%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE093+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 : n020.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 01:52:23 PM UTC 2026
% Result : Theorem 2.97s 1.18s
% Output : CNFRefutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 71 ( 60 unt; 2 def)
% Number of atoms : 112 ( 71 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 21 ~; 14 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 82 !; 1 ?; 40 :)
% 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(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(f14,axiom,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
fof(f17,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(f19,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(f21,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain5) ).
fof(f22,conjecture,
! [X0] : domain(star(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f23,negated_conjecture,
~ ! [X0] : domain(star(X0)) = one,
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f26,plain,
? [X0] : one != domain(star(X0)),
inference(ennf_transformation,[],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
& ( addition(X0,X1) != X1
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f28,plain,
one != domain(star(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f26]) ).
fof(f29,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f30,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f34,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f35,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f37,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f40,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f41,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f43,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f14]) ).
fof(f46,plain,
! [X0] : multiplication(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f48,plain,
! [X0] : one = addition(domain(X0),one),
inference(cnf_transformation,[],[f19]) ).
fof(f50,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[],[f21]) ).
fof(f51,plain,
one != domain(star(sK0)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f29]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f32]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f34]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f35]) ).
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,[],[f37]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_63,plain,
! [X0: $i] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[],[f43]) ).
tcf(c_66,plain,
! [X0: $i] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[],[f46]) ).
tcf(c_68,plain,
! [X0: $i] : addition(domain(X0),one) = one,
inference(cnf_transformation,[],[f48]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : addition(domain(X0),domain(X1)) = domain(addition(X0,X1)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_71,negated_conjecture,
domain(star(sK0)) != one,
inference(cnf_transformation,[],[f51]) ).
tcf(c_91,plain,
! [X0: $i] : addition(one,domain(X0)) = one,
inference(theory_normalisation,[status(thm)],[c_68,c_50,c_49]) ).
tcf(c_210,definition,
iPr_def_10 = star(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_211,definition,
iPr_def_11 = domain(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_212,negated_conjecture,
iPr_def_11 != one,
inference(demodulation,[status(thm)],[c_71,c_210,c_211]) ).
tcf(c_213,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_215,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_545,plain,
addition(one,iPr_def_11) = one,
inference(superposition,[status(thm)],[c_211,c_91]) ).
tcf(c_546,plain,
addition(iPr_def_11,one) = one,
inference(theory_normalisation,[status(thm)],[c_545,c_50,c_49]) ).
tcf(c_569,plain,
! [X0: $i,X1: $i] :
( leq(X1,X0)
| ( addition(X0,X1) != X0 ) ),
inference(superposition,[status(thm)],[c_49,c_60]) ).
tcf(c_624,plain,
! [X0: $i] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_63,c_61]) ).
tcf(c_635,plain,
! [X0: $i] : addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
inference(theory_normalisation,[status(thm)],[c_624,c_50,c_49]) ).
tcf(c_669,plain,
! [X0: $i] :
( ( iPr_def_11 = one )
| ( iPr_def_11 != X0 )
| ( one != X0 ) ),
inference(instantiation,[status(thm)],[c_215]) ).
tcf(c_679,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_694,plain,
( ( iPr_def_11 = one )
| ( iPr_def_11 != iPr_def_11 )
| ( one != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_669]) ).
tcf(c_695,plain,
iPr_def_11 = iPr_def_11,
inference(instantiation,[status(thm)],[c_213]) ).
tcf(c_1112,plain,
! [X0: $i,X1: $i] : addition(multiplication(one,X0),multiplication(domain(X1),X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[c_91,c_57]) ).
tcf(c_1133,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(domain(X1),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1112,c_55]) ).
tcf(c_1137,plain,
! [X0: $i] : multiplication(domain(X0),X0) = X0,
inference(demodulation,[status(thm)],[c_66,c_1133]) ).
tcf(c_1191,plain,
domain(one) = one,
inference(superposition,[status(thm)],[c_1137,c_54]) ).
tcf(c_2327,plain,
( leq(one,iPr_def_11)
| ( one != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_546,c_569]) ).
tcf(c_2489,plain,
one != iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_2327,c_212,c_694,c_695]) ).
tcf(c_3331,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_679,c_60]) ).
tcf(c_3454,plain,
! [X0: $i] : leq(one,star(X0)),
inference(superposition,[status(thm)],[c_635,c_3331]) ).
tcf(c_3607,plain,
leq(one,iPr_def_10),
inference(superposition,[status(thm)],[c_210,c_3454]) ).
tcf(c_3609,plain,
addition(one,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_3607,c_61]) ).
tcf(c_3610,plain,
addition(iPr_def_10,one) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_3609,c_50,c_49]) ).
tcf(c_3637,plain,
addition(domain(iPr_def_10),domain(one)) = domain(iPr_def_10),
inference(superposition,[status(thm)],[c_3610,c_70]) ).
tcf(c_3655,plain,
one = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_3637,c_211,c_546,c_1191]) ).
tcf(c_3656,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3655,c_2489]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE093+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 18:55:33 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 2.97/1.18 % SZS status Started for theBenchmark.p
% 2.97/1.18 % SZS status Theorem for theBenchmark.p
% 2.97/1.18
% 2.97/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.97/1.18
% 2.97/1.18 % ------ iProver source info
% 2.97/1.18
% 2.97/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.97/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.97/1.18 % git: non_committed_changes: false
% 2.97/1.18
% 2.97/1.18 % ------ Parsing...
% 2.97/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.97/1.18
% 2.97/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.97/1.18
% 2.97/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.97/1.18
% 2.97/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.97/1.18 % ------ Proving...
% 2.97/1.18 % ------ Problem Properties
% 2.97/1.18
% 2.97/1.18 %
% 2.97/1.18 % clauses 25
% 2.97/1.18 % conjectures 1
% 2.97/1.18 % EPR 1
% 2.97/1.18 % Horn 25
% 2.97/1.18 % unary 21
% 2.97/1.18 % binary 4
% 2.97/1.18 % lits 29
% 2.97/1.18 % lits eq 21
% 2.97/1.18 % fd_pure 0
% 2.97/1.18 % fd_pseudo 0
% 2.97/1.18 % fd_cond 0
% 2.97/1.18 % fd_pseudo_cond 0
% 2.97/1.18 % AC symbols 1
% 2.97/1.18
% 2.97/1.18 % ------ Schedule dynamic 5 is on
% 2.97/1.18
% 2.97/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.97/1.18
% 2.97/1.18
% 2.97/1.18 % ------
% 2.97/1.18 % Current options:
% 2.97/1.18 % ------
% 2.97/1.18
% 2.97/1.18
% 2.97/1.18 %
% 2.97/1.18
% 2.97/1.18 % ------ Proving...
% 2.97/1.18 %
% 2.97/1.18
% 2.97/1.18 % SZS status Theorem for theBenchmark.p
% 2.97/1.18
% 2.97/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.97/1.18
% 2.97/1.18
%------------------------------------------------------------------------------