%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL004+3 : 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 : n007.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 02:36:30 PM UTC 2026
% Result : Theorem 52.76s 9.38s
% Output : CNFRefutation 52.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 17
% Syntax : Number of formulae : 184 ( 184 unt; 4 def)
% Number of atoms : 345 ( 183 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 127 ( 0 sgn 126 !; 1 ?; 79 :)
% 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(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(f17,conjecture,
! [X0] : converse(complement(X0)) = complement(converse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0] : converse(complement(X0)) = complement(converse(X0)),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0] : converse(complement(X0)) != complement(converse(X0)),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
converse(complement(sK0)) != complement(converse(sK0)),
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(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,
converse(complement(sK0)) != complement(converse(sK0)),
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_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,
complement(converse(sK0)) != converse(complement(sK0)),
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 = converse(sK0),
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 = complement(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_130,definition,
iPr_def_13 = converse(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_131,negated_conjecture,
iPr_def_11 != iPr_def_13,
inference(demodulation,[status(thm)],[c_64,c_129,c_130,c_127,c_128]) ).
tcf(c_211,plain,
converse(iPr_def_10) = sK0,
inference(superposition,[status(thm)],[c_127,c_55]) ).
tcf(c_212,plain,
converse(iPr_def_13) = iPr_def_12,
inference(superposition,[status(thm)],[c_130,c_55]) ).
tcf(c_218,plain,
! [X0: $i] : join(complement(join(iPr_def_12,X0)),complement(join(iPr_def_12,complement(X0)))) = sK0,
inference(superposition,[status(thm)],[c_129,c_80]) ).
tcf(c_219,plain,
! [X0: $i] : join(complement(join(zero,X0)),complement(join(zero,complement(X0)))) = top,
inference(superposition,[status(thm)],[c_120,c_80]) ).
tcf(c_222,plain,
! [X0: $i] : join(complement(join(complement(X0),top)),complement(join(complement(X0),zero))) = X0,
inference(superposition,[status(thm)],[c_120,c_80]) ).
tcf(c_227,plain,
! [X0: $i] : join(complement(join(top,complement(X0))),complement(join(zero,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_222,c_50,c_49]) ).
tcf(c_231,plain,
join(sK0,iPr_def_12) = top,
inference(superposition,[status(thm)],[c_129,c_59]) ).
tcf(c_232,plain,
join(top,zero) = top,
inference(superposition,[status(thm)],[c_120,c_59]) ).
tcf(c_233,plain,
join(iPr_def_10,iPr_def_11) = top,
inference(superposition,[status(thm)],[c_128,c_59]) ).
tcf(c_234,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_59,c_80]) ).
tcf(c_235,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[status(thm)],[c_59,c_80]) ).
tcf(c_236,plain,
join(iPr_def_12,sK0) = top,
inference(theory_normalisation,[status(thm)],[c_231,c_50,c_49]) ).
tcf(c_237,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_234,c_50,c_49]) ).
tcf(c_238,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_237,c_120]) ).
tcf(c_239,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(light_normalisation,[status(thm)],[c_235,c_120]) ).
tcf(c_242,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_246,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_247,plain,
! [X0: $i] : join(iPr_def_10,converse(X0)) = converse(join(sK0,X0)),
inference(superposition,[status(thm)],[c_127,c_56]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_260,plain,
! [X0: $i] : composition(converse(X0),iPr_def_10) = converse(composition(sK0,X0)),
inference(superposition,[status(thm)],[c_127,c_57]) ).
tcf(c_263,plain,
! [X0: $i] : join(sK0,converse(X0)) = converse(join(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_211,c_56]) ).
tcf(c_264,plain,
converse(sK0) = iPr_def_10,
inference(superposition,[status(thm)],[c_211,c_55]) ).
tcf(c_265,plain,
! [X0: $i] : composition(converse(X0),sK0) = converse(composition(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_211,c_57]) ).
tcf(c_269,plain,
! [X0: $i] : join(iPr_def_12,converse(X0)) = converse(join(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_212,c_56]) ).
tcf(c_270,plain,
converse(iPr_def_12) = iPr_def_13,
inference(superposition,[status(thm)],[c_212,c_55]) ).
tcf(c_289,plain,
join(iPr_def_10,converse(complement(sK0))) = converse(top),
inference(superposition,[status(thm)],[c_59,c_247]) ).
tcf(c_295,plain,
join(iPr_def_10,iPr_def_13) = converse(top),
inference(light_normalisation,[status(thm)],[c_289,c_129,c_270]) ).
tcf(c_353,plain,
! [X0: $i] : join(top,join(zero,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_232,c_50]) ).
tcf(c_354,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_11,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_233,c_50]) ).
tcf(c_355,plain,
! [X0: $i] : join(iPr_def_12,join(sK0,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_236,c_50]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_458,plain,
composition(converse(one),iPr_def_10) = converse(sK0),
inference(superposition,[status(thm)],[c_53,c_260]) ).
tcf(c_468,plain,
composition(converse(one),iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_458,c_264]) ).
tcf(c_475,plain,
join(complement(iPr_def_10),composition(converse(converse(one)),complement(iPr_def_10))) = complement(iPr_def_10),
inference(superposition,[status(thm)],[c_468,c_81]) ).
tcf(c_477,plain,
join(iPr_def_11,composition(converse(converse(one)),iPr_def_11)) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_475,c_128]) ).
tcf(c_530,plain,
join(sK0,converse(iPr_def_11)) = converse(top),
inference(superposition,[status(thm)],[c_233,c_263]) ).
tcf(c_557,plain,
composition(converse(one),sK0) = converse(iPr_def_10),
inference(superposition,[status(thm)],[c_53,c_265]) ).
tcf(c_568,plain,
composition(converse(one),sK0) = sK0,
inference(light_normalisation,[status(thm)],[c_557,c_211]) ).
tcf(c_749,plain,
join(complement(sK0),composition(converse(converse(one)),complement(sK0))) = complement(sK0),
inference(superposition,[status(thm)],[c_568,c_81]) ).
tcf(c_754,plain,
join(iPr_def_12,composition(converse(converse(one)),iPr_def_12)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_749,c_129]) ).
tcf(c_816,plain,
join(iPr_def_12,converse(complement(iPr_def_13))) = converse(top),
inference(superposition,[status(thm)],[c_59,c_269]) ).
tcf(c_931,plain,
join(top,complement(zero)) = join(top,top),
inference(superposition,[status(thm)],[c_59,c_353]) ).
tcf(c_966,plain,
join(top,complement(iPr_def_11)) = join(iPr_def_10,top),
inference(superposition,[status(thm)],[c_59,c_354]) ).
tcf(c_976,plain,
join(top,converse(iPr_def_11)) = join(iPr_def_12,converse(top)),
inference(superposition,[status(thm)],[c_530,c_355]) ).
tcf(c_1012,plain,
join(iPr_def_11,composition(one,iPr_def_11)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_477,c_55]) ).
tcf(c_1014,plain,
join(top,composition(one,iPr_def_11)) = join(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_1012,c_354]) ).
tcf(c_1015,plain,
join(top,composition(one,iPr_def_11)) = top,
inference(light_normalisation,[status(thm)],[c_1014,c_233]) ).
tcf(c_1025,plain,
join(complement(join(zero,zero)),complement(top)) = top,
inference(superposition,[status(thm)],[c_59,c_219]) ).
tcf(c_1033,plain,
join(complement(top),complement(join(zero,zero))) = top,
inference(theory_normalisation,[status(thm)],[c_1025,c_50,c_49]) ).
tcf(c_1034,plain,
join(zero,complement(join(zero,zero))) = top,
inference(light_normalisation,[status(thm)],[c_1033,c_120]) ).
tcf(c_1048,plain,
join(top,complement(join(zero,zero))) = join(top,top),
inference(superposition,[status(thm)],[c_1034,c_353]) ).
tcf(c_1054,plain,
join(iPr_def_12,composition(one,iPr_def_12)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_754,c_55]) ).
tcf(c_1104,plain,
join(zero,complement(join(iPr_def_11,iPr_def_11))) = iPr_def_10,
inference(superposition,[status(thm)],[c_128,c_238]) ).
tcf(c_1153,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_59,c_246]) ).
tcf(c_1454,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_259]) ).
tcf(c_1512,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_1454,c_55]) ).
tcf(c_1551,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_1512,c_361]) ).
tcf(c_1553,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_1551,c_1512]) ).
tcf(c_1562,plain,
join(top,iPr_def_11) = top,
inference(demodulation,[status(thm)],[c_1015,c_1553]) ).
tcf(c_1563,plain,
join(iPr_def_11,iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1012,c_1553]) ).
tcf(c_1564,plain,
join(iPr_def_12,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1054,c_1553]) ).
tcf(c_1566,plain,
join(zero,complement(iPr_def_11)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_1104,c_1563]) ).
tcf(c_1567,plain,
join(iPr_def_11,top) = top,
inference(theory_normalisation,[status(thm)],[c_1562,c_50,c_49]) ).
tcf(c_1638,plain,
! [X0: $i] : join(iPr_def_11,join(iPr_def_11,X0)) = join(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_1563,c_50]) ).
tcf(c_1644,plain,
! [X0: $i] : join(iPr_def_12,join(iPr_def_12,X0)) = join(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_1564,c_50]) ).
tcf(c_1807,plain,
join(iPr_def_11,converse(top)) = converse(top),
inference(superposition,[status(thm)],[c_1153,c_1638]) ).
tcf(c_1823,plain,
join(iPr_def_12,converse(top)) = converse(top),
inference(superposition,[status(thm)],[c_1153,c_1644]) ).
tcf(c_1834,plain,
join(top,converse(iPr_def_11)) = converse(top),
inference(demodulation,[status(thm)],[c_976,c_1823]) ).
tcf(c_1837,plain,
join(top,top) = join(iPr_def_10,top),
inference(superposition,[status(thm)],[c_1567,c_354]) ).
tcf(c_1839,plain,
join(top,complement(zero)) = join(iPr_def_10,top),
inference(demodulation,[status(thm)],[c_931,c_1837]) ).
tcf(c_1892,plain,
join(converse(iPr_def_11),top) = converse(converse(top)),
inference(superposition,[status(thm)],[c_1807,c_249]) ).
tcf(c_1893,plain,
join(top,converse(iPr_def_11)) = converse(converse(top)),
inference(theory_normalisation,[status(thm)],[c_1892,c_50,c_49]) ).
tcf(c_1894,plain,
converse(converse(top)) = converse(top),
inference(light_normalisation,[status(thm)],[c_1893,c_1834]) ).
tcf(c_1895,plain,
converse(top) = top,
inference(demodulation,[status(thm)],[c_1894,c_55]) ).
tcf(c_1898,plain,
join(iPr_def_12,converse(complement(iPr_def_13))) = top,
inference(demodulation,[status(thm)],[c_816,c_1895]) ).
tcf(c_1901,plain,
join(iPr_def_10,iPr_def_13) = top,
inference(demodulation,[status(thm)],[c_295,c_1895]) ).
tcf(c_1995,plain,
join(complement(top),complement(join(iPr_def_12,complement(converse(complement(iPr_def_13)))))) = sK0,
inference(superposition,[status(thm)],[c_1898,c_218]) ).
tcf(c_2002,plain,
join(zero,complement(join(iPr_def_12,complement(converse(complement(iPr_def_13)))))) = sK0,
inference(light_normalisation,[status(thm)],[c_1995,c_120]) ).
tcf(c_2046,plain,
join(complement(join(top,complement(zero))),complement(top)) = zero,
inference(superposition,[status(thm)],[c_59,c_227]) ).
tcf(c_2048,plain,
join(complement(join(top,complement(join(zero,zero)))),complement(top)) = join(zero,zero),
inference(superposition,[status(thm)],[c_1034,c_227]) ).
tcf(c_2050,plain,
join(complement(join(top,complement(iPr_def_11))),complement(iPr_def_10)) = iPr_def_11,
inference(superposition,[status(thm)],[c_1566,c_227]) ).
tcf(c_2061,plain,
join(complement(iPr_def_10),complement(join(top,complement(iPr_def_11)))) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_2050,c_50,c_49]) ).
tcf(c_2062,plain,
join(iPr_def_11,complement(join(iPr_def_10,top))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_2061,c_128,c_966]) ).
tcf(c_2065,plain,
join(complement(top),complement(join(top,complement(zero)))) = zero,
inference(theory_normalisation,[status(thm)],[c_2046,c_50,c_49]) ).
tcf(c_2066,plain,
join(zero,complement(join(iPr_def_10,top))) = zero,
inference(light_normalisation,[status(thm)],[c_2065,c_120,c_1839]) ).
tcf(c_2084,plain,
join(complement(top),complement(join(top,complement(join(zero,zero))))) = join(zero,zero),
inference(theory_normalisation,[status(thm)],[c_2048,c_50,c_49]) ).
tcf(c_2085,plain,
join(zero,complement(join(iPr_def_10,top))) = join(zero,zero),
inference(light_normalisation,[status(thm)],[c_2084,c_120,c_1048,c_1837]) ).
tcf(c_2344,plain,
join(top,complement(join(iPr_def_10,top))) = join(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_2062,c_354]) ).
tcf(c_2347,plain,
join(top,complement(join(iPr_def_10,top))) = top,
inference(light_normalisation,[status(thm)],[c_2344,c_233]) ).
tcf(c_2508,plain,
join(complement(top),complement(join(zero,complement(join(iPr_def_10,top))))) = join(iPr_def_10,top),
inference(superposition,[status(thm)],[c_2347,c_227]) ).
tcf(c_2512,plain,
join(iPr_def_10,top) = top,
inference(light_normalisation,[status(thm)],[c_2508,c_120,c_1034,c_2085]) ).
tcf(c_2516,plain,
join(zero,complement(top)) = zero,
inference(demodulation,[status(thm)],[c_2066,c_2512]) ).
tcf(c_2524,plain,
join(zero,zero) = zero,
inference(light_normalisation,[status(thm)],[c_2516,c_120]) ).
tcf(c_2551,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_2524,c_50]) ).
tcf(c_2973,plain,
! [X0: $i] : join(complement(join(complement(complement(X0)),X0)),complement(top)) = complement(X0),
inference(superposition,[status(thm)],[c_59,c_242]) ).
tcf(c_3003,plain,
! [X0: $i] : join(complement(top),complement(join(X0,complement(complement(X0))))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_2973,c_50,c_49]) ).
tcf(c_3004,plain,
! [X0: $i] : join(zero,complement(join(X0,complement(complement(X0))))) = complement(X0),
inference(light_normalisation,[status(thm)],[c_3003,c_120]) ).
tcf(c_3052,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_239,c_3004]) ).
tcf(c_3056,plain,
complement(iPr_def_12) = sK0,
inference(superposition,[status(thm)],[c_129,c_3052]) ).
tcf(c_3058,plain,
complement(iPr_def_11) = iPr_def_10,
inference(superposition,[status(thm)],[c_128,c_3052]) ).
tcf(c_3065,plain,
! [X0: $i] : join(zero,complement(join(X0,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_3052,c_238]) ).
tcf(c_3072,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,X1)),complement(join(X0,complement(X1)))) = complement(X0),
inference(superposition,[status(thm)],[c_3052,c_80]) ).
tcf(c_3116,plain,
complement(sK0) = iPr_def_12,
inference(superposition,[status(thm)],[c_3056,c_3052]) ).
tcf(c_3144,plain,
complement(iPr_def_10) = iPr_def_11,
inference(superposition,[status(thm)],[c_3058,c_3052]) ).
tcf(c_3779,plain,
! [X0: $i] : join(zero,complement(X0)) = complement(X0),
inference(superposition,[status(thm)],[c_3065,c_2551]) ).
tcf(c_3788,plain,
! [X0: $i] : complement(join(X0,X0)) = complement(X0),
inference(demodulation,[status(thm)],[c_3065,c_3779]) ).
tcf(c_3797,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_3052,c_3779]) ).
tcf(c_4173,plain,
! [X0: $i] : join(X0,X0) = complement(complement(X0)),
inference(superposition,[status(thm)],[c_3788,c_3052]) ).
tcf(c_4190,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(light_normalisation,[status(thm)],[c_4173,c_3052]) ).
tcf(c_4232,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_4190,c_50]) ).
tcf(c_29254,plain,
complement(join(iPr_def_12,complement(converse(complement(iPr_def_13))))) = sK0,
inference(demodulation,[status(thm)],[c_2002,c_3797]) ).
tcf(c_29288,plain,
join(iPr_def_12,complement(converse(complement(iPr_def_13)))) = complement(sK0),
inference(superposition,[status(thm)],[c_29254,c_3052]) ).
tcf(c_29320,plain,
join(iPr_def_12,complement(converse(complement(iPr_def_13)))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_29288,c_3116]) ).
tcf(c_134295,plain,
join(complement(top),complement(join(iPr_def_10,complement(iPr_def_13)))) = complement(iPr_def_10),
inference(superposition,[status(thm)],[c_1901,c_3072]) ).
tcf(c_135022,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,X1)),complement(X0)) = complement(X0),
inference(superposition,[status(thm)],[c_3072,c_4232]) ).
tcf(c_135058,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(X0,X1))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_135022,c_50,c_49]) ).
tcf(c_135067,plain,
join(zero,complement(join(iPr_def_10,complement(iPr_def_13)))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_134295,c_120,c_3144]) ).
tcf(c_135803,plain,
complement(join(iPr_def_10,complement(iPr_def_13))) = iPr_def_11,
inference(demodulation,[status(thm)],[c_135067,c_3797]) ).
tcf(c_135889,plain,
join(iPr_def_10,complement(iPr_def_13)) = complement(iPr_def_11),
inference(superposition,[status(thm)],[c_135803,c_3052]) ).
tcf(c_135961,plain,
join(iPr_def_10,complement(iPr_def_13)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_135889,c_3058]) ).
tcf(c_136113,plain,
join(sK0,converse(complement(iPr_def_13))) = converse(iPr_def_10),
inference(superposition,[status(thm)],[c_135961,c_263]) ).
tcf(c_136141,plain,
join(sK0,converse(complement(iPr_def_13))) = sK0,
inference(light_normalisation,[status(thm)],[c_136113,c_211]) ).
tcf(c_136474,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(X1,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_49,c_135058]) ).
tcf(c_141241,plain,
join(complement(converse(complement(iPr_def_13))),complement(sK0)) = complement(converse(complement(iPr_def_13))),
inference(superposition,[status(thm)],[c_136141,c_136474]) ).
tcf(c_141934,plain,
join(complement(sK0),complement(converse(complement(iPr_def_13)))) = complement(converse(complement(iPr_def_13))),
inference(theory_normalisation,[status(thm)],[c_141241,c_50,c_49]) ).
tcf(c_141935,plain,
complement(converse(complement(iPr_def_13))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_141934,c_3116,c_29320]) ).
tcf(c_143424,plain,
converse(complement(iPr_def_13)) = complement(iPr_def_12),
inference(superposition,[status(thm)],[c_141935,c_3052]) ).
tcf(c_143511,plain,
converse(complement(iPr_def_13)) = sK0,
inference(light_normalisation,[status(thm)],[c_143424,c_3056]) ).
tcf(c_143713,plain,
complement(iPr_def_13) = converse(sK0),
inference(superposition,[status(thm)],[c_143511,c_55]) ).
tcf(c_143776,plain,
complement(iPr_def_13) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_143713,c_264]) ).
tcf(c_143986,plain,
complement(iPr_def_10) = iPr_def_13,
inference(superposition,[status(thm)],[c_143776,c_3052]) ).
tcf(c_144051,plain,
iPr_def_11 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_143986,c_3144]) ).
tcf(c_144052,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_144051,c_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL004+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n007.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 07:04:22 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
% 0.10/0.45 % Proving...
% 52.76/9.38 % SZS status Started for theBenchmark.p
% 52.76/9.38 % SZS status Theorem for theBenchmark.p
% 52.76/9.38
% 52.76/9.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 52.76/9.38
% 52.76/9.38 % ------ iProver source info
% 52.76/9.38
% 52.76/9.38 % git: date: 2026-07-19 20:42:38 +0200
% 52.76/9.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 52.76/9.38 % git: non_committed_changes: false
% 52.76/9.38
% 52.76/9.38 % ------ Parsing...
% 52.76/9.38 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 52.76/9.38 %
% 52.76/9.38
% 52.76/9.38 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 52.76/9.38
% 52.76/9.38 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 52.76/9.38 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 52.76/9.38
% 52.76/9.38 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 52.76/9.38 % ------ Proving...
% 52.76/9.38 % ------ Problem Properties
% 52.76/9.38
% 52.76/9.38 %
% 52.76/9.38 % clauses 20
% 52.76/9.38 % conjectures 1
% 52.76/9.38 % EPR 1
% 52.76/9.38 % Horn 20
% 52.76/9.38 % unary 20
% 52.76/9.38 % binary 0
% 52.76/9.38 % lits 20
% 52.76/9.38 % lits eq 20
% 52.76/9.38 % fd_pure 0
% 52.76/9.38 % fd_pseudo 0
% 52.76/9.38 % fd_cond 0
% 52.76/9.38 % fd_pseudo_cond 0
% 52.76/9.38 % AC symbols 1
% 52.76/9.38
% 52.76/9.38 % ------ Schedule UEQ
% 52.76/9.38
% 52.76/9.38 % ------ Option_UEQ Time Limit: 10.
% 52.76/9.38
% 52.76/9.38
% 52.76/9.38 % ------
% 52.76/9.38 % Current options:
% 52.76/9.38 % ------
% 52.76/9.38
% 52.76/9.38
% 52.76/9.38 %
% 52.76/9.38
% 52.76/9.38 % ------ Proving...
% 52.76/9.38 %
% 52.76/9.38
% 52.76/9.38 % SZS status Theorem for theBenchmark.p
% 52.76/9.38
% 52.76/9.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 52.76/9.38
% 52.76/9.38
%------------------------------------------------------------------------------