%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE138+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 : n006.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 2.44s 1.26s
% Output : CNFRefutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 30 unt; 1 def)
% Number of atoms : 36 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(f10,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(f15,axiom,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(f19,conjecture,
strong_iteration(zero) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f20,negated_conjecture,
strong_iteration(zero) != one,
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
one != strong_iteration(zero),
inference(flattening,[],[f20]) ).
fof(f26,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f27,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f28,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f35,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f40,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
one != strong_iteration(zero),
inference(cnf_transformation,[],[f21]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f26]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f35]) ).
tcf(c_63,plain,
! [X0: $i] : addition(multiplication(X0,strong_iteration(X0)),one) = strong_iteration(X0),
inference(cnf_transformation,[],[f40]) ).
tcf(c_68,negated_conjecture,
strong_iteration(zero) != one,
inference(cnf_transformation,[],[f45]) ).
tcf(c_86,plain,
! [X0: $i] : addition(one,multiplication(X0,strong_iteration(X0))) = strong_iteration(X0),
inference(theory_normalisation,[status(thm)],[c_63,c_50,c_49]) ).
tcf(c_206,definition,
iPr_def_10 = strong_iteration(zero),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_207,negated_conjecture,
iPr_def_10 != one,
inference(demodulation,[status(thm)],[c_68,c_206]) ).
tcf(c_509,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_515,plain,
addition(one,zero) = strong_iteration(zero),
inference(superposition,[status(thm)],[c_58,c_86]) ).
tcf(c_517,plain,
addition(zero,one) = strong_iteration(zero),
inference(theory_normalisation,[status(thm)],[c_515,c_50,c_49]) ).
tcf(c_518,plain,
addition(zero,one) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_517,c_206]) ).
tcf(c_565,plain,
one = iPr_def_10,
inference(demodulation,[status(thm)],[c_518,c_509]) ).
tcf(c_571,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_207,c_565]) ).
tcf(c_572,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_571]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE138+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 19:02:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.44/1.26 % SZS status Started for theBenchmark.p
% 2.44/1.26 % SZS status Theorem for theBenchmark.p
% 2.44/1.26
% 2.44/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.44/1.26
% 2.44/1.26 % ------ iProver source info
% 2.44/1.26
% 2.44/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 2.44/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.44/1.26 % git: non_committed_changes: false
% 2.44/1.26
% 2.44/1.26 % ------ Parsing...
% 2.44/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.44/1.26
% 2.44/1.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.44/1.26
% 2.44/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.44/1.26
% 2.44/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.44/1.26 % ------ Proving...
% 2.44/1.26 % ------ Problem Properties
% 2.44/1.26
% 2.44/1.26 %
% 2.44/1.26 % clauses 21
% 2.44/1.26 % conjectures 1
% 2.44/1.26 % EPR 1
% 2.44/1.26 % Horn 21
% 2.44/1.26 % unary 16
% 2.44/1.26 % binary 5
% 2.44/1.26 % lits 26
% 2.44/1.26 % lits eq 18
% 2.44/1.26 % fd_pure 0
% 2.44/1.26 % fd_pseudo 0
% 2.44/1.26 % fd_cond 0
% 2.44/1.26 % fd_pseudo_cond 0
% 2.44/1.26 % AC symbols 1
% 2.44/1.26
% 2.44/1.26 % ------ Schedule dynamic 5 is on
% 2.44/1.26
% 2.44/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.44/1.26
% 2.44/1.26
% 2.44/1.26 % ------
% 2.44/1.26 % Current options:
% 2.44/1.26 % ------
% 2.44/1.26
% 2.44/1.26
% 2.44/1.26 %
% 2.44/1.26
% 2.44/1.26 % ------ Proving...
% 2.44/1.26 %
% 2.44/1.26
% 2.44/1.26 % SZS status Theorem for theBenchmark.p
% 2.44/1.26
% 2.44/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.44/1.26
% 2.44/1.26
%------------------------------------------------------------------------------