%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE169+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 01:52:34 PM UTC 2026
% Result : Theorem 46.79s 16.26s
% Output : CNFRefutation 46.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 87 ( 81 unt; 6 def)
% Number of atoms : 155 ( 51 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 6 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 98 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+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/KLE002+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_identity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+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/KLE002+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/KLE002+0.ax',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).
fof(f14,axiom,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
fof(f17,axiom,
sigma = addition(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an) ).
fof(f18,conjecture,
leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a) ).
fof(f19,negated_conjecture,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
inference(flattening,[],[f19]) ).
fof(f23,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
& ( addition(X0,X1) != X1
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f25,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f26,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f27,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f30,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f32,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f35,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f36,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f38,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f41,plain,
sigma = addition(a,b),
inference(cnf_transformation,[],[f17]) ).
fof(f42,plain,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
inference(cnf_transformation,[],[f20]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f25]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f26]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f30]) ).
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,[],[f31]) ).
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,[],[f32]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_63,plain,
! [X0: $i] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_66,plain,
addition(a,b) = sigma,
inference(cnf_transformation,[],[f41]) ).
tcf(c_67,negated_conjecture,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
inference(cnf_transformation,[],[f42]) ).
tcf(c_188,definition,
iPr_def_10 = multiplication(b,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_189,definition,
iPr_def_11 = multiplication(a,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_190,definition,
iPr_def_12 = star(sigma),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_191,definition,
iPr_def_13 = multiplication(sigma,a),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_192,definition,
iPr_def_14 = multiplication(a,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_193,definition,
iPr_def_15 = multiplication(iPr_def_12,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_194,negated_conjecture,
~ leq(iPr_def_11,iPr_def_15),
inference(demodulation,[status(thm)],[c_67,c_191,c_192,c_190,c_193,c_188,c_189]) ).
tcf(c_1226,plain,
leq(addition(one,multiplication(iPr_def_12,sigma)),iPr_def_12),
inference(superposition,[status(thm)],[c_190,c_63]) ).
tcf(c_1622,plain,
addition(addition(one,multiplication(iPr_def_12,sigma)),iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_1226,c_61]) ).
tcf(c_1623,plain,
addition(iPr_def_12,addition(one,multiplication(iPr_def_12,sigma))) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_1622,c_50,c_49]) ).
tcf(c_1808,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_8538,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_1808,c_60]) ).
tcf(c_8556,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_8538]) ).
tcf(c_8987,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X2,X0))),
inference(superposition,[status(thm)],[c_50,c_8556]) ).
tcf(c_9109,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X0,X2))),
inference(superposition,[status(thm)],[c_49,c_8987]) ).
tcf(c_9463,plain,
leq(one,iPr_def_12),
inference(superposition,[status(thm)],[c_1623,c_9109]) ).
tcf(c_10289,plain,
addition(one,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_9463,c_61]) ).
tcf(c_10290,plain,
addition(iPr_def_12,one) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_10289,c_50,c_49]) ).
tcf(c_10344,plain,
! [X0: $i] : addition(iPr_def_12,addition(one,X0)) = addition(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_10290,c_50]) ).
tcf(c_234679,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_234794,plain,
addition(iPr_def_12,zero) = addition(iPr_def_12,one),
inference(superposition,[status(thm)],[c_51,c_10344]) ).
tcf(c_234800,plain,
addition(iPr_def_12,one) = iPr_def_12,
inference(demodulation,[status(thm)],[c_234794,c_51]) ).
tcf(c_235811,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_234679,c_60]) ).
tcf(c_235887,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_49,c_235811]) ).
tcf(c_235892,plain,
! [X0: $i,X1: $i,X2: $i] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(superposition,[status(thm)],[c_56,c_235811]) ).
tcf(c_235893,plain,
! [X0: $i,X1: $i,X2: $i] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(superposition,[status(thm)],[c_57,c_235811]) ).
tcf(c_235906,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X2,X0))),
inference(superposition,[status(thm)],[c_50,c_235887]) ).
tcf(c_235911,plain,
leq(b,sigma),
inference(superposition,[status(thm)],[c_66,c_235887]) ).
tcf(c_235924,plain,
addition(b,sigma) = sigma,
inference(superposition,[status(thm)],[c_235911,c_61]) ).
tcf(c_235925,plain,
addition(sigma,b) = sigma,
inference(theory_normalisation,[status(thm)],[c_235924,c_50,c_49]) ).
tcf(c_235948,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X0,X2))),
inference(superposition,[status(thm)],[c_49,c_235906]) ).
tcf(c_236650,plain,
! [X0: $i] : leq(iPr_def_11,multiplication(a,addition(iPr_def_10,X0))),
inference(superposition,[status(thm)],[c_189,c_235892]) ).
tcf(c_237510,plain,
! [X0: $i,X1: $i] : leq(X0,multiplication(addition(one,X1),X0)),
inference(superposition,[status(thm)],[c_55,c_235893]) ).
tcf(c_237513,plain,
! [X0: $i] : leq(iPr_def_10,multiplication(addition(b,X0),a)),
inference(superposition,[status(thm)],[c_188,c_235893]) ).
tcf(c_237671,plain,
! [X0: $i,X1: $i] : leq(X0,multiplication(addition(X1,one),X0)),
inference(superposition,[status(thm)],[c_49,c_237510]) ).
tcf(c_237681,plain,
! [X0: $i] : leq(iPr_def_10,multiplication(addition(X0,b),a)),
inference(superposition,[status(thm)],[c_49,c_237513]) ).
tcf(c_237788,plain,
! [X0: $i] : leq(X0,multiplication(iPr_def_12,X0)),
inference(superposition,[status(thm)],[c_234800,c_237671]) ).
tcf(c_237794,plain,
leq(iPr_def_14,iPr_def_15),
inference(superposition,[status(thm)],[c_193,c_237788]) ).
tcf(c_237799,plain,
addition(iPr_def_14,iPr_def_15) = iPr_def_15,
inference(superposition,[status(thm)],[c_237794,c_61]) ).
tcf(c_237883,plain,
leq(iPr_def_10,multiplication(sigma,a)),
inference(superposition,[status(thm)],[c_235925,c_237681]) ).
tcf(c_237886,plain,
leq(iPr_def_10,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_237883,c_191]) ).
tcf(c_237977,plain,
addition(iPr_def_10,iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_237886,c_61]) ).
tcf(c_237994,plain,
leq(iPr_def_11,multiplication(a,iPr_def_13)),
inference(superposition,[status(thm)],[c_237977,c_236650]) ).
tcf(c_237996,plain,
leq(iPr_def_11,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_237994,c_192]) ).
tcf(c_238026,plain,
addition(iPr_def_11,iPr_def_14) = iPr_def_14,
inference(superposition,[status(thm)],[c_237996,c_61]) ).
tcf(c_238051,plain,
! [X0: $i] : leq(iPr_def_11,addition(X0,iPr_def_14)),
inference(superposition,[status(thm)],[c_238026,c_235948]) ).
tcf(c_238089,plain,
! [X0: $i] : leq(iPr_def_11,addition(iPr_def_14,X0)),
inference(superposition,[status(thm)],[c_49,c_238051]) ).
tcf(c_238104,plain,
leq(iPr_def_11,iPr_def_15),
inference(superposition,[status(thm)],[c_237799,c_238089]) ).
tcf(c_238106,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_238104,c_194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE169+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.39 % Computer : n005.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Wed Sep 23 19:11:53 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.45 % Detected problem language: tptp
% 0.15/5.46 % Proving...
% 46.79/16.26 % SZS status Started for theBenchmark.p
% 46.79/16.26 % SZS status Theorem for theBenchmark.p
% 46.79/16.26
% 46.79/16.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 46.79/16.26
% 46.79/16.26 % ------ iProver source info
% 46.79/16.26
% 46.79/16.26 % git: date: 2026-07-19 20:42:38 +0200
% 46.79/16.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 46.79/16.26 % git: non_committed_changes: false
% 46.79/16.26
% 46.79/16.26 % ------ Parsing...
% 46.79/16.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 46.79/16.26
% 46.79/16.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 46.79/16.26
% 46.79/16.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 46.79/16.26
% 46.79/16.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 46.79/16.26 % ------ Proving...
% 46.79/16.26 % ------ Problem Properties
% 46.79/16.26
% 46.79/16.26 %
% 46.79/16.26 % clauses 25
% 46.79/16.26 % conjectures 1
% 46.79/16.26 % EPR 1
% 46.79/16.26 % Horn 25
% 46.79/16.26 % unary 21
% 46.79/16.26 % binary 4
% 46.79/16.26 % lits 29
% 46.79/16.26 % lits eq 20
% 46.79/16.26 % fd_pure 0
% 46.79/16.26 % fd_pseudo 0
% 46.79/16.26 % fd_cond 0
% 46.79/16.26 % fd_pseudo_cond 0
% 46.79/16.26 % AC symbols 1
% 46.79/16.26
% 46.79/16.26 % ------ Schedule dynamic 5 is on
% 46.79/16.26
% 46.79/16.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 46.79/16.26
% 46.79/16.26
% 46.79/16.26 % ------
% 46.79/16.26 % Current options:
% 46.79/16.26 % ------
% 46.79/16.26
% 46.79/16.26
% 46.79/16.26 %
% 46.79/16.26
% 46.79/16.26 % ------ Proving...
% 46.79/16.26 % Proof_search_loop: time out after: 5636 full_loop iterations
% 46.79/16.26
% 46.79/16.26 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 46.79/16.26
% 46.79/16.26
% 46.79/16.26 % ------
% 46.79/16.26 % Current options:
% 46.79/16.26 % ------
% 46.79/16.26
% 46.79/16.26
% 46.79/16.26 %
% 46.79/16.26
% 46.79/16.26 % ------ Proving...
% 46.79/16.26 %
% 46.79/16.26
% 46.79/16.26 % SZS status Theorem for theBenchmark.p
% 46.79/16.26
% 46.79/16.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 46.79/16.27
% 46.79/16.27
%------------------------------------------------------------------------------