%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE129+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 : n002.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 01:52:28 PM UTC 2026
% Result : Theorem 3.14s 1.16s
% Output : CNFRefutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 20 unt; 1 def)
% Number of atoms : 51 ( 45 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 16 ~; 9 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 3 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 : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 27 !; 1 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
fof(f27,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+7.ax',divergence1) ).
fof(f29,conjecture,
! [X0] :
( ! [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero )
=> divergence(X0) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero )
=> divergence(X0) = zero ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,plain,
? [X0] :
( ! [X1] :
( forward_diamond(X0,domain(X1)) != addition(domain(X1),forward_diamond(X0,domain(X1)))
| domain(X1) = zero )
& zero != divergence(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f33,plain,
( ! [X1] :
( forward_diamond(sK0,domain(X1)) != addition(domain(X1),forward_diamond(sK0,domain(X1)))
| domain(X1) = zero )
& zero != divergence(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f32]) ).
fof(f37,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f48,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f55,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f59,plain,
! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f61,plain,
! [X1] :
( forward_diamond(sK0,domain(X1)) != addition(domain(X1),forward_diamond(sK0,domain(X1)))
| zero = domain(X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f62,plain,
zero != divergence(sK0),
inference(cnf_transformation,[],[f33]) ).
fof(f67,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f55,f48,f48]) ).
fof(f69,plain,
! [X0] : divergence(X0) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))),
inference(definition_unfolding,[],[f59,f67]) ).
fof(f71,plain,
! [X1] :
( antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1))))))) != addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1))))))))
| zero = antidomain(antidomain(X1)) ),
inference(definition_unfolding,[],[f61,f48,f67,f48,f48,f67,f48]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f37]) ).
tcf(c_66,plain,
! [X0: $i] : antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))) = divergence(X0),
inference(cnf_transformation,[],[f69]) ).
tcf(c_68,negated_conjecture,
divergence(sK0) != zero,
inference(cnf_transformation,[],[f62]) ).
tcf(c_69,negated_conjecture,
! [X0: $i] :
( ( antidomain(antidomain(X0)) = zero )
| ( addition(antidomain(antidomain(X0)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0)))))))) != antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))) ) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_151,definition,
iPr_def_10 = divergence(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_152,negated_conjecture,
! [X0: $i] :
( ( antidomain(antidomain(X0)) = zero )
| ( addition(antidomain(antidomain(X0)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0)))))))) != antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))) ) ),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_153,negated_conjecture,
iPr_def_10 != zero,
inference(demodulation,[status(thm)],[c_68,c_151]) ).
tcf(c_396,plain,
! [X0: $i] :
( ( antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))) = zero )
| ( addition(divergence(X0),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0))))))) != antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0)))))) ) ),
inference(superposition,[status(thm)],[c_66,c_152]) ).
tcf(c_399,plain,
! [X0: $i] :
( ( divergence(X0) = zero )
| ( addition(divergence(X0),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0))))))) != antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0)))))) ) ),
inference(light_normalisation,[status(thm)],[c_396,c_66]) ).
tcf(c_615,plain,
( ( divergence(sK0) = zero )
| ( addition(divergence(sK0),divergence(sK0)) != divergence(sK0) ) ),
inference(superposition,[status(thm)],[c_66,c_399]) ).
tcf(c_618,plain,
divergence(sK0) = zero,
inference(ground_joinability,[status(thm)],[c_615,c_52,c_151]) ).
tcf(c_619,plain,
zero = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_618,c_151]) ).
tcf(c_636,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_153,c_619]) ).
tcf(c_637,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_636]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE129+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 19:04:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 0.09/0.40
% 0.09/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.40
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 3.14/1.16 % SZS status Started for theBenchmark.p
% 3.14/1.16 % SZS status Theorem for theBenchmark.p
% 3.14/1.16
% 3.14/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.14/1.16
% 3.14/1.16 % ------ iProver source info
% 3.14/1.16
% 3.14/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 3.14/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.14/1.16 % git: non_committed_changes: false
% 3.14/1.16
% 3.14/1.16 % ------ Parsing...
% 3.14/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.14/1.16
% 3.14/1.16 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.14/1.16
% 3.14/1.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.14/1.16
% 3.14/1.16 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.14/1.16 % ------ Proving...
% 3.14/1.16 % ------ Problem Properties
% 3.14/1.16
% 3.14/1.16 %
% 3.14/1.16 % clauses 22
% 3.14/1.16 % conjectures 2
% 3.14/1.16 % EPR 1
% 3.14/1.16 % Horn 22
% 3.14/1.16 % unary 20
% 3.14/1.16 % binary 2
% 3.14/1.16 % lits 24
% 3.14/1.16 % lits eq 24
% 3.14/1.16 % fd_pure 0
% 3.14/1.16 % fd_pseudo 0
% 3.14/1.16 % fd_cond 0
% 3.14/1.16 % fd_pseudo_cond 0
% 3.14/1.16 % AC symbols 1
% 3.14/1.16
% 3.14/1.16 % ------ Schedule dynamic 5 is on
% 3.14/1.16
% 3.14/1.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.14/1.16
% 3.14/1.16
% 3.14/1.16 % ------
% 3.14/1.16 % Current options:
% 3.14/1.16 % ------
% 3.14/1.16
% 3.14/1.16
% 3.14/1.16 %
% 3.14/1.16
% 3.14/1.16 % ------ Proving...
% 3.14/1.16 %
% 3.14/1.16
% 3.14/1.16 % SZS status Theorem for theBenchmark.p
% 3.14/1.16
% 3.14/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.14/1.16
% 3.14/1.16
%------------------------------------------------------------------------------