%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE048+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 : n016.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 01:52:16 PM UTC 2026
% Result : Theorem 27.47s 6.81s
% Output : CNFRefutation 27.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 67 ( 37 unt; 0 def)
% Number of atoms : 119 ( 54 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 89 ( 37 ~; 32 |; 14 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 88 !; 4 ?; 37 :)
% 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(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
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(f16,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X0)
=> leq(multiplication(X2,star(X1)),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_induction_right) ).
fof(f17,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+1.ax',test_1) ).
fof(f18,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(f21,conjecture,
! [X0] :
( test(X0)
=> star(X0) = one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f22,negated_conjecture,
~ ! [X0] :
( test(X0)
=> star(X0) = one ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0] :
( test(X0)
& one != star(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f28,plain,
( test(sK0)
& one != star(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f23]) ).
fof(f29,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f30,plain,
! [X0] :
( ( ~ test(X0)
| ? [X2] : complement(X2,X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(rectify,[],[f29]) ).
fof(f31,plain,
! [X0] :
( ( ~ test(X0)
| complement(sK1(X0),X0) )
& ( ! [X1] : ~ complement(X1,X0)
| test(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0))],[f30]) ).
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(nnf_transformation,[],[f18]) ).
fof(f34,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,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
& ( addition(X0,X1) != X1
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f36,plain,
test(sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f37,plain,
one != star(sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f41,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f42,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f43,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f44,plain,
! [X0] :
( ~ test(X0)
| complement(sK1(X0),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f47,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f48,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f54,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f34]) ).
fof(f58,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f59,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_49,negated_conjecture,
star(sK0) != one,
inference(cnf_transformation,[],[f37]) ).
tcf(c_50,negated_conjecture,
test(sK0),
inference(cnf_transformation,[],[f36]) ).
tcf(c_54,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f41]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f42]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f43]) ).
tcf(c_58,plain,
! [X0: $i] :
( complement(sK1(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_60,plain,
! [X0: $i] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[],[f47]) ).
tcf(c_61,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f48]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( addition(X1,X0) = one )
| ~ complement(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_1049,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_1057,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(superposition,[status(thm)],[c_54,c_1049]) ).
tcf(c_1132,plain,
! [X0: $i] :
( ( addition(X0,sK1(X0)) = one )
| ~ test(X0) ),
inference(superposition,[status(thm)],[c_58,c_70]) ).
tcf(c_1145,plain,
! [X0: $i] : leq(X0,X0),
inference(superposition,[status(thm)],[c_54,c_71]) ).
tcf(c_1168,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c_1057,c_71]) ).
tcf(c_1186,plain,
! [X0: $i] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_60,c_72]) ).
tcf(c_1191,plain,
! [X0: $i] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(theory_normalisation,[status(thm)],[c_1186,c_55,c_56]) ).
tcf(c_1248,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_56,c_1168]) ).
tcf(c_1524,plain,
! [X0: $i,X1: $i] :
( leq(multiplication(X1,star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(superposition,[status(thm)],[c_61,c_63]) ).
tcf(c_2043,plain,
! [X0: $i] : leq(one,star(X0)),
inference(superposition,[status(thm)],[c_1191,c_1248]) ).
tcf(c_2307,plain,
! [X0: $i] : addition(one,star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_2043,c_72]) ).
tcf(c_3636,plain,
addition(sK0,sK1(sK0)) = one,
inference(superposition,[status(thm)],[c_50,c_1132]) ).
tcf(c_3658,plain,
leq(sK0,one),
inference(superposition,[status(thm)],[c_3636,c_1248]) ).
tcf(c_3783,plain,
addition(sK0,one) = one,
inference(superposition,[status(thm)],[c_3658,c_72]) ).
tcf(c_3784,plain,
addition(one,sK0) = one,
inference(theory_normalisation,[status(thm)],[c_3783,c_55,c_56]) ).
tcf(c_120286,plain,
! [X0: $i] :
( leq(star(X0),one)
| ~ leq(addition(X0,one),one) ),
inference(superposition,[status(thm)],[c_61,c_1524]) ).
tcf(c_120309,plain,
! [X0: $i] :
( leq(star(X0),one)
| ~ leq(addition(one,X0),one) ),
inference(superposition,[status(thm)],[c_56,c_120286]) ).
tcf(c_120964,plain,
( leq(star(sK0),one)
| ~ leq(one,one) ),
inference(superposition,[status(thm)],[c_3784,c_120309]) ).
tcf(c_120987,plain,
leq(star(sK0),one),
inference(forward_subsumption_resolution,[status(thm)],[c_120964,c_1145]) ).
tcf(c_122202,plain,
addition(star(sK0),one) = one,
inference(superposition,[status(thm)],[c_120987,c_72]) ).
tcf(c_122203,plain,
addition(one,star(sK0)) = one,
inference(theory_normalisation,[status(thm)],[c_122202,c_55,c_56]) ).
tcf(c_122910,plain,
star(sK0) = one,
inference(demodulation,[status(thm)],[c_122203,c_2307]) ).
tcf(c_122911,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_122910,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Wed Sep 23 18:50:57 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 27.47/6.81 % SZS status Started for theBenchmark.p
% 27.47/6.81 % SZS status Theorem for theBenchmark.p
% 27.47/6.81
% 27.47/6.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 27.47/6.81
% 27.47/6.81 % ------ iProver source info
% 27.47/6.81
% 27.47/6.81 % git: date: 2026-07-19 20:42:38 +0200
% 27.47/6.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 27.47/6.81 % git: non_committed_changes: false
% 27.47/6.81
% 27.47/6.81 % ------ Parsing...
% 27.47/6.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 27.47/6.81
% 27.47/6.81 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 27.47/6.81
% 27.47/6.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 27.47/6.81
% 27.47/6.81 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 27.47/6.81 % ------ Proving...
% 27.47/6.81 % ------ Problem Properties
% 27.47/6.81
% 27.47/6.81 %
% 27.47/6.81 % clauses 28
% 27.47/6.81 % conjectures 2
% 27.47/6.81 % EPR 2
% 27.47/6.81 % Horn 27
% 27.47/6.81 % unary 15
% 27.47/6.81 % binary 11
% 27.47/6.81 % lits 44
% 27.47/6.81 % lits eq 22
% 27.47/6.81 % fd_pure 0
% 27.47/6.81 % fd_pseudo 0
% 27.47/6.81 % fd_cond 0
% 27.47/6.81 % fd_pseudo_cond 1
% 27.47/6.81 % AC symbols 1
% 27.47/6.81
% 27.47/6.81 % ------ Schedule dynamic 5 is on
% 27.47/6.81
% 27.47/6.81 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 27.47/6.81
% 27.47/6.81
% 27.47/6.81 % ------
% 27.47/6.81 % Current options:
% 27.47/6.81 % ------
% 27.47/6.81
% 27.47/6.81
% 27.47/6.81 %
% 27.47/6.81
% 27.47/6.81 % ------ Proving...
% 27.47/6.81 %
% 27.47/6.81
% 27.47/6.81 % SZS status Theorem for theBenchmark.p
% 27.47/6.81
% 27.47/6.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.47/6.81
% 27.47/6.81
%------------------------------------------------------------------------------