%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE170+1.002 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 25.76s 9.30s
% Output : CNFRefutation 25.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 59 unt; 0 def)
% Number of atoms : 73 ( 41 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 6 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn 112 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/KLE002+0.ax',left_distributivity) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).
fof(f13,axiom,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(f17,conjecture,
leq(multiplication(a,a),star(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
fof(f18,negated_conjecture,
~ leq(multiplication(a,a),star(a)),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
~ leq(multiplication(a,a),star(a)),
inference(flattening,[],[f18]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
& ( addition(X0,X1) != X1
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f23,plain,
~ leq(multiplication(a,a),star(a)),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f28,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f29,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f30,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f31,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f33,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f34,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f35,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f36,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f37,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
tcf(c_49,negated_conjecture,
~ leq(multiplication(a,a),star(a)),
inference(cnf_transformation,[],[f23]) ).
tcf(c_53,plain,
! [X0: $i] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f30]) ).
tcf(c_57,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_59,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f33]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f35]) ).
tcf(c_62,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f36]) ).
tcf(c_63,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f37]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(superposition,[status(thm)],[c_62,c_56]) ).
tcf(c_453,plain,
! [X0: $i] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_53,c_55]) ).
tcf(c_456,plain,
! [X0: $i] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(theory_normalisation,[status(thm)],[c_453,c_60,c_61]) ).
tcf(c_473,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_59,c_60]) ).
tcf(c_507,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_473,c_54]) ).
tcf(c_527,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_61,c_507]) ).
tcf(c_538,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X2,X0))),
inference(superposition,[status(thm)],[c_60,c_527]) ).
tcf(c_551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X3,X0),X1))),
inference(superposition,[status(thm)],[c_56,c_538]) ).
tcf(c_552,plain,
! [X0: $i,X1: $i,X2: $i] : leq(X0,addition(X1,addition(X0,X2))),
inference(superposition,[status(thm)],[c_61,c_538]) ).
tcf(c_575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,X3),X1))),
inference(superposition,[status(thm)],[c_56,c_552]) ).
tcf(c_753,plain,
! [X0: $i,X1: $i,X2: $i] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(superposition,[status(thm)],[c_57,c_507]) ).
tcf(c_1027,plain,
! [X0: $i,X1: $i] : leq(X0,multiplication(X0,addition(one,X1))),
inference(superposition,[status(thm)],[c_63,c_753]) ).
tcf(c_1687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : leq(multiplication(X0,X1),addition(multiplication(addition(X0,X2),X1),X3)),
inference(superposition,[status(thm)],[c_61,c_575]) ).
tcf(c_6376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),addition(X1,X3))),
inference(superposition,[status(thm)],[c_57,c_1687]) ).
tcf(c_21865,plain,
! [X0: $i] : addition(one,multiplication(addition(one,X0),star(X0))) = star(X0),
inference(demodulation,[status(thm)],[c_456,c_424]) ).
tcf(c_21931,plain,
! [X0: $i] : addition(one,star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_21865,c_473]) ).
tcf(c_22021,plain,
! [X0: $i,X1: $i] : leq(X0,multiplication(X0,star(X1))),
inference(superposition,[status(thm)],[c_21865,c_1027]) ).
tcf(c_22037,plain,
! [X0: $i] : leq(multiplication(X0,star(X0)),star(X0)),
inference(superposition,[status(thm)],[c_21865,c_551]) ).
tcf(c_23217,plain,
! [X0: $i] : addition(multiplication(X0,star(X0)),star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_22037,c_55]) ).
tcf(c_23218,plain,
! [X0: $i] : addition(star(X0),multiplication(X0,star(X0))) = star(X0),
inference(theory_normalisation,[status(thm)],[c_23217,c_60,c_61]) ).
tcf(c_24073,plain,
! [X0: $i] : multiplication(addition(one,X0),star(X0)) = star(X0),
inference(demodulation,[status(thm)],[c_23218,c_424]) ).
tcf(c_24075,plain,
! [X0: $i] : multiplication(addition(X0,one),star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_61,c_24073]) ).
tcf(c_24090,plain,
! [X0: $i] : leq(addition(one,X0),star(X0)),
inference(superposition,[status(thm)],[c_24073,c_22021]) ).
tcf(c_24670,plain,
! [X0: $i] : leq(addition(X0,one),star(X0)),
inference(superposition,[status(thm)],[c_61,c_24090]) ).
tcf(c_24812,plain,
! [X0: $i] : addition(addition(X0,one),star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_24670,c_55]) ).
tcf(c_24813,plain,
! [X0: $i] : addition(X0,addition(one,star(X0))) = star(X0),
inference(theory_normalisation,[status(thm)],[c_24812,c_60,c_61]) ).
tcf(c_24814,plain,
! [X0: $i] : addition(X0,star(X0)) = star(X0),
inference(light_normalisation,[status(thm)],[c_24813,c_21931]) ).
tcf(c_26609,plain,
! [X0: $i,X1: $i,X2: $i] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),star(X1))),
inference(superposition,[status(thm)],[c_24814,c_6376]) ).
tcf(c_53256,plain,
! [X0: $i] : leq(multiplication(X0,X0),star(X0)),
inference(superposition,[status(thm)],[c_24075,c_26609]) ).
tcf(c_53289,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_49,c_53256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE170+1.002 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/5.37 % Computer : n019.cluster.edu
% 0.12/5.37 % Model : x86_64 x86_64
% 0.12/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.37 % Memory : 8046.5625MB
% 0.12/5.37 % OS : Linux 6.8.0-71-generic
% 0.12/5.37 % CPULimit : 300
% 0.12/5.37 % WCLimit : 300
% 0.12/5.37 % DateTime : Wed Sep 23 19:12:12 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.42 Running first-order theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.44 % Proving...
% 25.76/9.30 % SZS status Started for theBenchmark.p
% 25.76/9.30 % SZS status Theorem for theBenchmark.p
% 25.76/9.30
% 25.76/9.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 25.76/9.30
% 25.76/9.30 % ------ iProver source info
% 25.76/9.30
% 25.76/9.30 % git: date: 2026-07-19 20:42:38 +0200
% 25.76/9.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 25.76/9.30 % git: non_committed_changes: false
% 25.76/9.30
% 25.76/9.30 % ------ Parsing...
% 25.76/9.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 25.76/9.30
% 25.76/9.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 25.76/9.30
% 25.76/9.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 25.76/9.30
% 25.76/9.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 25.76/9.30 % ------ Proving...
% 25.76/9.30 % ------ Problem Properties
% 25.76/9.30
% 25.76/9.30 %
% 25.76/9.30 % clauses 15
% 25.76/9.30 % conjectures 1
% 25.76/9.30 % EPR 0
% 25.76/9.30 % Horn 15
% 25.76/9.30 % unary 11
% 25.76/9.30 % binary 4
% 25.76/9.30 % lits 19
% 25.76/9.30 % lits eq 10
% 25.76/9.30 % fd_pure 0
% 25.76/9.30 % fd_pseudo 0
% 25.76/9.30 % fd_cond 0
% 25.76/9.30 % fd_pseudo_cond 0
% 25.76/9.30 % AC symbols 1
% 25.76/9.30
% 25.76/9.30 % ------ Schedule dynamic 5 is on
% 25.76/9.30
% 25.76/9.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 25.76/9.30
% 25.76/9.30
% 25.76/9.30 % ------
% 25.76/9.30 % Current options:
% 25.76/9.30 % ------
% 25.76/9.30
% 25.76/9.30
% 25.76/9.30 %
% 25.76/9.30
% 25.76/9.30 % ------ Proving...
% 25.76/9.30 %
% 25.76/9.30
% 25.76/9.30 % SZS status Theorem for theBenchmark.p
% 25.76/9.30
% 25.76/9.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.76/9.30
% 25.76/9.30
%------------------------------------------------------------------------------