%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE026+1 : 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 : n001.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 3.15s 6.18s
% Output : CNFRefutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 69 ( 45 unt; 4 def)
% Number of atoms : 147 ( 76 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 90 ( 35 ~; 25 |; 20 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 83 !; 6 ?; 26 :)
% 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(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
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(f17,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/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,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)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f20,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
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(ennf_transformation,[],[f18]) ).
fof(f24,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,[],[f23]) ).
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,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| c(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f31,plain,
( test(sK3)
& test(sK2)
& multiplication(sK2,sK1) = multiplication(multiplication(sK2,sK1),sK3)
& ~ leq(multiplication(sK2,sK1),multiplication(sK1,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f24]) ).
fof(f32,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f33,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f35,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X2,X0,X1] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f38,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f40,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f43,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f46,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f29]) ).
fof(f50,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
test(sK2),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
multiplication(sK2,sK1) = multiplication(multiplication(sK2,sK1),sK3),
inference(cnf_transformation,[],[f31]) ).
fof(f56,plain,
~ leq(multiplication(sK2,sK1),multiplication(sK1,sK3)),
inference(cnf_transformation,[],[f31]) ).
fof(f57,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f50]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f32]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f35]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f38]) ).
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,[],[f40]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_68,plain,
! [X0: $i] :
( complement(X0,c(X0))
| ~ test(X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_70,negated_conjecture,
~ leq(multiplication(sK2,sK1),multiplication(sK1,sK3)),
inference(cnf_transformation,[],[f56]) ).
tcf(c_71,negated_conjecture,
multiplication(multiplication(sK2,sK1),sK3) = multiplication(sK2,sK1),
inference(cnf_transformation,[],[f55]) ).
tcf(c_72,negated_conjecture,
test(sK2),
inference(cnf_transformation,[],[f54]) ).
tcf(c_203,plain,
multiplication(sK2,multiplication(sK1,sK3)) = multiplication(sK2,sK1),
inference(demodulation,[status(thm)],[c_71,c_53]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i] :
( ( multiplication(sK1,sK3) != X1 )
| ( multiplication(sK2,sK1) != X0 )
| ( addition(X0,X1) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_70]) ).
tcf(c_221,plain,
addition(multiplication(sK2,sK1),multiplication(sK1,sK3)) != multiplication(sK1,sK3),
inference(unflattening,[status(thm)],[c_220]) ).
tcf(c_854,definition,
iPr_def_10 = multiplication(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_855,definition,
iPr_def_11 = multiplication(sK1,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_856,definition,
iPr_def_12 = addition(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_857,definition,
iPr_def_13 = multiplication(sK2,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_858,plain,
iPr_def_12 != iPr_def_11,
inference(demodulation,[status(thm)],[c_221,c_855,c_854,c_856]) ).
tcf(c_859,plain,
iPr_def_13 = iPr_def_10,
inference(demodulation,[status(thm)],[c_203,c_857]) ).
tcf(c_861,negated_conjecture,
test(sK2),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_1107,plain,
multiplication(sK2,iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_857,c_859]) ).
tcf(c_1161,plain,
! [X0: $i] :
( ( addition(c(X0),X0) = one )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_68,c_66]) ).
tcf(c_1162,plain,
! [X0: $i] :
( ( addition(X0,c(X0)) = one )
| ~ test(X0) ),
inference(theory_normalisation,[status(thm)],[c_1161,c_50,c_49]) ).
tcf(c_1193,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_2123,plain,
addition(sK2,c(sK2)) = one,
inference(superposition,[status(thm)],[c_861,c_1162]) ).
tcf(c_3611,plain,
addition(sK2,one) = one,
inference(superposition,[status(thm)],[c_2123,c_1193]) ).
tcf(c_3651,plain,
addition(one,sK2) = one,
inference(theory_normalisation,[status(thm)],[c_3611,c_50,c_49]) ).
tcf(c_3719,plain,
! [X0: $i] : addition(multiplication(one,X0),multiplication(sK2,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_3651,c_57]) ).
tcf(c_3720,plain,
! [X0: $i] : addition(X0,multiplication(sK2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3719,c_55]) ).
tcf(c_4552,plain,
addition(iPr_def_11,iPr_def_10) = iPr_def_11,
inference(superposition,[status(thm)],[c_1107,c_3720]) ).
tcf(c_4574,plain,
addition(iPr_def_10,iPr_def_11) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_4552,c_50,c_49]) ).
tcf(c_4598,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_856,c_4574]) ).
tcf(c_4600,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_858,c_4598]) ).
tcf(c_4601,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_4600]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE026+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.36 % Computer : n001.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Wed Sep 23 18:45:57 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/5.40 Running first-order theorem proving
% 0.12/5.40 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
% 0.12/5.42
% 0.12/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/5.42
% 0.12/5.42 % Detected problem language: tptp
% 0.12/5.43 % Proving...
% 3.15/6.18 % SZS status Started for theBenchmark.p
% 3.15/6.18 % SZS status Theorem for theBenchmark.p
% 3.15/6.18
% 3.15/6.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.15/6.18
% 3.15/6.18 % ------ iProver source info
% 3.15/6.18
% 3.15/6.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.15/6.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.15/6.18 % git: non_committed_changes: false
% 3.15/6.18
% 3.15/6.18 % ------ Parsing...
% 3.15/6.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.15/6.18
% 3.15/6.18 % ------ 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 %
% 3.15/6.18
% 3.15/6.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.15/6.18
% 3.15/6.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.15/6.18 % ------ Proving...
% 3.15/6.18 % ------ Problem Properties
% 3.15/6.18
% 3.15/6.18 %
% 3.15/6.18 % clauses 28
% 3.15/6.18 % conjectures 2
% 3.15/6.18 % EPR 5
% 3.15/6.18 % Horn 27
% 3.15/6.18 % unary 19
% 3.15/6.18 % binary 7
% 3.15/6.18 % lits 40
% 3.15/6.18 % lits eq 25
% 3.15/6.18 % fd_pure 0
% 3.15/6.18 % fd_pseudo 0
% 3.15/6.18 % fd_cond 0
% 3.15/6.18 % fd_pseudo_cond 1
% 3.15/6.18 % AC symbols 1
% 3.15/6.18
% 3.15/6.18 % ------ Schedule dynamic 5 is on
% 3.15/6.18
% 3.15/6.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.15/6.18
% 3.15/6.18
% 3.15/6.18 % ------
% 3.15/6.18 % Current options:
% 3.15/6.18 % ------
% 3.15/6.18
% 3.15/6.18
% 3.15/6.18 %
% 3.15/6.18
% 3.15/6.18 % ------ Proving...
% 3.15/6.18 %
% 3.15/6.18
% 3.15/6.18 % SZS status Theorem for theBenchmark.p
% 3.15/6.18
% 3.15/6.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.15/6.18
% 3.15/6.18
%------------------------------------------------------------------------------