%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE113+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 : n008.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 01:52:26 PM UTC 2026
% Result : Theorem 3.99s 1.34s
% Output : CNFRefutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 42 !; 1 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+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/KLE001+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(f27,conjecture,
! [X0] : forward_diamond(X0,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f28,negated_conjecture,
~ ! [X0] : forward_diamond(X0,zero) = zero,
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
? [X0] : zero != forward_diamond(X0,zero),
inference(ennf_transformation,[],[f28]) ).
fof(f30,plain,
zero != forward_diamond(sK0,zero),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f29]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f32,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f40,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f42,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f44,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f52,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f56,plain,
zero != forward_diamond(sK0,zero),
inference(cnf_transformation,[],[f30]) ).
fof(f61,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f52,f45,f45]) ).
fof(f63,plain,
zero != antidomain(antidomain(multiplication(sK0,antidomain(antidomain(zero))))),
inference(definition_unfolding,[],[f56,f61]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f33]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f36]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f40]) ).
tcf(c_60,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f42]) ).
tcf(c_62,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f44]) ).
tcf(c_66,negated_conjecture,
antidomain(antidomain(multiplication(sK0,antidomain(antidomain(zero))))) != zero,
inference(cnf_transformation,[],[f63]) ).
tcf(c_82,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_317,plain,
antidomain(one) = zero,
inference(superposition,[status(thm)],[c_54,c_60]) ).
tcf(c_321,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_334,plain,
addition(zero,antidomain(zero)) = one,
inference(superposition,[status(thm)],[c_317,c_82]) ).
tcf(c_376,plain,
antidomain(zero) = one,
inference(superposition,[status(thm)],[c_321,c_334]) ).
tcf(c_381,plain,
antidomain(antidomain(multiplication(sK0,antidomain(one)))) != zero,
inference(superposition,[status(thm)],[c_376,c_66]) ).
tcf(c_401,plain,
antidomain(antidomain(multiplication(sK0,zero))) != zero,
inference(superposition,[status(thm)],[c_317,c_381]) ).
tcf(c_402,plain,
antidomain(antidomain(zero)) != zero,
inference(superposition,[status(thm)],[c_58,c_401]) ).
tcf(c_403,plain,
antidomain(one) != zero,
inference(superposition,[status(thm)],[c_376,c_402]) ).
tcf(c_404,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_403,c_317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE113+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n008.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Wed Sep 23 18:59:24 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.16/0.42
% 0.16/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.42
% 0.16/0.42 % Detected problem language: tptp
% 0.16/0.44 % Proving...
% 3.99/1.34 % SZS status Started for theBenchmark.p
% 3.99/1.34 % SZS status Theorem for theBenchmark.p
% 3.99/1.34
% 3.99/1.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.99/1.34
% 3.99/1.34 % ------ iProver source info
% 3.99/1.34
% 3.99/1.34 % git: date: 2026-07-19 20:42:38 +0200
% 3.99/1.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.99/1.34 % git: non_committed_changes: false
% 3.99/1.34
% 3.99/1.34 % ------ Parsing...
% 3.99/1.34 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.99/1.34
% 3.99/1.34 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.99/1.34
% 3.99/1.34 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.99/1.34
% 3.99/1.34 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.99/1.34 % ------ Proving...
% 3.99/1.34 % ------ Problem Properties
% 3.99/1.34
% 3.99/1.34 %
% 3.99/1.34 % clauses 18
% 3.99/1.34 % conjectures 1
% 3.99/1.34 % EPR 0
% 3.99/1.34 % Horn 18
% 3.99/1.34 % unary 18
% 3.99/1.34 % binary 0
% 3.99/1.34 % lits 18
% 3.99/1.34 % lits eq 18
% 3.99/1.34 % fd_pure 0
% 3.99/1.34 % fd_pseudo 0
% 3.99/1.34 % fd_cond 0
% 3.99/1.34 % fd_pseudo_cond 0
% 3.99/1.34 % AC symbols 1
% 3.99/1.34
% 3.99/1.34 % ------ Input Options Time Limit: Unbounded
% 3.99/1.34
% 3.99/1.34
% 3.99/1.34 % ------
% 3.99/1.34 % Current options:
% 3.99/1.34 % ------
% 3.99/1.34
% 3.99/1.34
% 3.99/1.34 %
% 3.99/1.34
% 3.99/1.34 % ------ Proving...
% 3.99/1.34 %
% 3.99/1.34
% 3.99/1.34 % SZS status Theorem for theBenchmark.p
% 3.99/1.34
% 3.99/1.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.99/1.34
% 3.99/1.34
%------------------------------------------------------------------------------