353,plain,
addition(sK2,sK3(sK2)) = one,
inference(superposition,[status(thm)],[c_52,c_795]) ).
tcf(c_1369,plain,
! [X0: $i] : addition(multiplication(X0,sK0),multiplication(X0,sK3(sK0))) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_1351,c_54]) ).
tcf(c_1374,plain,
! [X0: $i] : addition(multiplication(X0,sK0),multiplication(X0,sK3(sK0))) = X0,
inference(light_normalisation,[status(thm)],[c_1369,c_72]) ).
tcf(c_1413,plain,
addition(sK1,one) = one,
inference(superposition,[status(thm)],[c_1352,c_805]) ).
tcf(c_1420,plain,
addition(one,sK1) = one,
inference(theory_normalisation,[status(thm)],[c_1413,c_56,c_57]) ).
tcf(c_1495,plain,
! [X0: $i] : addition(multiplication(one,X0),multiplication(sK1,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_1420,c_53]) ).
tcf(c_1502,plain,
! [X0: $i] : addition(X0,multiplication(sK1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1495,c_71]) ).
tcf(c_1511,plain,
addition(sK2,one) = one,
inference(superposition,[status(thm)],[c_1353,c_805]) ).
tcf(c_1518,plain,
addition(one,sK2) = one,
inference(theory_normalisation,[status(thm)],[c_1511,c_56,c_57]) ).
tcf(c_1953,plain,
! [X0: $i] : addition(multiplication(X0,one),multiplication(X0,sK2)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_1518,c_54]) ).
tcf(c_1957,plain,
! [X0: $i] : addition(X0,multiplication(X0,sK2)) = X0,
inference(light_normalisation,[status(thm)],[c_1953,c_72]) ).
tcf(c_2177,plain,
! [X0: $i,X1: $i] : addition(X0,addition(multiplication(sK1,X0),X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_1502,c_56]) ).
tcf(c_2634,plain,
! [X0: $i,X1: $i] : addition(X0,addition(multiplication(X0,sK2),X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_1957,c_56]) ).
tcf(c_10705,plain,
addition(multiplication(sK0,sK0),zero) = sK0,
inference(superposition,[status(thm)],[c_828,c_1374]) ).
tcf(c_10715,plain,
addition(zero,multiplication(sK0,sK0)) = sK0,
inference(theory_normalisation,[status(thm)],[c_10705,c_56,c_57]) ).
tcf(c_10746,plain,
multiplication(sK0,sK0) = sK0,
inference(demodulation,[status(thm)],[c_10715,c_757]) ).
tcf(c_10749,plain,
addition(sK0,addition(multiplication(sK1,sK0),addition(multiplication(sK0,sK2),multiplication(sK1,sK2)))) != addition(sK0,multiplication(sK1,sK2)),
inference(demodulation,[status(thm)],[c_721,c_10746]) ).
tcf(c_10750,plain,
$false,
inference(ground_joinability,[status(thm)],[c_10749,c_2177,c_2634]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE020+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.60 % Computer : n018.cluster.edu
% 0.10/5.60 % Model : x86_64 x86_64
% 0.10/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.60 % Memory : 8046.5625MB
% 0.10/5.60 % OS : Linux 6.8.0-71-generic
% 0.10/5.60 % CPULimit : 300
% 0.10/5.60 % WCLimit : 300
% 0.10/5.60 % DateTime : Wed Sep 23 18:39:24 UTC 2026
% 0.10/5.61 % CPUTime :
% 0.10/5.61 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.64 Running first-order theorem proving
% 0.10/5.65 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
% 0.10/5.66
% 0.10/5.66 % ======== iProver multi-core TPTP/SMT =========
% 0.10/5.66
% 0.10/5.66 % Detected problem language: tptp
% 0.10/5.67 % Proving...
% 6.76/6.97 % SZS status Started for theBenchmark.p
% 6.76/6.97 % SZS status Theorem for theBenchmark.p
% 6.76/6.97
% 6.76/6.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.76/6.97
% 6.76/6.97 % ------ iProver source info
% 6.76/6.97
% 6.76/6.97 % git: date: 2026-07-19 20:42:38 +0200
% 6.76/6.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.76/6.97 % git: non_committed_changes: false
% 6.76/6.97
% 6.76/6.97 % ------ Parsing...
% 6.76/6.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.76/6.97
% 6.76/6.97 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 6.76/6.97
% 6.76/6.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.76/6.97
% 6.76/6.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.76/6.97 % ------ Proving...
% 6.76/6.97 % ------ Problem Properties
% 6.76/6.97
% 6.76/6.97 %
% 6.76/6.97 % clauses 24
% 6.76/6.97 % conjectures 4
% 6.76/6.97 % EPR 4
% 6.76/6.97 % Horn 23
% 6.76/6.97 % unary 15
% 6.76/6.97 % binary 7
% 6.76/6.97 % lits 36
% 6.76/6.97 % lits eq 20
% 6.76/6.97 % fd_pure 0
% 6.76/6.97 % fd_pseudo 0
% 6.76/6.97 % fd_cond 0
% 6.76/6.97 % fd_pseudo_cond 1
% 6.76/6.97 % AC symbols 1
% 6.76/6.97
% 6.76/6.97 % ------ Schedule dynamic 5 is on
% 6.76/6.97
% 6.76/6.97 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.76/6.97
% 6.76/6.97
% 6.76/6.97 % ------
% 6.76/6.97 % Current options:
% 6.76/6.97 % ------
% 6.76/6.97
% 6.76/6.97
% 6.76/6.97 %
% 6.76/6.97
% 6.76/6.97 % ------ Proving...
% 6.76/6.97 %
% 6.76/6.97
% 6.76/6.97 % SZS status Theorem for theBenchmark.p
% 6.76/6.97
% 6.76/6.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.76/6.98
% 6.76/6.98
%------------------------------------------------------------------------------