%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL050+3 : 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 : n020.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 02:37:06 PM UTC 2026
% Result : Theorem 2.34s 1.77s
% Output : CNFRefutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 17
% Syntax : Number of formulae : 156 ( 156 unt; 3 def)
% Number of atoms : 262 ( 155 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 : 153 ( 0 sgn 152 !; 1 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(f17,conjecture,
! [X0] : complement(composition(X0,top)) = composition(complement(composition(X0,top)),top),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0] : complement(composition(X0,top)) = composition(complement(composition(X0,top)),top),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0] : complement(composition(X0,top)) != composition(complement(composition(X0,top)),top),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
complement(composition(sK0,top)) != composition(complement(composition(sK0,top)),top),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f19]) ).
fof(f21,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f22,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f23,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f24,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f27,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f28,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f29,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f30,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f31,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f32,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f33,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f37,plain,
complement(composition(sK0,top)) != composition(complement(composition(sK0,top)),top),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f33,f24]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f22]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f23]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f25]) ).
tcf(c_53,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f26]) ).
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,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f29]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f31]) ).
tcf(c_59,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f32]) ).
tcf(c_60,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f38]) ).
tcf(c_64,negated_conjecture,
composition(complement(composition(sK0,top)),top) != complement(composition(sK0,top)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_80,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_81,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_120,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_127,definition,
iPr_def_10 = composition(sK0,top),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_128,definition,
iPr_def_11 = complement(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_129,definition,
iPr_def_12 = composition(iPr_def_11,top),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_130,negated_conjecture,
iPr_def_12 != iPr_def_11,
inference(demodulation,[status(thm)],[c_64,c_127,c_128,c_129]) ).
tcf(c_214,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_59,c_80]) ).
tcf(c_222,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_214,c_50,c_49]) ).
tcf(c_223,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_222,c_120]) ).
tcf(c_231,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_80]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_59,c_50]) ).
tcf(c_281,plain,
join(zero,complement(join(iPr_def_11,iPr_def_11))) = iPr_def_10,
inference(superposition,[status(thm)],[c_128,c_223]) ).
tcf(c_293,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_59,c_235]) ).
tcf(c_304,plain,
! [X0: $i] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(superposition,[status(thm)],[c_120,c_81]) ).
tcf(c_305,plain,
! [X0: $i] : join(iPr_def_11,composition(converse(X0),complement(composition(X0,iPr_def_10)))) = iPr_def_11,
inference(superposition,[status(thm)],[c_128,c_81]) ).
tcf(c_310,plain,
join(complement(top),composition(converse(sK0),complement(iPr_def_10))) = complement(top),
inference(superposition,[status(thm)],[c_127,c_81]) ).
tcf(c_315,plain,
join(zero,composition(converse(sK0),iPr_def_11)) = zero,
inference(light_normalisation,[status(thm)],[c_310,c_120,c_128]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_320,plain,
! [X0: $i] : composition(iPr_def_11,composition(top,X0)) = composition(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_129,c_52]) ).
tcf(c_328,plain,
! [X0: $i] : join(iPr_def_10,composition(X0,top)) = composition(join(sK0,X0),top),
inference(superposition,[status(thm)],[c_127,c_54]) ).
tcf(c_329,plain,
! [X0: $i] : join(iPr_def_12,composition(X0,top)) = composition(join(iPr_def_11,X0),top),
inference(superposition,[status(thm)],[c_129,c_54]) ).
tcf(c_608,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_240]) ).
tcf(c_632,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_608,c_55]) ).
tcf(c_654,plain,
! [X0: $i] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_632,c_81]) ).
tcf(c_657,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_632,c_317]) ).
tcf(c_659,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_657,c_632]) ).
tcf(c_820,plain,
! [X0: $i] : join(top,complement(complement(X0))) = join(X0,top),
inference(superposition,[status(thm)],[c_59,c_243]) ).
tcf(c_1219,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_654,c_659]) ).
tcf(c_1220,plain,
! [X0: $i] : join(zero,complement(complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_223,c_1219]) ).
tcf(c_1224,plain,
join(zero,zero) = zero,
inference(superposition,[status(thm)],[c_120,c_1219]) ).
tcf(c_1225,plain,
join(iPr_def_11,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_128,c_1219]) ).
tcf(c_1231,plain,
! [X0: $i] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(superposition,[status(thm)],[c_1219,c_243]) ).
tcf(c_1240,plain,
! [X0: $i] : join(top,complement(X0)) = top,
inference(light_normalisation,[status(thm)],[c_1231,c_59]) ).
tcf(c_1256,plain,
join(zero,complement(iPr_def_11)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_281,c_1225]) ).
tcf(c_1257,plain,
! [X0: $i] : join(X0,top) = top,
inference(demodulation,[status(thm)],[c_820,c_1240]) ).
tcf(c_1261,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_1224,c_50]) ).
tcf(c_1295,plain,
! [X0: $i] : join(top,X0) = top,
inference(superposition,[status(thm)],[c_1257,c_49]) ).
tcf(c_1319,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = top,
inference(demodulation,[status(thm)],[c_243,c_1295]) ).
tcf(c_1330,plain,
converse(top) = top,
inference(superposition,[status(thm)],[c_1295,c_293]) ).
tcf(c_1342,plain,
! [X0: $i] : composition(top,converse(X0)) = converse(composition(X0,top)),
inference(superposition,[status(thm)],[c_1330,c_239]) ).
tcf(c_1347,plain,
! [X0: $i] : composition(converse(X0),top) = converse(composition(top,X0)),
inference(superposition,[status(thm)],[c_1330,c_57]) ).
tcf(c_1426,plain,
! [X0: $i,X1: $i] : join(join(complement(X0),X1),X0) = top,
inference(superposition,[status(thm)],[c_80,c_1319]) ).
tcf(c_1456,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(X0))) = top,
inference(theory_normalisation,[status(thm)],[c_1426,c_50,c_49]) ).
tcf(c_1536,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_1220,c_1261]) ).
tcf(c_1545,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_1220,c_1536]) ).
tcf(c_1546,plain,
complement(iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_1256,c_1536]) ).
tcf(c_1548,plain,
composition(converse(sK0),iPr_def_11) = zero,
inference(demodulation,[status(thm)],[c_315,c_1536]) ).
tcf(c_1615,plain,
! [X0: $i] : join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_1536,c_49]) ).
tcf(c_1617,plain,
complement(zero) = top,
inference(superposition,[status(thm)],[c_1536,c_59]) ).
tcf(c_1620,plain,
! [X0: $i] : join(converse(zero),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_1536,c_236]) ).
tcf(c_1629,plain,
! [X0: $i] : join(converse(zero),X0) = X0,
inference(light_normalisation,[status(thm)],[c_1620,c_55]) ).
tcf(c_1684,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(superposition,[status(thm)],[c_1545,c_1219]) ).
tcf(c_1737,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_1684,c_50]) ).
tcf(c_1779,plain,
composition(converse(iPr_def_11),sK0) = converse(zero),
inference(superposition,[status(thm)],[c_1548,c_240]) ).
tcf(c_1843,plain,
converse(zero) = zero,
inference(superposition,[status(thm)],[c_1629,c_1615]) ).
tcf(c_1869,plain,
! [X0: $i] : composition(converse(X0),zero) = converse(composition(zero,X0)),
inference(superposition,[status(thm)],[c_1843,c_57]) ).
tcf(c_1918,plain,
composition(converse(iPr_def_11),sK0) = zero,
inference(light_normalisation,[status(thm)],[c_1779,c_1843]) ).
tcf(c_1923,plain,
! [X0: $i] : composition(converse(iPr_def_11),composition(sK0,X0)) = composition(zero,X0),
inference(superposition,[status(thm)],[c_1918,c_52]) ).
tcf(c_2083,plain,
composition(top,converse(iPr_def_11)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_129,c_1342]) ).
tcf(c_2206,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_2083,c_54]) ).
tcf(c_2216,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_2206,c_50,c_49]) ).
tcf(c_2217,plain,
! [X0: $i] : join(converse(iPr_def_12),composition(X0,converse(iPr_def_11))) = converse(iPr_def_12),
inference(light_normalisation,[status(thm)],[c_2216,c_1257,c_2083]) ).
tcf(c_2503,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),X0) = X0,
inference(superposition,[status(thm)],[c_231,c_1737]) ).
tcf(c_2512,plain,
! [X0: $i,X1: $i] : join(X0,complement(join(complement(X0),X1))) = X0,
inference(theory_normalisation,[status(thm)],[c_2503,c_50,c_49]) ).
tcf(c_2678,plain,
! [X0: $i] : join(iPr_def_11,complement(join(iPr_def_10,X0))) = iPr_def_11,
inference(superposition,[status(thm)],[c_1546,c_2512]) ).
tcf(c_3467,plain,
composition(converse(iPr_def_11),iPr_def_10) = composition(zero,top),
inference(superposition,[status(thm)],[c_127,c_1923]) ).
tcf(c_3494,plain,
composition(converse(iPr_def_10),iPr_def_11) = converse(composition(zero,top)),
inference(superposition,[status(thm)],[c_3467,c_240]) ).
tcf(c_3664,plain,
composition(converse(iPr_def_10),iPr_def_11) = composition(top,zero),
inference(demodulation,[status(thm)],[c_3494,c_1330,c_1869]) ).
tcf(c_4209,plain,
join(converse(iPr_def_12),converse(iPr_def_11)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_659,c_2217]) ).
tcf(c_4217,plain,
join(converse(iPr_def_11),converse(iPr_def_12)) = converse(iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_4209,c_50,c_49]) ).
tcf(c_4220,plain,
converse(join(iPr_def_11,iPr_def_12)) = converse(iPr_def_12),
inference(demodulation,[status(thm)],[c_4217,c_56]) ).
tcf(c_4231,plain,
join(iPr_def_11,iPr_def_12) = converse(converse(iPr_def_12)),
inference(superposition,[status(thm)],[c_4220,c_55]) ).
tcf(c_4248,plain,
join(iPr_def_11,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_4231,c_55]) ).
tcf(c_4251,plain,
! [X0: $i] : join(iPr_def_11,join(iPr_def_12,X0)) = join(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_4248,c_50]) ).
tcf(c_5298,plain,
! [X0: $i] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(demodulation,[status(thm)],[c_304,c_1536]) ).
tcf(c_5300,plain,
composition(top,complement(composition(top,top))) = zero,
inference(superposition,[status(thm)],[c_1330,c_5298]) ).
tcf(c_5977,plain,
join(iPr_def_10,composition(complement(sK0),top)) = composition(top,top),
inference(superposition,[status(thm)],[c_59,c_328]) ).
tcf(c_6044,plain,
join(iPr_def_11,complement(composition(top,top))) = iPr_def_11,
inference(superposition,[status(thm)],[c_5977,c_2678]) ).
tcf(c_6056,plain,
join(iPr_def_12,composition(top,top)) = composition(top,top),
inference(superposition,[status(thm)],[c_1257,c_329]) ).
tcf(c_6165,plain,
join(composition(top,top),iPr_def_11) = top,
inference(superposition,[status(thm)],[c_6044,c_1456]) ).
tcf(c_6172,plain,
join(iPr_def_11,composition(top,top)) = top,
inference(theory_normalisation,[status(thm)],[c_6165,c_50,c_49]) ).
tcf(c_6226,plain,
join(iPr_def_11,composition(top,top)) = composition(top,top),
inference(superposition,[status(thm)],[c_6056,c_4251]) ).
tcf(c_6228,plain,
composition(top,top) = top,
inference(light_normalisation,[status(thm)],[c_6226,c_6172]) ).
tcf(c_6236,plain,
composition(top,complement(top)) = zero,
inference(demodulation,[status(thm)],[c_5300,c_6228]) ).
tcf(c_6237,plain,
composition(top,zero) = zero,
inference(light_normalisation,[status(thm)],[c_6236,c_120]) ).
tcf(c_6239,plain,
composition(converse(iPr_def_10),iPr_def_11) = zero,
inference(demodulation,[status(thm)],[c_3664,c_6237]) ).
tcf(c_6263,plain,
composition(iPr_def_11,top) = composition(iPr_def_12,top),
inference(superposition,[status(thm)],[c_6228,c_320]) ).
tcf(c_6266,plain,
composition(iPr_def_12,top) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_6263,c_129]) ).
tcf(c_6283,plain,
! [X0: $i] : join(composition(X0,zero),zero) = composition(join(X0,top),zero),
inference(superposition,[status(thm)],[c_6237,c_54]) ).
tcf(c_6292,plain,
! [X0: $i] : join(zero,composition(X0,zero)) = composition(join(X0,top),zero),
inference(theory_normalisation,[status(thm)],[c_6283,c_50,c_49]) ).
tcf(c_6293,plain,
! [X0: $i] : join(zero,composition(X0,zero)) = zero,
inference(light_normalisation,[status(thm)],[c_6292,c_1257,c_6237]) ).
tcf(c_6375,plain,
composition(top,converse(iPr_def_12)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_6266,c_1342]) ).
tcf(c_6398,plain,
! [X0: $i] : composition(converse(iPr_def_10),composition(iPr_def_11,X0)) = composition(zero,X0),
inference(superposition,[status(thm)],[c_6239,c_52]) ).
tcf(c_6602,plain,
! [X0: $i] : composition(X0,zero) = zero,
inference(demodulation,[status(thm)],[c_6293,c_1536]) ).
tcf(c_6621,plain,
! [X0: $i] : composition(converse(zero),X0) = converse(zero),
inference(superposition,[status(thm)],[c_6602,c_240]) ).
tcf(c_6632,plain,
! [X0: $i] : composition(zero,X0) = zero,
inference(light_normalisation,[status(thm)],[c_6621,c_1843]) ).
tcf(c_6834,plain,
composition(converse(converse(iPr_def_12)),top) = converse(converse(iPr_def_12)),
inference(superposition,[status(thm)],[c_6375,c_1347]) ).
tcf(c_7066,plain,
! [X0: $i] : composition(converse(iPr_def_10),composition(iPr_def_11,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_6398,c_6632]) ).
tcf(c_7068,plain,
composition(converse(iPr_def_10),iPr_def_12) = zero,
inference(superposition,[status(thm)],[c_129,c_7066]) ).
tcf(c_7102,plain,
composition(converse(iPr_def_12),iPr_def_10) = converse(zero),
inference(superposition,[status(thm)],[c_7068,c_240]) ).
tcf(c_7103,plain,
composition(converse(iPr_def_12),iPr_def_10) = zero,
inference(light_normalisation,[status(thm)],[c_7102,c_1843]) ).
tcf(c_7131,plain,
join(iPr_def_11,composition(converse(converse(iPr_def_12)),complement(zero))) = iPr_def_11,
inference(superposition,[status(thm)],[c_7103,c_305]) ).
tcf(c_7133,plain,
join(iPr_def_11,converse(converse(iPr_def_12))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_7131,c_1617,c_6834]) ).
tcf(c_7146,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_7133,c_55,c_4248]) ).
tcf(c_7185,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_130,c_7146]) ).
tcf(c_7186,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_7185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL050+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 07:39:35 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.34/1.77 % SZS status Started for theBenchmark.p
% 2.34/1.77 % SZS status Theorem for theBenchmark.p
% 2.34/1.77
% 2.34/1.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.34/1.77
% 2.34/1.77 % ------ iProver source info
% 2.34/1.77
% 2.34/1.77 % git: date: 2026-07-19 20:42:38 +0200
% 2.34/1.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.34/1.77 % git: non_committed_changes: false
% 2.34/1.77
% 2.34/1.77 % ------ Parsing...
% 2.34/1.77 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 2.34/1.77 %
% 2.34/1.77
% 2.34/1.77 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.34/1.77
% 2.34/1.77 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 2.34/1.77 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.34/1.77
% 2.34/1.77 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.34/1.77 % ------ Proving...
% 2.34/1.77 % ------ Problem Properties
% 2.34/1.77
% 2.34/1.77 %
% 2.34/1.77 % clauses 19
% 2.34/1.77 % conjectures 1
% 2.34/1.77 % EPR 1
% 2.34/1.77 % Horn 19
% 2.34/1.77 % unary 19
% 2.34/1.77 % binary 0
% 2.34/1.77 % lits 19
% 2.34/1.77 % lits eq 19
% 2.34/1.77 % fd_pure 0
% 2.34/1.77 % fd_pseudo 0
% 2.34/1.77 % fd_cond 0
% 2.34/1.77 % fd_pseudo_cond 0
% 2.34/1.77 % AC symbols 1
% 2.34/1.77
% 2.34/1.77 % ------ Schedule UEQ
% 2.34/1.77
% 2.34/1.77 % ------ Option_UEQ Time Limit: 10.
% 2.34/1.77
% 2.34/1.77
% 2.34/1.77 % ------
% 2.34/1.77 % Current options:
% 2.34/1.77 % ------
% 2.34/1.77
% 2.34/1.77
% 2.34/1.77 %
% 2.34/1.77
% 2.34/1.77 % ------ Proving...
% 2.34/1.77 %
% 2.34/1.77
% 2.34/1.77 % SZS status Theorem for theBenchmark.p
% 2.34/1.77
% 2.34/1.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.34/1.78
% 2.34/1.78
%------------------------------------------------------------------------------