%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE128+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 : 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 31.90s 5.79s
% Output : CNFRefutation 31.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 75 ( 66 unt; 0 def)
% Number of atoms : 88 ( 87 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 10 ~; 4 |; 4 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 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; 4 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 75 !; 2 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f10,axiom,
! [X0] : multiplication(X0,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(f11,axiom,
! [X0] : multiplication(zero,X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+4.ax',domain3) ).
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(f28,axiom,
! [X0,X1,X2] :
( addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) = addition(forward_diamond(X1,domain(X0)),domain(X2))
=> addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+7.ax',divergence2) ).
fof(f29,conjecture,
! [X0] :
( divergence(X0) = zero
=> ! [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( divergence(X0) = zero
=> ! [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
=> domain(X1) = zero ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( addition(forward_diamond(X1,domain(X0)),domain(X2)) != addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2)))
| addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))) ),
inference(ennf_transformation,[],[f28]) ).
fof(f32,plain,
? [X0] :
( divergence(X0) = zero
& ? [X1] :
( addition(domain(X1),forward_diamond(X0,domain(X1))) = forward_diamond(X0,domain(X1))
& zero != domain(X1) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f33,plain,
( zero = divergence(sK0)
& forward_diamond(sK0,domain(sK1)) = addition(domain(sK1),forward_diamond(sK0,domain(sK1)))
& zero != domain(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f32]) ).
fof(f34,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f35,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f36,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f39,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f40,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f43,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f44,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f45,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(cnf_transformation,[],[f13]) ).
fof(f47,plain,
! [X0] : one = addition(antidomain(antidomain(X0)),antidomain(X0)),
inference(cnf_transformation,[],[f15]) ).
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(f60,plain,
! [X2,X0,X1] :
( addition(forward_diamond(X1,domain(X0)),domain(X2)) != addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2)))
| addition(divergence(X1),forward_diamond(star(X1),domain(X2))) = addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) ),
inference(cnf_transformation,[],[f31]) ).
fof(f61,plain,
zero = divergence(sK0),
inference(cnf_transformation,[],[f33]) ).
fof(f62,plain,
forward_diamond(sK0,domain(sK1)) = addition(domain(sK1),forward_diamond(sK0,domain(sK1))),
inference(cnf_transformation,[],[f33]) ).
fof(f63,plain,
zero != domain(sK1),
inference(cnf_transformation,[],[f33]) ).
fof(f68,plain,
! [X0,X1] : forward_diamond(X0,X1) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(X1))))),
inference(definition_unfolding,[],[f55,f48,f48]) ).
fof(f70,plain,
! [X0] : divergence(X0) = antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))),
inference(definition_unfolding,[],[f59,f68]) ).
fof(f71,plain,
! [X2,X0,X1] :
( addition(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(X2))) != addition(antidomain(antidomain(X0)),addition(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(X2))))
| addition(divergence(X1),antidomain(antidomain(multiplication(star(X1),antidomain(antidomain(antidomain(antidomain(X2)))))))) = addition(antidomain(antidomain(X0)),addition(divergence(X1),antidomain(antidomain(multiplication(star(X1),antidomain(antidomain(antidomain(antidomain(X2))))))))) ),
inference(definition_unfolding,[],[f60,f68,f48,f48,f68,f48,f68,f48,f48,f48,f68,f48,f48]) ).
fof(f72,plain,
zero != antidomain(antidomain(sK1)),
inference(definition_unfolding,[],[f63,f48]) ).
fof(f73,plain,
antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))) = addition(antidomain(antidomain(sK1)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1)))))))),
inference(definition_unfolding,[],[f62,f68,f48,f48,f68,f48]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f34]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f36]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f39]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f40]) ).
tcf(c_58,plain,
! [X0: $i] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[],[f43]) ).
tcf(c_59,plain,
! [X0: $i] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[],[f44]) ).
tcf(c_60,plain,
! [X0: $i] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[],[f45]) ).
tcf(c_62,plain,
! [X0: $i] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[],[f47]) ).
tcf(c_66,plain,
! [X0: $i] : antidomain(antidomain(multiplication(X0,antidomain(antidomain(divergence(X0)))))) = divergence(X0),
inference(cnf_transformation,[],[f70]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( addition(antidomain(antidomain(X0)),addition(divergence(X1),antidomain(antidomain(multiplication(star(X1),antidomain(antidomain(antidomain(antidomain(X2))))))))) = addition(divergence(X1),antidomain(antidomain(multiplication(star(X1),antidomain(antidomain(antidomain(antidomain(X2)))))))) )
| ( addition(antidomain(antidomain(X0)),addition(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(X2)))) != addition(antidomain(antidomain(multiplication(X1,antidomain(antidomain(antidomain(antidomain(X0))))))),antidomain(antidomain(X2))) ) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_68,negated_conjecture,
antidomain(antidomain(sK1)) != zero,
inference(cnf_transformation,[],[f72]) ).
tcf(c_69,negated_conjecture,
addition(antidomain(antidomain(sK1)),antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1)))))))) = antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),
inference(cnf_transformation,[],[f73]) ).
tcf(c_70,negated_conjecture,
divergence(sK0) = zero,
inference(cnf_transformation,[],[f61]) ).
tcf(c_88,plain,
! [X0: $i] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_1036,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_49,c_51]) ).
tcf(c_1956,plain,
antidomain(one) = zero,
inference(superposition,[status(thm)],[c_54,c_60]) ).
tcf(c_1965,plain,
! [X0: $i] : addition(antidomain(antidomain(sK1)),addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),X0)) = addition(antidomain(antidomain(multiplication(sK0,antidomain(antidomain(antidomain(antidomain(sK1))))))),X0),
inference(superposition,[status(thm)],[c_69,c_50]) ).
tcf(c_2081,plain,
antidomain(antidomain(zero)) = divergence(zero),
inference(superposition,[status(thm)],[c_59,c_66]) ).
tcf(c_2082,plain,
antidomain(antidomain(multiplication(sK0,antidomain(antidomain(zero))))) = zero,
inference(superposition,[status(thm)],[c_70,c_66]) ).
tcf(c_2086,plain,
antidomain(antidomain(multiplication(sK0,divergence(zero)))) = zero,
inference(light_normalisation,[status(thm)],[c_2082,c_2081]) ).
tcf(c_2146,plain,
addition(antidomain(multiplication(sK0,divergence(zero))),zero) = one,
inference(superposition,[status(thm)],[c_2086,c_88]) ).
tcf(c_2147,plain,
addition(zero,antidomain(multiplication(sK0,divergence(zero)))) = one,
inference(theory_normalisation,[status(thm)],[c_2146,c_50,c_49]) ).
tcf(c_2148,plain,
antidomain(multiplication(sK0,divergence(zero))) = one,
inference(demodulation,[status(thm)],[c_2147,c_1036]) ).
tcf(c_2151,plain,
multiplication(one,multiplication(sK0,divergence(zero))) = zero,
inference(superposition,[status(thm)],[c_2148,c_60]) ).
tcf(c_2216,plain,
multiplication(sK0,divergence(zero)) = zero,
inference(demodulation,[status(thm)],[c_2151,c_55]) ).
tcf(c_2217,plain,
antidomain(zero) = one,
inference(demodulation,[status(thm)],[c_2148,c_2216]) ).
tcf(c_2489,plain,
! [X0: $i] : addition(antidomain(antidomain(sK1)),addition(divergence(sK0),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(antidomain(antidomain(X0))))))))) = addition(divergence(sK0),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(antidomain(antidomain(X0)))))))),
inference(superposition,[status(thm)],[c_1965,c_67]) ).
tcf(c_2519,plain,
! [X0: $i] : addition(divergence(sK0),addition(antidomain(antidomain(sK1)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(antidomain(antidomain(X0))))))))) = addition(divergence(sK0),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(antidomain(antidomain(X0)))))))),
inference(theory_normalisation,[status(thm)],[c_2489,c_50,c_49]) ).
tcf(c_2961,plain,
! [X0: $i] : addition(zero,addition(antidomain(antidomain(sK1)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(antidomain(antidomain(X0))))))))) = addition(zero,antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(antidomain(antidomain(X0)))))))),
inference(light_normalisation,[status(thm)],[c_2519,c_70]) ).
tcf(c_2962,plain,
! [X0: $i] : addition(antidomain(antidomain(sK1)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(antidomain(antidomain(X0)))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(antidomain(antidomain(X0))))))),
inference(demodulation,[status(thm)],[c_2961,c_1036]) ).
tcf(c_2965,plain,
! [X0: $i] : addition(antidomain(antidomain(sK1)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(divergence(X0))))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(divergence(X0)))))),
inference(superposition,[status(thm)],[c_66,c_2962]) ).
tcf(c_3028,plain,
addition(antidomain(antidomain(sK1)),antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(zero)))))) = antidomain(antidomain(multiplication(star(sK0),antidomain(antidomain(zero))))),
inference(superposition,[status(thm)],[c_70,c_2965]) ).
tcf(c_3048,plain,
addition(antidomain(antidomain(sK1)),antidomain(antidomain(multiplication(star(sK0),zero)))) = antidomain(antidomain(multiplication(star(sK0),zero))),
inference(light_normalisation,[status(thm)],[c_3028,c_1956,c_2217]) ).
tcf(c_3049,plain,
antidomain(antidomain(sK1)) = zero,
inference(demodulation,[status(thm)],[c_3048,c_51,c_58,c_1956,c_2217]) ).
tcf(c_3050,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3049,c_68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE128+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 19:01:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 31.90/5.79 % SZS status Started for theBenchmark.p
% 31.90/5.79 % SZS status Theorem for theBenchmark.p
% 31.90/5.79
% 31.90/5.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 31.90/5.79
% 31.90/5.79 % ------ iProver source info
% 31.90/5.79
% 31.90/5.79 % git: date: 2026-07-19 20:42:38 +0200
% 31.90/5.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 31.90/5.79 % git: non_committed_changes: false
% 31.90/5.79
% 31.90/5.79 % ------ Parsing...
% 31.90/5.79 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 31.90/5.79
% 31.90/5.79 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 31.90/5.79
% 31.90/5.79 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 31.90/5.79
% 31.90/5.79 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 31.90/5.79 % ------ Proving...
% 31.90/5.79 % ------ Problem Properties
% 31.90/5.79
% 31.90/5.79 %
% 31.90/5.79 % clauses 22
% 31.90/5.79 % conjectures 3
% 31.90/5.79 % EPR 0
% 31.90/5.79 % Horn 22
% 31.90/5.79 % unary 21
% 31.90/5.79 % binary 1
% 31.90/5.79 % lits 23
% 31.90/5.79 % lits eq 23
% 31.90/5.79 % fd_pure 0
% 31.90/5.79 % fd_pseudo 0
% 31.90/5.79 % fd_cond 0
% 31.90/5.79 % fd_pseudo_cond 0
% 31.90/5.79 % AC symbols 1
% 31.90/5.79
% 31.90/5.79 % ------ Input Options Time Limit: Unbounded
% 31.90/5.79
% 31.90/5.79
% 31.90/5.79 % ------
% 31.90/5.79 % Current options:
% 31.90/5.79 % ------
% 31.90/5.79
% 31.90/5.79
% 31.90/5.79 %
% 31.90/5.79
% 31.90/5.79 % ------ Proving...
% 31.90/5.79 %
% 31.90/5.79
% 31.90/5.79 % SZS status Theorem for theBenchmark.p
% 31.90/5.79
% 31.90/5.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.90/5.79
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