%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE082+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 : n004.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 01:52:21 PM UTC 2026
% Result : Theorem 3.77s 6.23s
% Output : CNFRefutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 84 ( 80 unt; 6 def)
% Number of atoms : 155 ( 91 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 7 ~; 0 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 90 !; 2 ?; 46 :)
% 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(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain2) ).
fof(f18,conjecture,
! [X0,X1] :
( ! [X2] :
( multiplication(domain(X2),antidomain(X2)) = zero
& addition(domain(X2),antidomain(X2)) = one )
=> addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f19,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( multiplication(domain(X2),antidomain(X2)) = zero
& addition(domain(X2),antidomain(X2)) = one )
=> addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
? [X0,X1] :
( ! [X2] :
( multiplication(domain(X2),antidomain(X2)) = zero
& addition(domain(X2),antidomain(X2)) = one )
& antidomain(multiplication(X0,domain(X1))) != addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) ),
inference(ennf_transformation,[],[f19]) ).
fof(f21,plain,
( ! [X2] :
( multiplication(domain(X2),antidomain(X2)) = zero
& addition(domain(X2),antidomain(X2)) = one )
& antidomain(multiplication(sK0,domain(sK1))) != addition(antidomain(multiplication(sK0,sK1)),antidomain(multiplication(sK0,domain(sK1)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
fof(f22,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f23,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f2]) ).
fof(f24,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f25,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f27,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f28,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f29,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f30,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f34,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[],[f14]) ).
fof(f38,plain,
! [X2] : zero = multiplication(domain(X2),antidomain(X2)),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X2] : one = addition(domain(X2),antidomain(X2)),
inference(cnf_transformation,[],[f21]) ).
fof(f40,plain,
antidomain(multiplication(sK0,domain(sK1))) != addition(antidomain(multiplication(sK0,sK1)),antidomain(multiplication(sK0,domain(sK1)))),
inference(cnf_transformation,[],[f21]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f22]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f23]) ).
tcf(c_51,plain,
! [X0: $i] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f24]) ).
tcf(c_52,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f25]) ).
tcf(c_54,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f29]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f30]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_65,negated_conjecture,
addition(antidomain(multiplication(sK0,sK1)),antidomain(multiplication(sK0,domain(sK1)))) != antidomain(multiplication(sK0,domain(sK1))),
inference(cnf_transformation,[],[f40]) ).
tcf(c_66,negated_conjecture,
! [X0: $i] : addition(domain(X0),antidomain(X0)) = one,
inference(cnf_transformation,[],[f39]) ).
tcf(c_67,negated_conjecture,
! [X0: $i] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(cnf_transformation,[],[f38]) ).
tcf(c_129,definition,
iPr_def_10 = multiplication(sK0,sK1),
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 = domain(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_132,definition,
iPr_def_13 = multiplication(sK0,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_133,definition,
iPr_def_14 = antidomain(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_134,definition,
iPr_def_15 = addition(iPr_def_11,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_135,negated_conjecture,
! [X0: $i] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_136,negated_conjecture,
! [X0: $i] : addition(domain(X0),antidomain(X0)) = one,
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_137,negated_conjecture,
iPr_def_15 != iPr_def_14,
inference(demodulation,[status(thm)],[c_65,c_131,c_132,c_133,c_129,c_130,c_134]) ).
tcf(c_226,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_255,plain,
! [X0: $i,X1: $i] : addition(domain(X0),addition(X1,antidomain(X0))) = addition(X1,one),
inference(superposition,[status(thm)],[c_136,c_226]) ).
tcf(c_267,plain,
! [X0: $i] : addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c_51,c_49]) ).
tcf(c_275,plain,
! [X0: $i] : domain(multiplication(X0,sK1)) = domain(multiplication(X0,iPr_def_12)),
inference(superposition,[status(thm)],[c_131,c_61]) ).
tcf(c_278,plain,
! [X0: $i,X1: $i] : multiplication(domain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = zero,
inference(superposition,[status(thm)],[c_61,c_135]) ).
tcf(c_350,plain,
! [X0: $i] : addition(domain(X0),antidomain(X0)) = addition(antidomain(X0),one),
inference(superposition,[status(thm)],[c_52,c_255]) ).
tcf(c_370,plain,
! [X0: $i] : addition(domain(X0),antidomain(X0)) = addition(one,antidomain(X0)),
inference(theory_normalisation,[status(thm)],[c_350,c_50,c_49]) ).
tcf(c_371,plain,
! [X0: $i] : addition(one,antidomain(X0)) = one,
inference(light_normalisation,[status(thm)],[c_370,c_136]) ).
tcf(c_378,plain,
addition(one,iPr_def_11) = one,
inference(superposition,[status(thm)],[c_130,c_371]) ).
tcf(c_379,plain,
addition(one,iPr_def_14) = one,
inference(superposition,[status(thm)],[c_133,c_371]) ).
tcf(c_385,plain,
addition(iPr_def_14,one) = one,
inference(theory_normalisation,[status(thm)],[c_379,c_50,c_49]) ).
tcf(c_386,plain,
addition(iPr_def_11,one) = one,
inference(theory_normalisation,[status(thm)],[c_378,c_50,c_49]) ).
tcf(c_463,plain,
multiplication(domain(iPr_def_10),antidomain(multiplication(sK0,domain(sK1)))) = zero,
inference(superposition,[status(thm)],[c_129,c_278]) ).
tcf(c_480,plain,
multiplication(domain(iPr_def_10),iPr_def_14) = zero,
inference(light_normalisation,[status(thm)],[c_463,c_131,c_132,c_133]) ).
tcf(c_680,plain,
! [X0: $i,X1: $i] : addition(multiplication(domain(X0),X1),multiplication(antidomain(X0),X1)) = multiplication(one,X1),
inference(superposition,[status(thm)],[c_136,c_57]) ).
tcf(c_720,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_14),multiplication(X0,one)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_385,c_56]) ).
tcf(c_726,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_14),X0) = X0,
inference(light_normalisation,[status(thm)],[c_720,c_54]) ).
tcf(c_727,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_14)) = X0,
inference(theory_normalisation,[status(thm)],[c_726,c_50,c_49]) ).
tcf(c_731,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),multiplication(X0,one)) = multiplication(X0,one),
inference(superposition,[status(thm)],[c_386,c_56]) ).
tcf(c_737,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_11),X0) = X0,
inference(light_normalisation,[status(thm)],[c_731,c_54]) ).
tcf(c_738,plain,
! [X0: $i] : addition(X0,multiplication(X0,iPr_def_11)) = X0,
inference(theory_normalisation,[status(thm)],[c_737,c_50,c_49]) ).
tcf(c_810,plain,
! [X0: $i,X1: $i] : addition(multiplication(domain(X0),X1),multiplication(antidomain(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_680,c_55]) ).
tcf(c_940,plain,
addition(zero,multiplication(antidomain(iPr_def_10),iPr_def_14)) = iPr_def_14,
inference(superposition,[status(thm)],[c_480,c_810]) ).
tcf(c_941,plain,
addition(zero,multiplication(iPr_def_11,iPr_def_14)) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_940,c_130]) ).
tcf(c_942,plain,
addition(multiplication(iPr_def_11,iPr_def_14),zero) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_941,c_50,c_49]) ).
tcf(c_1658,plain,
multiplication(iPr_def_11,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_942,c_51]) ).
tcf(c_1665,plain,
addition(iPr_def_11,iPr_def_14) = iPr_def_11,
inference(superposition,[status(thm)],[c_1658,c_727]) ).
tcf(c_1666,plain,
iPr_def_11 = iPr_def_15,
inference(demodulation,[status(thm)],[c_134,c_1665]) ).
tcf(c_1668,plain,
iPr_def_11 != iPr_def_14,
inference(demodulation,[status(thm)],[c_137,c_1666]) ).
tcf(c_2841,plain,
! [X0: $i] : multiplication(domain(multiplication(X0,iPr_def_12)),antidomain(multiplication(X0,sK1))) = zero,
inference(superposition,[status(thm)],[c_275,c_135]) ).
tcf(c_3027,plain,
! [X0: $i] : addition(zero,multiplication(antidomain(multiplication(X0,iPr_def_12)),antidomain(multiplication(X0,sK1)))) = antidomain(multiplication(X0,sK1)),
inference(superposition,[status(thm)],[c_2841,c_810]) ).
tcf(c_6245,plain,
! [X0: $i] : multiplication(antidomain(multiplication(X0,iPr_def_12)),antidomain(multiplication(X0,sK1))) = antidomain(multiplication(X0,sK1)),
inference(demodulation,[status(thm)],[c_3027,c_267]) ).
tcf(c_6258,plain,
multiplication(antidomain(multiplication(sK0,iPr_def_12)),antidomain(iPr_def_10)) = antidomain(iPr_def_10),
inference(superposition,[status(thm)],[c_129,c_6245]) ).
tcf(c_6276,plain,
multiplication(iPr_def_14,iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_6258,c_130,c_132,c_133]) ).
tcf(c_6690,plain,
addition(iPr_def_14,iPr_def_11) = iPr_def_14,
inference(superposition,[status(thm)],[c_6276,c_738]) ).
tcf(c_6691,plain,
addition(iPr_def_11,iPr_def_14) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_6690,c_50,c_49]) ).
tcf(c_6692,plain,
iPr_def_11 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_6691,c_1665]) ).
tcf(c_6693,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6692,c_1668]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE082+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.39 % Computer : n004.cluster.edu
% 0.10/5.39 % Model : x86_64 x86_64
% 0.10/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.39 % Memory : 8046.5625MB
% 0.10/5.39 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Wed Sep 23 18:52:45 UTC 2026
% 0.14/5.40 % CPUTime :
% 0.14/5.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.44 Running first-order theorem proving
% 0.14/5.44 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
% 0.14/5.45
% 0.14/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.45
% 0.14/5.45 % Detected problem language: tptp
% 0.14/5.46 % Proving...
% 3.77/6.23 % SZS status Started for theBenchmark.p
% 3.77/6.23 % SZS status Theorem for theBenchmark.p
% 3.77/6.23
% 3.77/6.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.77/6.23
% 3.77/6.23 % ------ iProver source info
% 3.77/6.23
% 3.77/6.23 % git: date: 2026-07-19 20:42:38 +0200
% 3.77/6.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.77/6.23 % git: non_committed_changes: false
% 3.77/6.23
% 3.77/6.23 % ------ Parsing...
% 3.77/6.23 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 3.77/6.23 %
% 3.77/6.23
% 3.77/6.23 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.77/6.23
% 3.77/6.23 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.77/6.23 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.77/6.23
% 3.77/6.23 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.77/6.23 % ------ Proving...
% 3.77/6.23 % ------ Problem Properties
% 3.77/6.23
% 3.77/6.23 %
% 3.77/6.23 % clauses 25
% 3.77/6.23 % conjectures 3
% 3.77/6.23 % EPR 1
% 3.77/6.23 % Horn 25
% 3.77/6.23 % unary 25
% 3.77/6.23 % binary 0
% 3.77/6.23 % lits 25
% 3.77/6.23 % lits eq 25
% 3.77/6.23 % fd_pure 0
% 3.77/6.23 % fd_pseudo 0
% 3.77/6.23 % fd_cond 0
% 3.77/6.23 % fd_pseudo_cond 0
% 3.77/6.23 % AC symbols 1
% 3.77/6.23
% 3.77/6.23 % ------ Schedule UEQ
% 3.77/6.23
% 3.77/6.23 % ------ Option_UEQ Time Limit: 10.
% 3.77/6.23
% 3.77/6.23
% 3.77/6.23 % ------
% 3.77/6.23 % Current options:
% 3.77/6.23 % ------
% 3.77/6.23
% 3.77/6.23
% 3.77/6.23 %
% 3.77/6.23
% 3.77/6.23 % ------ Proving...
% 3.77/6.23 %
% 3.77/6.23
% 3.77/6.23 % SZS status Theorem for theBenchmark.p
% 3.77/6.23
% 3.77/6.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.77/6.23
% 3.77/6.23
%------------------------------------------------------------------------------