%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE140+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 01:52:29 PM UTC 2026
% Result : Theorem 1.24s 1.74s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 33 unt; 0 def)
% Number of atoms : 65 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 15 ~; 10 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 75 !; 2 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+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/KLE004+0.ax',additive_associativity) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(f16,axiom,
! [X0,X1,X2] :
( leq(X2,addition(multiplication(X0,X2),X1))
=> leq(X2,multiplication(strong_iteration(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(f18,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(f19,conjecture,
! [X0,X1] :
( leq(X0,X1)
=> leq(strong_iteration(X0),strong_iteration(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( leq(X0,X1)
=> leq(strong_iteration(X0),strong_iteration(X1)) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0,X1] :
( leq(X0,X1)
& ~ leq(strong_iteration(X0),strong_iteration(X1)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ leq(X2,addition(multiplication(X0,X2),X1))
| leq(X2,multiplication(strong_iteration(X0),X1)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f25,plain,
( leq(sK0,sK1)
& ~ leq(strong_iteration(sK0),strong_iteration(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f21]) ).
fof(f26,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| addition(X0,X1) = X1 )
& ( addition(X0,X1) != X1
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f27,plain,
leq(sK0,sK1),
inference(cnf_transformation,[],[f25]) ).
fof(f28,plain,
~ leq(strong_iteration(sK0),strong_iteration(sK1)),
inference(cnf_transformation,[],[f25]) ).
fof(f29,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f30,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ leq(X2,addition(multiplication(X0,X2),X1))
| leq(X2,multiplication(strong_iteration(X0),X1)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f36,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f39,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f40,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f41,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f47,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
tcf(c_49,negated_conjecture,
~ leq(strong_iteration(sK0),strong_iteration(sK1)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_50,negated_conjecture,
leq(sK0,sK1),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ( addition(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( addition(X0,X1) = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(X0,multiplication(strong_iteration(X1),X2))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_57,plain,
! [X0: $i] : addition(multiplication(X0,strong_iteration(X0)),one) = strong_iteration(X0),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f36]) ).
tcf(c_61,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f39]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f40]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f41]) ).
tcf(c_69,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f47]) ).
tcf(c_87,plain,
! [X0: $i] : addition(one,multiplication(X0,strong_iteration(X0))) = strong_iteration(X0),
inference(theory_normalisation,[status(thm)],[c_57,c_62,c_63]) ).
tcf(c_537,plain,
addition(sK0,sK1) = sK1,
inference(superposition,[status(thm)],[c_50,c_52]) ).
tcf(c_597,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_61,c_62]) ).
tcf(c_642,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(X0,multiplication(strong_iteration(X2),X1))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(superposition,[status(thm)],[c_63,c_53]) ).
tcf(c_966,plain,
! [X0: $i] : addition(multiplication(sK0,X0),multiplication(sK1,X0)) = multiplication(sK1,X0),
inference(superposition,[status(thm)],[c_537,c_58]) ).
tcf(c_4424,plain,
! [X0: $i,X1: $i] : leq(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c_597,c_51]) ).
tcf(c_4485,plain,
! [X0: $i,X1: $i,X2: $i] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(superposition,[status(thm)],[c_62,c_4424]) ).
tcf(c_8525,plain,
! [X0: $i,X1: $i] : leq(addition(X0,multiplication(sK0,X1)),addition(X0,multiplication(sK1,X1))),
inference(superposition,[status(thm)],[c_966,c_4485]) ).
tcf(c_9900,plain,
leq(strong_iteration(sK0),addition(one,multiplication(sK1,strong_iteration(sK0)))),
inference(superposition,[status(thm)],[c_87,c_8525]) ).
tcf(c_10815,plain,
leq(strong_iteration(sK0),multiplication(strong_iteration(sK1),one)),
inference(superposition,[status(thm)],[c_9900,c_642]) ).
tcf(c_10960,plain,
leq(strong_iteration(sK0),strong_iteration(sK1)),
inference(demodulation,[status(thm)],[c_10815,c_69]) ).
tcf(c_10961,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10960,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE140+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 19:09:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.24/1.74 % SZS status Started for theBenchmark.p
% 1.24/1.74 % SZS status Theorem for theBenchmark.p
% 1.24/1.74
% 1.24/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.24/1.74
% 1.24/1.74 % ------ iProver source info
% 1.24/1.74
% 1.24/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 1.24/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.24/1.74 % git: non_committed_changes: false
% 1.24/1.74
% 1.24/1.74 % ------ Parsing...
% 1.24/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.24/1.74
% 1.24/1.74 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.24/1.74
% 1.24/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.24/1.74
% 1.24/1.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.24/1.74 % ------ Proving...
% 1.24/1.74 % ------ Problem Properties
% 1.24/1.74
% 1.24/1.74 %
% 1.24/1.74 % clauses 21
% 1.24/1.74 % conjectures 2
% 1.24/1.74 % EPR 1
% 1.24/1.74 % Horn 21
% 1.24/1.74 % unary 16
% 1.24/1.74 % binary 5
% 1.24/1.74 % lits 26
% 1.24/1.74 % lits eq 16
% 1.24/1.74 % fd_pure 0
% 1.24/1.74 % fd_pseudo 0
% 1.24/1.74 % fd_cond 0
% 1.24/1.74 % fd_pseudo_cond 0
% 1.24/1.74 % AC symbols 1
% 1.24/1.74
% 1.24/1.74 % ------ Schedule dynamic 5 is on
% 1.24/1.74
% 1.24/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.24/1.74
% 1.24/1.74
% 1.24/1.74 % ------
% 1.24/1.74 % Current options:
% 1.24/1.74 % ------
% 1.24/1.74
% 1.24/1.74
% 1.24/1.74 %
% 1.24/1.74
% 1.24/1.74 % ------ Proving...
% 1.24/1.74 %
% 1.24/1.74
% 1.24/1.74 % SZS status Theorem for theBenchmark.p
% 1.24/1.74
% 1.24/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.24/1.74
% 1.24/1.74
%------------------------------------------------------------------------------