%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE025+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 01:52:12 PM UTC 2026
% Result : Theorem 4.39s 1.28s
% Output : CNFRefutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 72 ( 55 unt; 6 def)
% Number of atoms : 159 ( 82 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 : 81 ( 0 sgn 75 !; 6 ?; 24 :)
% 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(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(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox2/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/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(f17,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/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,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)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f21,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,[],[f18]) ).
fof(f22,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,[],[f21]) ).
fof(f26,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(f27,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,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f29,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)],[f22]) ).
fof(f30,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f31,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f34,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f35,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f37,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f40,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f43,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
test(sK3),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
zero = multiplication(multiplication(sK2,sK1),c(sK3)),
inference(cnf_transformation,[],[f29]) ).
fof(f53,plain,
multiplication(sK2,sK1) != multiplication(multiplication(sK2,sK1),sK3),
inference(cnf_transformation,[],[f29]) ).
fof(f54,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f47]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f30]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f31]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f32]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f35]) ).
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,[],[f37]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f40]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_67,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_69,negated_conjecture,
multiplication(multiplication(sK2,sK1),sK3) != multiplication(sK2,sK1),
inference(cnf_transformation,[],[f53]) ).
tcf(c_70,negated_conjecture,
multiplication(multiplication(sK2,sK1),c(sK3)) = zero,
inference(cnf_transformation,[],[f52]) ).
tcf(c_72,negated_conjecture,
test(sK3),
inference(cnf_transformation,[],[f50]) ).
tcf(c_193,plain,
multiplication(sK2,multiplication(sK1,sK3)) != multiplication(sK2,sK1),
inference(demodulation,[status(thm)],[c_69,c_53]) ).
tcf(c_194,plain,
multiplication(sK2,multiplication(sK1,c(sK3))) = zero,
inference(demodulation,[status(thm)],[c_70,c_53]) ).
tcf(c_474,definition,
iPr_def_10 = c(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_475,definition,
iPr_def_11 = multiplication(sK1,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_476,definition,
iPr_def_12 = multiplication(sK2,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_477,definition,
iPr_def_13 = multiplication(sK1,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_478,definition,
iPr_def_14 = multiplication(sK2,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_479,definition,
iPr_def_15 = multiplication(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_480,plain,
iPr_def_12 = zero,
inference(demodulation,[status(thm)],[c_194,c_474,c_475,c_476]) ).
tcf(c_481,plain,
iPr_def_14 != iPr_def_15,
inference(demodulation,[status(thm)],[c_193,c_479,c_477,c_478]) ).
tcf(c_482,negated_conjecture,
test(sK3),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_745,plain,
! [X0: $i] : addition(X0,iPr_def_12) = X0,
inference(light_normalisation,[status(thm)],[c_51,c_480]) ).
tcf(c_747,plain,
! [X0: $i] : multiplication(iPr_def_12,X0) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_59,c_480]) ).
tcf(c_759,plain,
( complement(sK3,iPr_def_10)
| ~ test(sK3) ),
inference(superposition,[status(thm)],[c_474,c_67]) ).
tcf(c_763,plain,
complement(sK3,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_759,c_482]) ).
tcf(c_777,plain,
! [X0: $i] : addition(iPr_def_12,X0) = X0,
inference(superposition,[status(thm)],[c_745,c_49]) ).
tcf(c_846,plain,
addition(iPr_def_10,sK3) = one,
inference(superposition,[status(thm)],[c_763,c_65]) ).
tcf(c_983,plain,
! [X0: $i] : multiplication(sK2,multiplication(iPr_def_11,X0)) = multiplication(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_476,c_53]) ).
tcf(c_995,plain,
! [X0: $i] : multiplication(sK2,multiplication(iPr_def_11,X0)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_983,c_747]) ).
tcf(c_1052,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,sK3)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_846,c_56]) ).
tcf(c_1069,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_10),multiplication(X0,sK3)) = X0,
inference(light_normalisation,[status(thm)],[c_1052,c_54]) ).
tcf(c_1206,plain,
multiplication(sK2,iPr_def_11) = iPr_def_12,
inference(superposition,[status(thm)],[c_54,c_995]) ).
tcf(c_2479,plain,
addition(multiplication(sK1,iPr_def_10),iPr_def_13) = sK1,
inference(superposition,[status(thm)],[c_477,c_1069]) ).
tcf(c_2492,plain,
addition(iPr_def_13,multiplication(sK1,iPr_def_10)) = sK1,
inference(theory_normalisation,[status(thm)],[c_2479,c_50,c_49]) ).
tcf(c_2493,plain,
addition(iPr_def_13,iPr_def_11) = sK1,
inference(light_normalisation,[status(thm)],[c_2492,c_475]) ).
tcf(c_2494,plain,
addition(iPr_def_11,iPr_def_13) = sK1,
inference(theory_normalisation,[status(thm)],[c_2493,c_50,c_49]) ).
tcf(c_2504,plain,
multiplication(sK2,addition(iPr_def_11,iPr_def_13)) = iPr_def_15,
inference(demodulation,[status(thm)],[c_479,c_2494]) ).
tcf(c_2624,plain,
iPr_def_14 = iPr_def_15,
inference(demodulation,[status(thm)],[c_2504,c_56,c_478,c_777,c_1206]) ).
tcf(c_2625,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2624,c_481]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE025+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 18:42:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 4.39/1.28 % SZS status Started for theBenchmark.p
% 4.39/1.28 % SZS status Theorem for theBenchmark.p
% 4.39/1.28
% 4.39/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.39/1.28
% 4.39/1.28 % ------ iProver source info
% 4.39/1.28
% 4.39/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.39/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.39/1.28 % git: non_committed_changes: false
% 4.39/1.28
% 4.39/1.28 % ------ Parsing...
% 4.39/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.39/1.28
% 4.39/1.28 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.39/1.28
% 4.39/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.39/1.28
% 4.39/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.39/1.28 % ------ Proving...
% 4.39/1.28 % ------ Problem Properties
% 4.39/1.28
% 4.39/1.28 %
% 4.39/1.28 % clauses 30
% 4.39/1.28 % conjectures 2
% 4.39/1.28 % EPR 5
% 4.39/1.28 % Horn 29
% 4.39/1.28 % unary 21
% 4.39/1.28 % binary 7
% 4.39/1.28 % lits 42
% 4.39/1.28 % lits eq 27
% 4.39/1.28 % fd_pure 0
% 4.39/1.28 % fd_pseudo 0
% 4.39/1.28 % fd_cond 0
% 4.39/1.28 % fd_pseudo_cond 1
% 4.39/1.28 % AC symbols 1
% 4.39/1.28
% 4.39/1.28 % ------ Schedule dynamic 5 is on
% 4.39/1.28
% 4.39/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.39/1.28
% 4.39/1.28
% 4.39/1.28 % ------
% 4.39/1.28 % Current options:
% 4.39/1.28 % ------
% 4.39/1.28
% 4.39/1.28
% 4.39/1.28 %
% 4.39/1.28
% 4.39/1.28 % ------ Proving...
% 4.39/1.28 %
% 4.39/1.28
% 4.39/1.28 % SZS status Theorem for theBenchmark.p
% 4.39/1.28
% 4.39/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.39/1.29
% 4.39/1.29
%------------------------------------------------------------------------------