%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE131+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 : n010.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 3.50s 21.28s
% Output : CNFRefutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 47 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 16 ( 3 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 : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 60 !; 1 ?; 15 :)
% 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(f22,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',domain_difference) ).
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,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+7.ax',divergence1) ).
fof(f29,conjecture,
! [X0] :
( ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))
=> divergence(X0) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))
=> divergence(X0) = zero ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
? [X0] :
( ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))
& zero != divergence(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f33,plain,
( ! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))))
& zero != divergence(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f31]) ).
fof(f34,plain,
! [X1] : forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1)))) = addition(domain(X1),forward_diamond(star(sK0),domain_difference(domain(X1),forward_diamond(sK0,domain(X1))))),
inference(cnf_transformation,[],[f33]) ).
fof(f35,plain,
zero != divergence(sK0),
inference(cnf_transformation,[],[f33]) ).
fof(f39,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f40,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f42,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f44,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f45,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f46,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f23]) ).
fof(f47,plain,
! [X0] : antidomain(antidomain(X0)) = domain(X0),
inference(cnf_transformation,[],[f16]) ).
fof(f48,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[],[f22]) ).
fof(f50,plain,
! [X0] : divergence(X0) = forward_diamond(X0,divergence(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f54,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f57,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f58,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(antidomain(antidomain(X0)),antidomain(X1)),
inference(definition_unfolding,[],[f48,f47]) ).
fof(f59,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f46,f47,f47]) ).
fof(f60,plain,
! [X1] : antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1)))))))))))))) = addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X1))))))))))))))),
inference(definition_unfolding,[],[f34,f59,f58,f47,f59,f47,f47,f59,f58,f47,f59,f47]) ).
fof(f62,plain,
! [X0] : divergence(X0) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))),
inference(definition_unfolding,[],[f50,f59]) ).
tcf(c_49,negated_conjecture,
divergence(sK0) != zero,
inference(cnf_transformation,[],[f35]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X0)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0))))))))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X0)))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(X0)))))))))))))),
inference(cnf_transformation,[],[f60]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f39]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f40]) ).
tcf(c_57,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f42]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f44]) ).
tcf(c_60,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f45]) ).
tcf(c_62,plain,
! [X0: $i] : antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))) = divergence(X0),
inference(cnf_transformation,[],[f62]) ).
tcf(c_66,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f54]) ).
tcf(c_69,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f57]) ).
tcf(c_89,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_66,c_54,c_55]) ).
tcf(c_245,plain,
antidomain(one) = zero,
inference(superposition,[status(thm)],[c_69,c_57]) ).
tcf(c_247,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_60,c_55]) ).
tcf(c_253,plain,
addition(zero,antidomain(zero)) = one,
inference(superposition,[status(thm)],[c_245,c_89]) ).
tcf(c_264,plain,
antidomain(zero) = one,
inference(demodulation,[status(thm)],[c_253,c_247]) ).
tcf(c_455,plain,
! [X0: $i] : addition(divergence(X0),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(X0))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0)))))))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(X0))),antidomain(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(divergence(X0))))))))))))),
inference(superposition,[status(thm)],[c_62,c_50]) ).
tcf(c_768,plain,
addition(divergence(sK0),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(sK0))),antidomain(divergence(sK0))))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(multiplication(antidomain(antidomain(divergence(sK0))),antidomain(divergence(sK0)))))))),
inference(superposition,[status(thm)],[c_62,c_455]) ).
tcf(c_929,plain,
divergence(sK0) = zero,
inference(demodulation,[status(thm)],[c_768,c_57,c_59,c_60,c_245,c_264]) ).
tcf(c_930,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_929,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE131+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/20.45 % Computer : n010.cluster.edu
% 0.17/20.45 % Model : x86_64 x86_64
% 0.17/20.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/20.45 % Memory : 8046.5625MB
% 0.17/20.45 % OS : Linux 6.8.0-71-generic
% 0.17/20.45 % CPULimit : 300
% 0.17/20.45 % WCLimit : 300
% 0.17/20.45 % DateTime : Wed Sep 23 19:02:53 UTC 2026
% 0.17/20.45 % CPUTime :
% 0.17/20.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/20.49 Running first-order theorem proving
% 0.17/20.49 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
% 0.21/20.50
% 0.21/20.50 % ======== iProver multi-core TPTP/SMT =========
% 0.21/20.50
% 0.21/20.50 % Detected problem language: tptp
% 0.21/20.51 % Proving...
% 3.50/21.28 % SZS status Started for theBenchmark.p
% 3.50/21.28 % SZS status Theorem for theBenchmark.p
% 3.50/21.28
% 3.50/21.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.50/21.28
% 3.50/21.28 % ------ iProver source info
% 3.50/21.28
% 3.50/21.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.50/21.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.50/21.28 % git: non_committed_changes: false
% 3.50/21.28
% 3.50/21.28 % ------ Parsing...
% 3.50/21.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.50/21.28
% 3.50/21.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.50/21.28
% 3.50/21.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.50/21.28
% 3.50/21.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.50/21.28 % ------ Proving...
% 3.50/21.28 % ------ Problem Properties
% 3.50/21.28
% 3.50/21.28 %
% 3.50/21.28 % clauses 21
% 3.50/21.28 % conjectures 2
% 3.50/21.28 % EPR 0
% 3.50/21.28 % Horn 21
% 3.50/21.28 % unary 20
% 3.50/21.28 % binary 1
% 3.50/21.28 % lits 22
% 3.50/21.28 % lits eq 22
% 3.50/21.28 % fd_pure 0
% 3.50/21.28 % fd_pseudo 0
% 3.50/21.28 % fd_cond 0
% 3.50/21.28 % fd_pseudo_cond 0
% 3.50/21.28 % AC symbols 1
% 3.50/21.28
% 3.50/21.28 % ------ Schedule dynamic 5 is on
% 3.50/21.28
% 3.50/21.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.50/21.28
% 3.50/21.28
% 3.50/21.28 % ------
% 3.50/21.28 % Current options:
% 3.50/21.28 % ------
% 3.50/21.28
% 3.50/21.28
% 3.50/21.28 %
% 3.50/21.28
% 3.50/21.28 % ------ Proving...
% 3.50/21.28 %
% 3.50/21.28
% 3.50/21.28 % SZS status Theorem for theBenchmark.p
% 3.50/21.28
% 3.50/21.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.50/21.28
% 3.50/21.28
%------------------------------------------------------------------------------