%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE085+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 : 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 01:52:22 PM UTC 2026
% Result : Theorem 2.35s 1.27s
% Output : CNFRefutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 35 ( 35 unt; 3 def)
% Number of atoms : 57 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 29 !; 1 ?; 11 :)
% 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(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
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(f21,conjecture,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f22,negated_conjecture,
~ ! [X0] : addition(domain(X0),one) = one,
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
? [X0] : one != addition(domain(X0),one),
inference(ennf_transformation,[],[f22]) ).
fof(f24,plain,
one != addition(domain(sK0),one),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f23]) ).
fof(f25,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f26,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f28,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f38,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f39,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f44,plain,
one != addition(domain(sK0),one),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
one != addition(antidomain(antidomain(sK0)),one),
inference(definition_unfolding,[],[f44,f39]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f25]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_62,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f38]) ).
tcf(c_66,negated_conjecture,
addition(antidomain(antidomain(sK0)),one) != one,
inference(cnf_transformation,[],[f45]) ).
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_84,negated_conjecture,
addition(one,antidomain(antidomain(sK0))) != one,
inference(theory_normalisation,[status(thm)],[c_66,c_50,c_49]) ).
tcf(c_129,definition,
iPr_def_10 = antidomain(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_130,definition,
iPr_def_11 = antidomain(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_131,definition,
iPr_def_12 = addition(one,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_132,negated_conjecture,
iPr_def_12 != one,
inference(demodulation,[status(thm)],[c_84,c_129,c_130,c_131]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_216,plain,
addition(iPr_def_10,antidomain(iPr_def_10)) = one,
inference(superposition,[status(thm)],[c_129,c_82]) ).
tcf(c_218,plain,
addition(iPr_def_10,iPr_def_11) = one,
inference(light_normalisation,[status(thm)],[c_216,c_130]) ).
tcf(c_222,plain,
addition(iPr_def_10,iPr_def_11) != iPr_def_12,
inference(demodulation,[status(thm)],[c_132,c_218]) ).
tcf(c_223,plain,
addition(iPr_def_11,one) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_131,c_50,c_49]) ).
tcf(c_224,plain,
addition(iPr_def_11,addition(iPr_def_10,iPr_def_11)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_223,c_218]) ).
tcf(c_225,plain,
addition(iPr_def_10,iPr_def_11) = iPr_def_12,
inference(demodulation,[status(thm)],[c_224,c_52,c_213]) ).
tcf(c_236,plain,
$false,
inference(ground_joinability,[status(thm)],[c_222,c_225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE085+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 18:52:43 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.35/1.27 % SZS status Started for theBenchmark.p
% 2.35/1.27 % SZS status Theorem for theBenchmark.p
% 2.35/1.27
% 2.35/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.35/1.27
% 2.35/1.27 % ------ iProver source info
% 2.35/1.27
% 2.35/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.35/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.35/1.27 % git: non_committed_changes: false
% 2.35/1.27
% 2.35/1.27 % ------ Parsing...
% 2.35/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 2.35/1.27 %
% 2.35/1.27
% 2.35/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.35/1.27
% 2.35/1.27 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 2.35/1.27 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.35/1.27
% 2.35/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.35/1.27 % ------ Proving...
% 2.35/1.27 % ------ Problem Properties
% 2.35/1.27
% 2.35/1.27 %
% 2.35/1.27 % clauses 21
% 2.35/1.27 % conjectures 1
% 2.35/1.27 % EPR 1
% 2.35/1.27 % Horn 21
% 2.35/1.27 % unary 21
% 2.35/1.27 % binary 0
% 2.35/1.27 % lits 21
% 2.35/1.27 % lits eq 21
% 2.35/1.27 % fd_pure 0
% 2.35/1.27 % fd_pseudo 0
% 2.35/1.27 % fd_cond 0
% 2.35/1.27 % fd_pseudo_cond 0
% 2.35/1.27 % AC symbols 1
% 2.35/1.27
% 2.35/1.27 % ------ Schedule UEQ
% 2.35/1.27
% 2.35/1.27 % ------ Option_UEQ Time Limit: 10.
% 2.35/1.27
% 2.35/1.27
% 2.35/1.27 % ------
% 2.35/1.27 % Current options:
% 2.35/1.27 % ------
% 2.35/1.27
% 2.35/1.27
% 2.35/1.27 %
% 2.35/1.27
% 2.35/1.27 % ------ Proving...
% 2.35/1.27 %
% 2.35/1.27
% 2.35/1.27 % SZS status Theorem for theBenchmark.p
% 2.35/1.27
% 2.35/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.35/1.27
% 2.35/1.27
%------------------------------------------------------------------------------