%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL019+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 : n009.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 02:36:50 PM UTC 2026
% Result : Theorem 35.93s 7.29s
% Output : CNFRefutation 35.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 21
% Syntax : Number of formulae : 191 ( 186 unt; 7 def)
% Number of atoms : 484 ( 200 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 19 ( 9 ~; 0 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 157 ( 0 sgn 153 !; 4 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(f14,conjecture,
! [X0,X1] :
( ( composition(X1,top) = X1
& composition(X0,top) = X0 )
=> composition(meet(X0,X1),top) = meet(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( ( composition(X1,top) = X1
& composition(X0,top) = X0 )
=> composition(meet(X0,X1),top) = meet(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1] :
( composition(X1,top) = X1
& composition(X0,top) = X0
& meet(X0,X1) != composition(meet(X0,X1),top) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
? [X0,X1] :
( composition(X1,top) = X1
& composition(X0,top) = X0
& meet(X0,X1) != composition(meet(X0,X1),top) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( sK1 = composition(sK1,top)
& sK0 = composition(sK0,top)
& meet(sK0,sK1) != composition(meet(sK0,sK1),top) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f17]) ).
fof(f19,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f20,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f22,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f23,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f25,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f26,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f27,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f28,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f29,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f30,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f31,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f32,plain,
sK1 = composition(sK1,top),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
sK0 = composition(sK0,top),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
meet(sK0,sK1) != composition(meet(sK0,sK1),top),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f31,f22]) ).
fof(f36,plain,
complement(join(complement(sK0),complement(sK1))) != composition(complement(join(complement(sK0),complement(sK1))),top),
inference(definition_unfolding,[],[f34,f22,f22]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f19]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f21]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f23]) ).
tcf(c_53,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f24]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(cnf_transformation,[],[f25]) ).
tcf(c_55,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f26]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f29]) ).
tcf(c_59,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f30]) ).
tcf(c_60,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f35]) ).
tcf(c_61,negated_conjecture,
composition(complement(join(complement(sK0),complement(sK1))),top) != complement(join(complement(sK0),complement(sK1))),
inference(cnf_transformation,[],[f36]) ).
tcf(c_62,negated_conjecture,
composition(sK0,top) = sK0,
inference(cnf_transformation,[],[f33]) ).
tcf(c_63,negated_conjecture,
composition(sK1,top) = sK1,
inference(cnf_transformation,[],[f32]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(theory_normalisation,[status(thm)],[c_51,c_50,c_49]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_58,c_50,c_49]) ).
tcf(c_110,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_117,definition,
iPr_def_10 = composition(sK1,top),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_118,definition,
iPr_def_11 = composition(sK0,top),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_119,definition,
iPr_def_12 = complement(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_120,definition,
iPr_def_13 = complement(sK1),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_121,definition,
iPr_def_14 = join(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_122,definition,
iPr_def_15 = complement(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_123,definition,
iPr_def_16 = composition(iPr_def_15,top),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_124,negated_conjecture,
iPr_def_10 = sK1,
inference(demodulation,[status(thm)],[c_63,c_117]) ).
tcf(c_125,negated_conjecture,
iPr_def_11 = sK0,
inference(demodulation,[status(thm)],[c_62,c_118]) ).
tcf(c_126,negated_conjecture,
iPr_def_16 != iPr_def_15,
inference(demodulation,[status(thm)],[c_61,c_120,c_119,c_121,c_122,c_123]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(superposition,[status(thm)],[c_50,c_49]) ).
tcf(c_210,plain,
complement(iPr_def_11) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_119,c_125]) ).
tcf(c_211,plain,
complement(iPr_def_10) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_120,c_124]) ).
tcf(c_219,plain,
! [X0: $i] : join(complement(join(iPr_def_15,X0)),complement(join(iPr_def_15,complement(X0)))) = iPr_def_14,
inference(superposition,[status(thm)],[c_122,c_76]) ).
tcf(c_220,plain,
! [X0: $i] : join(complement(join(iPr_def_12,X0)),complement(join(iPr_def_12,complement(X0)))) = iPr_def_11,
inference(superposition,[status(thm)],[c_210,c_76]) ).
tcf(c_221,plain,
! [X0: $i] : join(complement(join(iPr_def_13,X0)),complement(join(iPr_def_13,complement(X0)))) = iPr_def_10,
inference(superposition,[status(thm)],[c_211,c_76]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(join(complement(X0),X1)),join(complement(X0),complement(X1)))),complement(X0)) = join(complement(X0),X1),
inference(superposition,[status(thm)],[c_76,c_76]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(complement(X0),join(complement(X1),complement(join(complement(X0),X1)))))) = join(complement(X0),X1),
inference(theory_normalisation,[status(thm)],[c_226,c_50,c_49]) ).
tcf(c_234,plain,
composition(iPr_def_10,top) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_117,c_124]) ).
tcf(c_235,plain,
composition(iPr_def_11,top) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_118,c_125]) ).
tcf(c_238,plain,
join(iPr_def_11,iPr_def_12) = top,
inference(superposition,[status(thm)],[c_210,c_59]) ).
tcf(c_241,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[status(thm)],[c_59,c_76]) ).
tcf(c_244,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(light_normalisation,[status(thm)],[c_241,c_110]) ).
tcf(c_250,plain,
join(complement(join(iPr_def_12,iPr_def_14)),complement(join(iPr_def_12,iPr_def_15))) = iPr_def_11,
inference(superposition,[status(thm)],[c_122,c_220]) ).
tcf(c_252,plain,
join(complement(join(iPr_def_12,iPr_def_10)),complement(join(iPr_def_12,iPr_def_13))) = iPr_def_11,
inference(superposition,[status(thm)],[c_211,c_220]) ).
tcf(c_258,plain,
join(complement(join(iPr_def_10,iPr_def_12)),complement(join(iPr_def_12,iPr_def_13))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_252,c_50,c_49]) ).
tcf(c_259,plain,
join(complement(join(iPr_def_10,iPr_def_12)),iPr_def_15) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_258,c_121,c_122]) ).
tcf(c_260,plain,
join(iPr_def_15,complement(join(iPr_def_10,iPr_def_12))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_259,c_50,c_49]) ).
tcf(c_272,plain,
join(complement(join(iPr_def_13,iPr_def_11)),complement(join(iPr_def_13,iPr_def_12))) = iPr_def_10,
inference(superposition,[status(thm)],[c_210,c_221]) ).
tcf(c_280,plain,
join(complement(join(iPr_def_11,iPr_def_13)),complement(join(iPr_def_12,iPr_def_13))) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_272,c_50,c_49]) ).
tcf(c_281,plain,
join(complement(join(iPr_def_11,iPr_def_13)),iPr_def_15) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_280,c_121,c_122]) ).
tcf(c_282,plain,
join(iPr_def_15,complement(join(iPr_def_11,iPr_def_13))) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_281,c_50,c_49]) ).
tcf(c_385,plain,
! [X0: $i] : join(iPr_def_15,composition(converse(X0),complement(composition(X0,iPr_def_14)))) = iPr_def_15,
inference(superposition,[status(thm)],[c_122,c_77]) ).
tcf(c_386,plain,
! [X0: $i] : join(iPr_def_12,composition(converse(X0),complement(composition(X0,iPr_def_11)))) = iPr_def_12,
inference(superposition,[status(thm)],[c_210,c_77]) ).
tcf(c_391,plain,
join(complement(top),composition(converse(iPr_def_10),complement(iPr_def_10))) = complement(top),
inference(superposition,[status(thm)],[c_234,c_77]) ).
tcf(c_392,plain,
join(complement(top),composition(converse(iPr_def_11),complement(iPr_def_11))) = complement(top),
inference(superposition,[status(thm)],[c_235,c_77]) ).
tcf(c_394,plain,
join(zero,composition(converse(iPr_def_11),iPr_def_12)) = zero,
inference(light_normalisation,[status(thm)],[c_392,c_110,c_210]) ).
tcf(c_395,plain,
join(zero,composition(converse(iPr_def_10),iPr_def_13)) = zero,
inference(light_normalisation,[status(thm)],[c_391,c_110,c_211]) ).
tcf(c_415,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_416,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_420,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_59,c_50]) ).
tcf(c_432,plain,
! [X0: $i] : join(iPr_def_11,join(iPr_def_12,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_238,c_50]) ).
tcf(c_450,plain,
! [X0: $i] : join(iPr_def_12,composition(X0,complement(composition(converse(X0),iPr_def_11)))) = iPr_def_12,
inference(superposition,[status(thm)],[c_55,c_386]) ).
tcf(c_464,plain,
! [X0: $i] : join(iPr_def_11,join(X0,iPr_def_12)) = join(top,X0),
inference(superposition,[status(thm)],[c_49,c_432]) ).
tcf(c_548,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(X0))) = join(X1,top),
inference(superposition,[status(thm)],[c_59,c_209]) ).
tcf(c_556,plain,
! [X0: $i] : join(iPr_def_11,join(X0,iPr_def_12)) = join(X0,top),
inference(superposition,[status(thm)],[c_238,c_209]) ).
tcf(c_593,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_595,plain,
! [X0: $i] : composition(iPr_def_15,composition(top,X0)) = composition(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_123,c_52]) ).
tcf(c_608,plain,
! [X0: $i] : join(iPr_def_10,composition(X0,top)) = composition(join(iPr_def_10,X0),top),
inference(superposition,[status(thm)],[c_234,c_54]) ).
tcf(c_609,plain,
! [X0: $i] : join(iPr_def_11,composition(X0,top)) = composition(join(iPr_def_11,X0),top),
inference(superposition,[status(thm)],[c_235,c_54]) ).
tcf(c_995,plain,
join(complement(join(iPr_def_15,join(iPr_def_10,iPr_def_12))),complement(iPr_def_11)) = iPr_def_14,
inference(superposition,[status(thm)],[c_260,c_219]) ).
tcf(c_1014,plain,
join(complement(iPr_def_11),complement(join(iPr_def_10,join(iPr_def_12,iPr_def_15)))) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_995,c_50,c_49]) ).
tcf(c_1015,plain,
join(iPr_def_12,complement(join(iPr_def_10,join(iPr_def_12,iPr_def_15)))) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_1014,c_210]) ).
tcf(c_2212,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_59,c_415]) ).
tcf(c_2545,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_420]) ).
tcf(c_2571,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_2545,c_55]) ).
tcf(c_2585,plain,
! [X0: $i] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_2571,c_77]) ).
tcf(c_2596,plain,
join(iPr_def_12,composition(one,complement(iPr_def_11))) = iPr_def_12,
inference(superposition,[status(thm)],[c_2571,c_450]) ).
tcf(c_2600,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_2571,c_593]) ).
tcf(c_2602,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_2600,c_2571]) ).
tcf(c_2604,plain,
join(iPr_def_12,composition(one,iPr_def_12)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_2596,c_210]) ).
tcf(c_2635,plain,
! [X0: $i,X1: $i] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(superposition,[status(thm)],[c_2602,c_54]) ).
tcf(c_2729,plain,
join(iPr_def_12,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2604,c_2602]) ).
tcf(c_2731,plain,
! [X0: $i] : join(iPr_def_12,join(iPr_def_12,X0)) = join(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_2729,c_50]) ).
tcf(c_3237,plain,
join(complement(join(iPr_def_12,iPr_def_14)),complement(join(complement(join(iPr_def_12,iPr_def_14)),join(complement(complement(join(iPr_def_12,iPr_def_15))),complement(iPr_def_11))))) = iPr_def_11,
inference(superposition,[status(thm)],[c_250,c_232]) ).
tcf(c_3268,plain,
join(complement(join(iPr_def_12,iPr_def_14)),complement(join(complement(iPr_def_11),join(complement(join(iPr_def_12,iPr_def_14)),complement(complement(join(iPr_def_12,iPr_def_15))))))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_3237,c_50,c_49]) ).
tcf(c_3269,plain,
join(complement(join(iPr_def_12,iPr_def_14)),complement(join(iPr_def_12,join(complement(join(iPr_def_12,iPr_def_14)),complement(complement(join(iPr_def_12,iPr_def_15))))))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_3268,c_210]) ).
tcf(c_3396,plain,
join(iPr_def_12,iPr_def_14) = iPr_def_14,
inference(superposition,[status(thm)],[c_1015,c_2731]) ).
tcf(c_3515,plain,
join(iPr_def_15,complement(join(iPr_def_12,join(iPr_def_15,complement(complement(join(iPr_def_12,iPr_def_15))))))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_3269,c_122,c_3396]) ).
tcf(c_4888,plain,
! [X0: $i] : join(top,complement(complement(X0))) = join(X0,top),
inference(superposition,[status(thm)],[c_59,c_424]) ).
tcf(c_7033,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_2585,c_2602]) ).
tcf(c_7041,plain,
join(zero,zero) = zero,
inference(superposition,[status(thm)],[c_110,c_7033]) ).
tcf(c_7042,plain,
join(iPr_def_15,iPr_def_15) = iPr_def_15,
inference(superposition,[status(thm)],[c_122,c_7033]) ).
tcf(c_7055,plain,
! [X0: $i] : join(X0,complement(X0)) = join(complement(X0),top),
inference(superposition,[status(thm)],[c_7033,c_548]) ).
tcf(c_7056,plain,
! [X0: $i] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(theory_normalisation,[status(thm)],[c_7055,c_50,c_49]) ).
tcf(c_7057,plain,
! [X0: $i] : join(top,complement(X0)) = top,
inference(light_normalisation,[status(thm)],[c_7056,c_59]) ).
tcf(c_7068,plain,
! [X0: $i] : join(X0,top) = top,
inference(demodulation,[status(thm)],[c_4888,c_7057]) ).
tcf(c_7076,plain,
! [X0: $i] : join(iPr_def_11,join(X0,iPr_def_12)) = top,
inference(demodulation,[status(thm)],[c_556,c_7068]) ).
tcf(c_7078,plain,
! [X0: $i] : join(top,X0) = top,
inference(demodulation,[status(thm)],[c_464,c_7076]) ).
tcf(c_7099,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_7041,c_50]) ).
tcf(c_7104,plain,
! [X0: $i] : join(iPr_def_15,join(iPr_def_15,X0)) = join(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_7042,c_50]) ).
tcf(c_7642,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_244,c_7099]) ).
tcf(c_7671,plain,
composition(converse(iPr_def_11),iPr_def_12) = zero,
inference(demodulation,[status(thm)],[c_394,c_7642]) ).
tcf(c_7672,plain,
composition(converse(iPr_def_10),iPr_def_13) = zero,
inference(demodulation,[status(thm)],[c_395,c_7642]) ).
tcf(c_7721,plain,
join(iPr_def_15,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_282,c_7104]) ).
tcf(c_7725,plain,
join(iPr_def_15,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_3515,c_7104]) ).
tcf(c_7735,plain,
join(iPr_def_11,iPr_def_15) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_7725,c_50,c_49]) ).
tcf(c_7736,plain,
join(iPr_def_10,iPr_def_15) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_7721,c_50,c_49]) ).
tcf(c_7921,plain,
converse(top) = top,
inference(superposition,[status(thm)],[c_7078,c_2212]) ).
tcf(c_8732,plain,
! [X0: $i] : composition(top,converse(X0)) = converse(composition(X0,top)),
inference(superposition,[status(thm)],[c_7921,c_419]) ).
tcf(c_8753,plain,
! [X0: $i] : join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_7642,c_49]) ).
tcf(c_8758,plain,
complement(zero) = top,
inference(superposition,[status(thm)],[c_7642,c_59]) ).
tcf(c_8763,plain,
! [X0: $i] : join(converse(zero),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_7642,c_416]) ).
tcf(c_8773,plain,
! [X0: $i] : join(converse(zero),X0) = X0,
inference(light_normalisation,[status(thm)],[c_8763,c_55]) ).
tcf(c_9020,plain,
join(iPr_def_11,composition(iPr_def_15,top)) = composition(iPr_def_11,top),
inference(superposition,[status(thm)],[c_7735,c_609]) ).
tcf(c_9023,plain,
join(iPr_def_11,iPr_def_16) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_9020,c_123,c_235]) ).
tcf(c_9031,plain,
join(iPr_def_10,composition(iPr_def_15,top)) = composition(iPr_def_10,top),
inference(superposition,[status(thm)],[c_7736,c_608]) ).
tcf(c_9034,plain,
join(iPr_def_10,iPr_def_16) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_9031,c_123,c_234]) ).
tcf(c_9466,plain,
! [X0: $i] : composition(join(converse(iPr_def_11),X0),iPr_def_12) = join(zero,composition(X0,iPr_def_12)),
inference(superposition,[status(thm)],[c_7671,c_54]) ).
tcf(c_9473,plain,
! [X0: $i] : composition(join(converse(iPr_def_10),X0),iPr_def_13) = join(zero,composition(X0,iPr_def_13)),
inference(superposition,[status(thm)],[c_7672,c_54]) ).
tcf(c_9507,plain,
converse(zero) = zero,
inference(superposition,[status(thm)],[c_8773,c_8753]) ).
tcf(c_11426,plain,
! [X0: $i] : join(iPr_def_15,composition(X0,complement(composition(converse(X0),iPr_def_14)))) = iPr_def_15,
inference(superposition,[status(thm)],[c_55,c_385]) ).
tcf(c_12165,plain,
! [X0: $i] : join(X0,composition(complement(one),X0)) = composition(top,X0),
inference(superposition,[status(thm)],[c_59,c_2635]) ).
tcf(c_12168,plain,
! [X0: $i] : join(X0,composition(top,X0)) = composition(top,X0),
inference(superposition,[status(thm)],[c_7068,c_2635]) ).
tcf(c_12260,plain,
composition(top,top) = top,
inference(superposition,[status(thm)],[c_12165,c_7078]) ).
tcf(c_12314,plain,
composition(iPr_def_15,top) = composition(iPr_def_16,top),
inference(superposition,[status(thm)],[c_12260,c_595]) ).
tcf(c_12315,plain,
composition(iPr_def_16,top) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_12314,c_123]) ).
tcf(c_24888,plain,
! [X0: $i] : composition(join(converse(iPr_def_11),X0),iPr_def_12) = composition(X0,iPr_def_12),
inference(demodulation,[status(thm)],[c_9466,c_7642]) ).
tcf(c_24893,plain,
! [X0: $i] : composition(converse(join(iPr_def_11,X0)),iPr_def_12) = composition(converse(X0),iPr_def_12),
inference(superposition,[status(thm)],[c_56,c_24888]) ).
tcf(c_25518,plain,
composition(converse(iPr_def_11),iPr_def_12) = composition(converse(iPr_def_16),iPr_def_12),
inference(superposition,[status(thm)],[c_9023,c_24893]) ).
tcf(c_25563,plain,
composition(converse(iPr_def_16),iPr_def_12) = zero,
inference(light_normalisation,[status(thm)],[c_25518,c_7671]) ).
tcf(c_25750,plain,
composition(converse(iPr_def_12),iPr_def_16) = converse(zero),
inference(superposition,[status(thm)],[c_25563,c_420]) ).
tcf(c_25755,plain,
composition(converse(iPr_def_12),iPr_def_16) = zero,
inference(light_normalisation,[status(thm)],[c_25750,c_9507]) ).
tcf(c_25803,plain,
! [X0: $i] : composition(join(converse(iPr_def_12),X0),iPr_def_16) = join(zero,composition(X0,iPr_def_16)),
inference(superposition,[status(thm)],[c_25755,c_54]) ).
tcf(c_26067,plain,
! [X0: $i] : composition(join(converse(iPr_def_10),X0),iPr_def_13) = composition(X0,iPr_def_13),
inference(demodulation,[status(thm)],[c_9473,c_7642]) ).
tcf(c_26072,plain,
! [X0: $i] : composition(converse(join(iPr_def_10,X0)),iPr_def_13) = composition(converse(X0),iPr_def_13),
inference(superposition,[status(thm)],[c_56,c_26067]) ).
tcf(c_26927,plain,
composition(converse(iPr_def_10),iPr_def_13) = composition(converse(iPr_def_16),iPr_def_13),
inference(superposition,[status(thm)],[c_9034,c_26072]) ).
tcf(c_26975,plain,
composition(converse(iPr_def_16),iPr_def_13) = zero,
inference(light_normalisation,[status(thm)],[c_26927,c_7672]) ).
tcf(c_27322,plain,
composition(converse(iPr_def_13),iPr_def_16) = converse(zero),
inference(superposition,[status(thm)],[c_26975,c_420]) ).
tcf(c_27327,plain,
composition(converse(iPr_def_13),iPr_def_16) = zero,
inference(light_normalisation,[status(thm)],[c_27322,c_9507]) ).
tcf(c_61225,plain,
! [X0: $i] : composition(join(converse(iPr_def_12),X0),iPr_def_16) = composition(X0,iPr_def_16),
inference(demodulation,[status(thm)],[c_25803,c_7642]) ).
tcf(c_61230,plain,
! [X0: $i] : composition(converse(join(iPr_def_12,X0)),iPr_def_16) = composition(converse(X0),iPr_def_16),
inference(superposition,[status(thm)],[c_56,c_61225]) ).
tcf(c_61317,plain,
composition(converse(iPr_def_13),iPr_def_16) = composition(converse(iPr_def_14),iPr_def_16),
inference(superposition,[status(thm)],[c_121,c_61230]) ).
tcf(c_61396,plain,
composition(converse(iPr_def_14),iPr_def_16) = zero,
inference(light_normalisation,[status(thm)],[c_61317,c_27327]) ).
tcf(c_61500,plain,
composition(converse(iPr_def_16),iPr_def_14) = converse(zero),
inference(superposition,[status(thm)],[c_61396,c_420]) ).
tcf(c_61503,plain,
composition(converse(iPr_def_16),iPr_def_14) = zero,
inference(light_normalisation,[status(thm)],[c_61500,c_9507]) ).
tcf(c_61523,plain,
join(iPr_def_15,composition(iPr_def_16,complement(zero))) = iPr_def_15,
inference(superposition,[status(thm)],[c_61503,c_11426]) ).
tcf(c_61525,plain,
join(iPr_def_15,iPr_def_16) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_61523,c_8758,c_12315]) ).
tcf(c_70323,plain,
composition(top,converse(iPr_def_15)) = converse(iPr_def_16),
inference(superposition,[status(thm)],[c_123,c_8732]) ).
tcf(c_99497,plain,
join(converse(iPr_def_15),converse(iPr_def_16)) = converse(iPr_def_16),
inference(superposition,[status(thm)],[c_70323,c_12168]) ).
tcf(c_100924,plain,
converse(iPr_def_15) = converse(iPr_def_16),
inference(demodulation,[status(thm)],[c_99497,c_56,c_61525]) ).
tcf(c_100992,plain,
converse(converse(iPr_def_15)) = iPr_def_16,
inference(superposition,[status(thm)],[c_100924,c_55]) ).
tcf(c_101018,plain,
iPr_def_15 = iPr_def_16,
inference(demodulation,[status(thm)],[c_100992,c_55]) ).
tcf(c_101142,plain,
iPr_def_15 != iPr_def_15,
inference(demodulation,[status(thm)],[c_126,c_101018]) ).
tcf(c_101143,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_101142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL019+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 07:16:13 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 35.93/7.29 % SZS status Started for theBenchmark.p
% 35.93/7.29 % SZS status Theorem for theBenchmark.p
% 35.93/7.29
% 35.93/7.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 35.93/7.29
% 35.93/7.29 % ------ iProver source info
% 35.93/7.29
% 35.93/7.29 % git: date: 2026-07-19 20:42:38 +0200
% 35.93/7.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 35.93/7.29 % git: non_committed_changes: false
% 35.93/7.29
% 35.93/7.29 % ------ Parsing...
% 35.93/7.29 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 35.93/7.29 %
% 35.93/7.29
% 35.93/7.29 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 35.93/7.29
% 35.93/7.29 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 35.93/7.29 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 35.93/7.29
% 35.93/7.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 35.93/7.29 % ------ Proving...
% 35.93/7.29 % ------ Problem Properties
% 35.93/7.29
% 35.93/7.29 %
% 35.93/7.29 % clauses 22
% 35.93/7.29 % conjectures 3
% 35.93/7.29 % EPR 3
% 35.93/7.29 % Horn 22
% 35.93/7.29 % unary 22
% 35.93/7.29 % binary 0
% 35.93/7.29 % lits 22
% 35.93/7.29 % lits eq 22
% 35.93/7.29 % fd_pure 0
% 35.93/7.29 % fd_pseudo 0
% 35.93/7.29 % fd_cond 0
% 35.93/7.29 % fd_pseudo_cond 0
% 35.93/7.29 % AC symbols 1
% 35.93/7.29
% 35.93/7.29 % ------ Schedule UEQ
% 35.93/7.29
% 35.93/7.29 % ------ Option_UEQ Time Limit: 10.
% 35.93/7.29
% 35.93/7.29
% 35.93/7.29 % ------
% 35.93/7.29 % Current options:
% 35.93/7.29 % ------
% 35.93/7.29
% 35.93/7.29
% 35.93/7.29 %
% 35.93/7.29
% 35.93/7.29 % ------ Proving...
% 35.93/7.29 %
% 35.93/7.29
% 35.93/7.29 % SZS status Theorem for theBenchmark.p
% 35.93/7.29
% 35.93/7.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 35.93/7.29
% 35.93/7.29
%------------------------------------------------------------------------------