%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL050+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 02:37:02 PM UTC 2026
% Result : Theorem 3.75s 1.19s
% Output : CNFRefutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 17
% Syntax : Number of formulae : 165 ( 165 unt; 3 def)
% Number of atoms : 285 ( 164 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 158 ( 0 sgn 157 !; 1 ?; 104 :)
% 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] : complement(composition(X0,top)) = composition(complement(composition(X0,top)),top),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0] : complement(composition(X0,top)) = composition(complement(composition(X0,top)),top),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0] : complement(composition(X0,top)) != composition(complement(composition(X0,top)),top),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
complement(composition(sK0,top)) != composition(complement(composition(sK0,top)),top),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f16]) ).
fof(f18,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f19,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f20,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f22,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f23,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f24,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f25,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f27,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f29,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f30,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f31,plain,
complement(composition(sK0,top)) != composition(complement(composition(sK0,top)),top),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f30,f21]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f18]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f20]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f22]) ).
tcf(c_53,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f23]) ).
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,[],[f24]) ).
tcf(c_55,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f25]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f28]) ).
tcf(c_59,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f29]) ).
tcf(c_60,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f32]) ).
tcf(c_61,negated_conjecture,
composition(complement(composition(sK0,top)),top) != complement(composition(sK0,top)),
inference(cnf_transformation,[],[f31]) ).
tcf(c_74,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_75,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_104,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_111,definition,
iPr_def_10 = composition(sK0,top),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_112,definition,
iPr_def_11 = complement(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_113,definition,
iPr_def_12 = composition(iPr_def_11,top),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_114,negated_conjecture,
iPr_def_12 != iPr_def_11,
inference(demodulation,[status(thm)],[c_61,c_111,c_112,c_113]) ).
tcf(c_187,plain,
join(iPr_def_10,iPr_def_11) = top,
inference(superposition,[status(thm)],[c_112,c_59]) ).
tcf(c_192,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_59,c_74]) ).
tcf(c_200,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_192,c_50,c_49]) ).
tcf(c_201,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_200,c_104]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X1),complement(X0)))) = X0,
inference(superposition,[status(thm)],[c_49,c_74]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_59,c_50]) ).
tcf(c_225,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_11,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_187,c_50]) ).
tcf(c_259,plain,
join(zero,complement(join(iPr_def_11,iPr_def_11))) = iPr_def_10,
inference(superposition,[status(thm)],[c_112,c_201]) ).
tcf(c_271,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_59,c_213]) ).
tcf(c_282,plain,
! [X0: $i] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(superposition,[status(thm)],[c_104,c_75]) ).
tcf(c_283,plain,
! [X0: $i] : join(iPr_def_11,composition(converse(X0),complement(composition(X0,iPr_def_10)))) = iPr_def_11,
inference(superposition,[status(thm)],[c_112,c_75]) ).
tcf(c_288,plain,
join(complement(top),composition(converse(sK0),complement(iPr_def_10))) = complement(top),
inference(superposition,[status(thm)],[c_111,c_75]) ).
tcf(c_293,plain,
join(zero,composition(converse(sK0),iPr_def_11)) = zero,
inference(light_normalisation,[status(thm)],[c_288,c_104,c_112]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_306,plain,
! [X0: $i] : join(iPr_def_10,composition(X0,top)) = composition(join(sK0,X0),top),
inference(superposition,[status(thm)],[c_111,c_54]) ).
tcf(c_307,plain,
! [X0: $i] : join(iPr_def_12,composition(X0,top)) = composition(join(iPr_def_11,X0),top),
inference(superposition,[status(thm)],[c_113,c_54]) ).
tcf(c_453,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_218]) ).
tcf(c_473,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_453,c_55]) ).
tcf(c_487,plain,
! [X0: $i] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_473,c_75]) ).
tcf(c_490,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_473,c_295]) ).
tcf(c_492,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_490,c_473]) ).
tcf(c_593,plain,
! [X0: $i] : join(top,complement(complement(X0))) = join(X0,top),
inference(superposition,[status(thm)],[c_59,c_221]) ).
tcf(c_926,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_487,c_492]) ).
tcf(c_927,plain,
! [X0: $i] : join(zero,complement(complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_201,c_926]) ).
tcf(c_931,plain,
join(zero,zero) = zero,
inference(superposition,[status(thm)],[c_104,c_926]) ).
tcf(c_932,plain,
join(iPr_def_11,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_112,c_926]) ).
tcf(c_936,plain,
! [X0: $i] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(superposition,[status(thm)],[c_926,c_221]) ).
tcf(c_938,plain,
! [X0: $i] : join(top,complement(X0)) = top,
inference(light_normalisation,[status(thm)],[c_936,c_59]) ).
tcf(c_946,plain,
join(zero,complement(iPr_def_11)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_259,c_932]) ).
tcf(c_947,plain,
! [X0: $i] : join(X0,top) = top,
inference(demodulation,[status(thm)],[c_593,c_938]) ).
tcf(c_951,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_931,c_50]) ).
tcf(c_954,plain,
! [X0: $i] : join(iPr_def_11,join(iPr_def_11,X0)) = join(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_932,c_50]) ).
tcf(c_956,plain,
join(top,iPr_def_11) = join(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_932,c_225]) ).
tcf(c_958,plain,
join(iPr_def_10,iPr_def_11) = join(iPr_def_11,top),
inference(theory_normalisation,[status(thm)],[c_956,c_50,c_49]) ).
tcf(c_959,plain,
join(iPr_def_11,top) = top,
inference(light_normalisation,[status(thm)],[c_958,c_187]) ).
tcf(c_1068,plain,
! [X0: $i] : join(top,join(iPr_def_11,X0)) = join(iPr_def_10,join(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_954,c_225]) ).
tcf(c_1071,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_11,X0)) = join(iPr_def_11,join(X0,top)),
inference(theory_normalisation,[status(thm)],[c_1068,c_50,c_49]) ).
tcf(c_1072,plain,
! [X0: $i] : join(top,X0) = top,
inference(light_normalisation,[status(thm)],[c_1071,c_225,c_947,c_959]) ).
tcf(c_1079,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = top,
inference(demodulation,[status(thm)],[c_221,c_1072]) ).
tcf(c_1149,plain,
converse(top) = top,
inference(superposition,[status(thm)],[c_1072,c_271]) ).
tcf(c_1159,plain,
! [X0: $i] : composition(top,converse(X0)) = converse(composition(X0,top)),
inference(superposition,[status(thm)],[c_1149,c_217]) ).
tcf(c_1162,plain,
! [X0: $i] : composition(converse(X0),top) = converse(composition(top,X0)),
inference(superposition,[status(thm)],[c_1149,c_57]) ).
tcf(c_1176,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_927,c_951]) ).
tcf(c_1182,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_927,c_1176]) ).
tcf(c_1183,plain,
complement(iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_946,c_1176]) ).
tcf(c_1185,plain,
composition(converse(sK0),iPr_def_11) = zero,
inference(demodulation,[status(thm)],[c_293,c_1176]) ).
tcf(c_1205,plain,
! [X0: $i] : join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_1176,c_49]) ).
tcf(c_1207,plain,
complement(zero) = top,
inference(superposition,[status(thm)],[c_1176,c_59]) ).
tcf(c_1209,plain,
! [X0: $i] : join(converse(zero),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_1176,c_214]) ).
tcf(c_1215,plain,
! [X0: $i] : join(converse(zero),X0) = X0,
inference(light_normalisation,[status(thm)],[c_1209,c_55]) ).
tcf(c_1232,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(superposition,[status(thm)],[c_1182,c_926]) ).
tcf(c_1302,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_1232,c_50]) ).
tcf(c_1320,plain,
! [X0: $i] : composition(converse(sK0),composition(iPr_def_11,X0)) = composition(zero,X0),
inference(superposition,[status(thm)],[c_1185,c_52]) ).
tcf(c_1323,plain,
composition(converse(iPr_def_11),sK0) = converse(zero),
inference(superposition,[status(thm)],[c_1185,c_218]) ).
tcf(c_1345,plain,
converse(zero) = zero,
inference(superposition,[status(thm)],[c_1215,c_1205]) ).
tcf(c_1366,plain,
! [X0: $i] : composition(converse(X0),zero) = converse(composition(zero,X0)),
inference(superposition,[status(thm)],[c_1345,c_57]) ).
tcf(c_1454,plain,
composition(converse(iPr_def_11),sK0) = zero,
inference(light_normalisation,[status(thm)],[c_1323,c_1345]) ).
tcf(c_1456,plain,
! [X0: $i] : composition(converse(iPr_def_11),composition(sK0,X0)) = composition(zero,X0),
inference(superposition,[status(thm)],[c_1454,c_52]) ).
tcf(c_1549,plain,
! [X0: $i,X1: $i] : join(complement(X0),join(X0,X1)) = top,
inference(superposition,[status(thm)],[c_1182,c_1079]) ).
tcf(c_1570,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(X0))) = top,
inference(theory_normalisation,[status(thm)],[c_1549,c_50,c_49]) ).
tcf(c_1680,plain,
composition(top,converse(iPr_def_11)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_113,c_1159]) ).
tcf(c_1771,plain,
! [X0: $i] : join(composition(X0,converse(iPr_def_11)),converse(iPr_def_12)) = composition(join(X0,top),converse(iPr_def_11)),
inference(superposition,[status(thm)],[c_1680,c_54]) ).
tcf(c_1779,plain,
! [X0: $i] : join(converse(iPr_def_12),composition(X0,converse(iPr_def_11))) = composition(join(X0,top),converse(iPr_def_11)),
inference(theory_normalisation,[status(thm)],[c_1771,c_50,c_49]) ).
tcf(c_1780,plain,
! [X0: $i] : join(converse(iPr_def_12),composition(X0,converse(iPr_def_11))) = converse(iPr_def_12),
inference(light_normalisation,[status(thm)],[c_1779,c_947,c_1680]) ).
tcf(c_1970,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),X0) = X0,
inference(superposition,[status(thm)],[c_209,c_1302]) ).
tcf(c_1979,plain,
! [X0: $i,X1: $i] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(theory_normalisation,[status(thm)],[c_1970,c_50,c_49]) ).
tcf(c_2135,plain,
! [X0: $i] : join(iPr_def_11,complement(join(iPr_def_10,X0))) = iPr_def_11,
inference(superposition,[status(thm)],[c_1183,c_1979]) ).
tcf(c_2580,plain,
composition(converse(sK0),iPr_def_12) = composition(zero,top),
inference(superposition,[status(thm)],[c_113,c_1320]) ).
tcf(c_2594,plain,
composition(converse(iPr_def_12),sK0) = converse(composition(zero,top)),
inference(superposition,[status(thm)],[c_2580,c_218]) ).
tcf(c_2598,plain,
composition(converse(iPr_def_11),iPr_def_10) = composition(zero,top),
inference(superposition,[status(thm)],[c_111,c_1456]) ).
tcf(c_2614,plain,
composition(converse(iPr_def_10),iPr_def_11) = converse(composition(zero,top)),
inference(superposition,[status(thm)],[c_2598,c_218]) ).
tcf(c_2621,plain,
composition(converse(iPr_def_10),iPr_def_11) = composition(converse(iPr_def_12),sK0),
inference(light_normalisation,[status(thm)],[c_2594,c_2614]) ).
tcf(c_2628,plain,
composition(converse(iPr_def_10),iPr_def_11) = composition(top,zero),
inference(demodulation,[status(thm)],[c_2614,c_1149,c_1366]) ).
tcf(c_2629,plain,
composition(converse(iPr_def_12),sK0) = composition(top,zero),
inference(demodulation,[status(thm)],[c_2621,c_2628]) ).
tcf(c_3538,plain,
join(converse(iPr_def_12),converse(iPr_def_11)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_492,c_1780]) ).
tcf(c_3546,plain,
join(converse(iPr_def_11),converse(iPr_def_12)) = converse(iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_3538,c_50,c_49]) ).
tcf(c_3574,plain,
converse(join(iPr_def_11,iPr_def_12)) = converse(iPr_def_12),
inference(demodulation,[status(thm)],[c_3546,c_56]) ).
tcf(c_3583,plain,
join(iPr_def_11,iPr_def_12) = converse(converse(iPr_def_12)),
inference(superposition,[status(thm)],[c_3574,c_55]) ).
tcf(c_3598,plain,
join(iPr_def_11,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_3583,c_55]) ).
tcf(c_3601,plain,
! [X0: $i] : join(iPr_def_11,join(iPr_def_12,X0)) = join(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_3598,c_50]) ).
tcf(c_4657,plain,
! [X0: $i] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(demodulation,[status(thm)],[c_282,c_1176]) ).
tcf(c_4659,plain,
composition(top,complement(composition(top,top))) = zero,
inference(superposition,[status(thm)],[c_1149,c_4657]) ).
tcf(c_5476,plain,
join(iPr_def_10,composition(complement(sK0),top)) = composition(top,top),
inference(superposition,[status(thm)],[c_59,c_306]) ).
tcf(c_5514,plain,
join(iPr_def_11,complement(composition(top,top))) = iPr_def_11,
inference(superposition,[status(thm)],[c_5476,c_2135]) ).
tcf(c_5527,plain,
join(iPr_def_12,composition(top,top)) = composition(top,top),
inference(superposition,[status(thm)],[c_947,c_307]) ).
tcf(c_5631,plain,
join(composition(top,top),iPr_def_11) = top,
inference(superposition,[status(thm)],[c_5514,c_1570]) ).
tcf(c_5638,plain,
join(iPr_def_11,composition(top,top)) = top,
inference(theory_normalisation,[status(thm)],[c_5631,c_50,c_49]) ).
tcf(c_5683,plain,
join(iPr_def_11,composition(top,top)) = composition(top,top),
inference(superposition,[status(thm)],[c_5527,c_3601]) ).
tcf(c_5685,plain,
composition(top,top) = top,
inference(light_normalisation,[status(thm)],[c_5683,c_5638]) ).
tcf(c_5693,plain,
composition(top,complement(top)) = zero,
inference(demodulation,[status(thm)],[c_4659,c_5685]) ).
tcf(c_5694,plain,
composition(top,zero) = zero,
inference(light_normalisation,[status(thm)],[c_5693,c_104]) ).
tcf(c_5696,plain,
composition(converse(iPr_def_12),sK0) = zero,
inference(demodulation,[status(thm)],[c_2629,c_5694]) ).
tcf(c_5710,plain,
! [X0: $i] : composition(top,composition(top,X0)) = composition(top,X0),
inference(superposition,[status(thm)],[c_5685,c_52]) ).
tcf(c_5731,plain,
! [X0: $i] : join(composition(X0,zero),zero) = composition(join(X0,top),zero),
inference(superposition,[status(thm)],[c_5694,c_54]) ).
tcf(c_5740,plain,
! [X0: $i] : join(zero,composition(X0,zero)) = composition(join(X0,top),zero),
inference(theory_normalisation,[status(thm)],[c_5731,c_50,c_49]) ).
tcf(c_5741,plain,
! [X0: $i] : join(zero,composition(X0,zero)) = zero,
inference(light_normalisation,[status(thm)],[c_5740,c_947,c_5694]) ).
tcf(c_5800,plain,
composition(top,converse(iPr_def_12)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_1680,c_5710]) ).
tcf(c_5869,plain,
! [X0: $i] : composition(converse(iPr_def_12),composition(sK0,X0)) = composition(zero,X0),
inference(superposition,[status(thm)],[c_5696,c_52]) ).
tcf(c_5923,plain,
! [X0: $i] : composition(X0,zero) = zero,
inference(demodulation,[status(thm)],[c_5741,c_1176]) ).
tcf(c_5936,plain,
! [X0: $i] : composition(converse(zero),X0) = converse(zero),
inference(superposition,[status(thm)],[c_5923,c_218]) ).
tcf(c_5947,plain,
! [X0: $i] : composition(zero,X0) = zero,
inference(light_normalisation,[status(thm)],[c_5936,c_1345]) ).
tcf(c_5998,plain,
composition(converse(converse(iPr_def_12)),top) = converse(converse(iPr_def_12)),
inference(superposition,[status(thm)],[c_5800,c_1162]) ).
tcf(c_6088,plain,
! [X0: $i] : composition(converse(iPr_def_12),composition(sK0,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_5869,c_5947]) ).
tcf(c_6090,plain,
composition(converse(iPr_def_12),iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_111,c_6088]) ).
tcf(c_6133,plain,
join(iPr_def_11,composition(converse(converse(iPr_def_12)),complement(zero))) = iPr_def_11,
inference(superposition,[status(thm)],[c_6090,c_283]) ).
tcf(c_6135,plain,
join(iPr_def_11,converse(converse(iPr_def_12))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_6133,c_1207,c_5998]) ).
tcf(c_6166,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_6135,c_55,c_3598]) ).
tcf(c_6204,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_114,c_6166]) ).
tcf(c_6205,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_6204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL050+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % 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 07:38:01 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 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...
% 3.75/1.19 % SZS status Started for theBenchmark.p
% 3.75/1.19 % SZS status Theorem for theBenchmark.p
% 3.75/1.19
% 3.75/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.75/1.19
% 3.75/1.19 % ------ iProver source info
% 3.75/1.19
% 3.75/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.75/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.75/1.19 % git: non_committed_changes: false
% 3.75/1.19
% 3.75/1.19 % ------ Parsing...
% 3.75/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 3.75/1.19 %
% 3.75/1.19
% 3.75/1.19 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.75/1.19
% 3.75/1.19 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.75/1.19 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.75/1.19
% 3.75/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.75/1.19 % ------ Proving...
% 3.75/1.19 % ------ Problem Properties
% 3.75/1.19
% 3.75/1.19 %
% 3.75/1.19 % clauses 16
% 3.75/1.19 % conjectures 1
% 3.75/1.19 % EPR 1
% 3.75/1.19 % Horn 16
% 3.75/1.19 % unary 16
% 3.75/1.19 % binary 0
% 3.75/1.19 % lits 16
% 3.75/1.19 % lits eq 16
% 3.75/1.19 % fd_pure 0
% 3.75/1.19 % fd_pseudo 0
% 3.75/1.19 % fd_cond 0
% 3.75/1.19 % fd_pseudo_cond 0
% 3.75/1.19 % AC symbols 1
% 3.75/1.19
% 3.75/1.19 % ------ Schedule UEQ
% 3.75/1.19
% 3.75/1.19 % ------ Option_UEQ Time Limit: 10.
% 3.75/1.19
% 3.75/1.19
% 3.75/1.19 % ------
% 3.75/1.19 % Current options:
% 3.75/1.19 % ------
% 3.75/1.19
% 3.75/1.19
% 3.75/1.19 %
% 3.75/1.19
% 3.75/1.19 % ------ Proving...
% 3.75/1.19 %
% 3.75/1.19
% 3.75/1.19 % SZS status Theorem for theBenchmark.p
% 3.75/1.19
% 3.75/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.75/1.19
%------------------------------------------------------------------------------