%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE025+2 : 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 : 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 01:52:12 PM UTC 2026
% Result : Theorem 4.84s 7.25s
% Output : CNFRefutation 4.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 76 ( 59 unt; 6 def)
% Number of atoms : 177 ( 86 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 74 ( 27 ~; 19 |; 20 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 76 !; 6 ?; 25 :)
% 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(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f5,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
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,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ),
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,X2] :
( test(X2)
& test(X1)
& multiplication(multiplication(X1,X0),c(X2)) = zero
& multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f28,plain,
? [X0,X1,X2] :
( test(X2)
& test(X1)
& multiplication(multiplication(X1,X0),c(X2)) = zero
& multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2) ),
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(sK3)
& test(sK2)
& zero = multiplication(multiplication(sK2,sK1),c(sK3))
& multiplication(sK2,sK1) != multiplication(multiplication(sK2,sK1),sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[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(f38,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f40,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f41,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f43,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f46,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
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(sK3),
inference(cnf_transformation,[],[f35]) ).
fof(f60,plain,
zero = multiplication(multiplication(sK2,sK1),c(sK3)),
inference(cnf_transformation,[],[f35]) ).
fof(f61,plain,
multiplication(sK2,sK1) != multiplication(multiplication(sK2,sK1),sK3),
inference(cnf_transformation,[],[f35]) ).
fof(f62,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_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f38]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f40]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f41]) ).
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_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f46]) ).
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,[],[f62]) ).
tcf(c_71,negated_conjecture,
multiplication(multiplication(sK2,sK1),sK3) != multiplication(sK2,sK1),
inference(cnf_transformation,[],[f61]) ).
tcf(c_72,negated_conjecture,
multiplication(multiplication(sK2,sK1),c(sK3)) = zero,
inference(cnf_transformation,[],[f60]) ).
tcf(c_74,negated_conjecture,
test(sK3),
inference(cnf_transformation,[],[f58]) ).
tcf(c_209,plain,
multiplication(sK2,multiplication(sK1,sK3)) != multiplication(sK2,sK1),
inference(demodulation,[status(thm)],[c_71,c_53]) ).
tcf(c_210,plain,
multiplication(sK2,multiplication(sK1,c(sK3))) = zero,
inference(demodulation,[status(thm)],[c_72,c_53]) ).
tcf(c_383,definition,
iPr_def_10 = c(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_384,definition,
iPr_def_11 = multiplication(sK1,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_385,definition,
iPr_def_12 = multiplication(sK2,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_386,definition,
iPr_def_13 = multiplication(sK1,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_387,definition,
iPr_def_14 = multiplication(sK2,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_388,definition,
iPr_def_15 = multiplication(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_389,plain,
iPr_def_12 = zero,
inference(demodulation,[status(thm)],[c_210,c_383,c_384,c_385]) ).
tcf(c_390,plain,
iPr_def_14 != iPr_def_15,
inference(demodulation,[status(thm)],[c_209,c_388,c_386,c_387]) ).
tcf(c_391,negated_conjecture,
test(sK3),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_678,plain,
! [X0: $i] : addition(X0,iPr_def_12) = X0,
inference(light_normalisation,[status(thm)],[c_51,c_389]) ).
tcf(c_680,plain,
! [X0: $i] : multiplication(iPr_def_12,X0) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_59,c_389]) ).
tcf(c_692,plain,
( complement(sK3,iPr_def_10)
| ~ test(sK3) ),
inference(superposition,[status(thm)],[c_383,c_67]) ).
tcf(c_696,plain,
complement(sK3,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_692,c_391]) ).
tcf(c_710,plain,
! [X0: $i] : addition(iPr_def_12,X0) = X0,
inference(superposition,[status(thm)],[c_678,c_49]) ).
tcf(c_779,plain,
addition(iPr_def_10,sK3) = one,
inference(superposition,[status(thm)],[c_696,c_65]) ).
tcf(c_909,plain,
! [X0: $i] : multiplication(sK2,multiplication(sK1,X0)) = multiplication(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_388,c_53]) ).
tcf(c_912,plain,
! [X0: $i] : multiplication(sK2,multiplication(iPr_def_11,X0)) = multiplication(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_385,c_53]) ).
tcf(c_924,plain,
! [X0: $i] : multiplication(sK2,multiplication(iPr_def_11,X0)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_912,c_680]) ).
tcf(c_985,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,sK3)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_779,c_56]) ).
tcf(c_1002,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,sK3)) = X0,
inference(light_normalisation,[status(thm)],[c_985,c_54]) ).
tcf(c_1147,plain,
multiplication(sK2,iPr_def_11) = iPr_def_12,
inference(superposition,[status(thm)],[c_54,c_924]) ).
tcf(c_6618,plain,
multiplication(sK2,iPr_def_13) = multiplication(iPr_def_15,sK3),
inference(superposition,[status(thm)],[c_386,c_909]) ).
tcf(c_6620,plain,
multiplication(sK2,iPr_def_11) = multiplication(iPr_def_15,iPr_def_10),
inference(superposition,[status(thm)],[c_384,c_909]) ).
tcf(c_6627,plain,
multiplication(iPr_def_15,iPr_def_10) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_6620,c_1147]) ).
tcf(c_6628,plain,
multiplication(iPr_def_15,sK3) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_6618,c_387]) ).
tcf(c_8843,plain,
addition(multiplication(iPr_def_15,iPr_def_10),iPr_def_14) = iPr_def_15,
inference(superposition,[status(thm)],[c_6628,c_1002]) ).
tcf(c_8858,plain,
addition(iPr_def_14,multiplication(iPr_def_15,iPr_def_10)) = iPr_def_15,
inference(theory_normalisation,[status(thm)],[c_8843,c_50,c_49]) ).
tcf(c_8859,plain,
addition(iPr_def_14,iPr_def_12) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_8858,c_6627]) ).
tcf(c_8860,plain,
addition(iPr_def_12,iPr_def_14) = iPr_def_15,
inference(theory_normalisation,[status(thm)],[c_8859,c_50,c_49]) ).
tcf(c_9183,plain,
iPr_def_14 = iPr_def_15,
inference(demodulation,[status(thm)],[c_8860,c_710]) ).
tcf(c_9184,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_9183,c_390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE025+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.37 % Computer : n007.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Wed Sep 23 18:38:13 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 4.84/7.25 % SZS status Started for theBenchmark.p
% 4.84/7.25 % SZS status Theorem for theBenchmark.p
% 4.84/7.25
% 4.84/7.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.84/7.25
% 4.84/7.25 % ------ iProver source info
% 4.84/7.25
% 4.84/7.25 % git: date: 2026-07-19 20:42:38 +0200
% 4.84/7.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.84/7.25 % git: non_committed_changes: false
% 4.84/7.25
% 4.84/7.25 % ------ Parsing...
% 4.84/7.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.84/7.25
% 4.84/7.25 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.84/7.25
% 4.84/7.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.84/7.25
% 4.84/7.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.84/7.25 % ------ Proving...
% 4.84/7.25 % ------ Problem Properties
% 4.84/7.25
% 4.84/7.25 %
% 4.84/7.25 % clauses 32
% 4.84/7.25 % conjectures 2
% 4.84/7.25 % EPR 5
% 4.84/7.25 % Horn 31
% 4.84/7.25 % unary 21
% 4.84/7.25 % binary 7
% 4.84/7.25 % lits 48
% 4.84/7.25 % lits eq 29
% 4.84/7.25 % fd_pure 0
% 4.84/7.25 % fd_pseudo 0
% 4.84/7.25 % fd_cond 0
% 4.84/7.25 % fd_pseudo_cond 1
% 4.84/7.25 % AC symbols 1
% 4.84/7.25
% 4.84/7.25 % ------ Schedule dynamic 5 is on
% 4.84/7.25
% 4.84/7.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.84/7.25
% 4.84/7.25
% 4.84/7.25 % ------
% 4.84/7.25 % Current options:
% 4.84/7.25 % ------
% 4.84/7.25
% 4.84/7.25
% 4.84/7.25 %
% 4.84/7.25
% 4.84/7.25 % ------ Proving...
% 4.84/7.25 %
% 4.84/7.25
% 4.84/7.25 % SZS status Theorem for theBenchmark.p
% 4.84/7.25
% 4.84/7.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.84/7.25
% 4.84/7.25
%------------------------------------------------------------------------------