%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL050+4 : 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 : n011.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 18.54s 3.27s
% Output : CNFRefutation 18.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 18
% Syntax : Number of formulae : 158 ( 149 unt; 4 def)
% Number of atoms : 256 ( 166 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 16 ~; 7 |; 2 &)
% ( 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 : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 160 ( 0 sgn 159 !; 1 ?; 106 :)
% 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(f17,conjecture,
! [X0] :
( join(composition(complement(composition(X0,top)),top),complement(composition(X0,top))) = complement(composition(X0,top))
& join(complement(composition(X0,top)),composition(complement(composition(X0,top)),top)) = composition(complement(composition(X0,top)),top) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0] :
( join(composition(complement(composition(X0,top)),top),complement(composition(X0,top))) = complement(composition(X0,top))
& join(complement(composition(X0,top)),composition(complement(composition(X0,top)),top)) = composition(complement(composition(X0,top)),top) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0] :
( complement(composition(X0,top)) != join(composition(complement(composition(X0,top)),top),complement(composition(X0,top)))
| composition(complement(composition(X0,top)),top) != join(complement(composition(X0,top)),composition(complement(composition(X0,top)),top)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
( complement(composition(sK0,top)) != join(composition(complement(composition(sK0,top)),top),complement(composition(sK0,top)))
| composition(complement(composition(sK0,top)),top) != join(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)) != join(composition(complement(composition(sK0,top)),top),complement(composition(sK0,top)))
| composition(complement(composition(sK0,top)),top) != join(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,
( ( join(complement(composition(sK0,top)),composition(complement(composition(sK0,top)),top)) != composition(complement(composition(sK0,top)),top) )
| ( join(composition(complement(composition(sK0,top)),top),complement(composition(sK0,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_84,negated_conjecture,
( ( join(complement(composition(sK0,top)),composition(complement(composition(sK0,top)),top)) != complement(composition(sK0,top)) )
| ( join(complement(composition(sK0,top)),composition(complement(composition(sK0,top)),top)) != composition(complement(composition(sK0,top)),top) ) ),
inference(theory_normalisation,[status(thm)],[c_64,c_50,c_49]) ).
tcf(c_123,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_132,definition,
iPr_def_10 = composition(sK0,top),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_133,definition,
iPr_def_11 = complement(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_134,definition,
iPr_def_12 = composition(iPr_def_11,top),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_135,definition,
iPr_def_13 = join(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_136,negated_conjecture,
( ( iPr_def_13 != iPr_def_12 )
| ( iPr_def_13 != iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_84,c_134,c_132,c_133,c_135]) ).
tcf(c_217,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_242,plain,
join(top,zero) = top,
inference(superposition,[status(thm)],[c_123,c_59]) ).
tcf(c_244,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_59,c_80]) ).
tcf(c_246,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_244,c_50,c_49]) ).
tcf(c_247,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_246,c_123]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_275,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_59,c_258]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i,X2: $i] : composition(join(converse(X0),X1),converse(X2)) = converse(composition(X2,join(X0,converse(X1)))),
inference(superposition,[status(thm)],[c_259,c_57]) ).
tcf(c_374,plain,
! [X0: $i] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(superposition,[status(thm)],[c_123,c_81]) ).
tcf(c_375,plain,
! [X0: $i] : join(iPr_def_11,composition(converse(X0),complement(composition(X0,iPr_def_10)))) = iPr_def_11,
inference(superposition,[status(thm)],[c_133,c_81]) ).
tcf(c_382,plain,
join(complement(top),composition(converse(sK0),complement(iPr_def_10))) = complement(top),
inference(superposition,[status(thm)],[c_132,c_81]) ).
tcf(c_386,plain,
join(zero,composition(converse(sK0),iPr_def_11)) = zero,
inference(light_normalisation,[status(thm)],[c_382,c_123,c_133]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_59,c_50]) ).
tcf(c_415,plain,
! [X0: $i] : join(top,join(zero,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_242,c_50]) ).
tcf(c_461,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_464,plain,
! [X0: $i] : composition(iPr_def_11,composition(top,X0)) = composition(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_134,c_52]) ).
tcf(c_670,plain,
! [X0: $i] : join(top,join(X0,zero)) = join(top,X0),
inference(superposition,[status(thm)],[c_49,c_415]) ).
tcf(c_1114,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_265]) ).
tcf(c_1138,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_1114,c_55]) ).
tcf(c_1201,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_1138,c_53]) ).
tcf(c_1210,plain,
! [X0: $i] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_1138,c_81]) ).
tcf(c_1213,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_1138,c_461]) ).
tcf(c_1215,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_1213,c_1138]) ).
tcf(c_1298,plain,
! [X0: $i,X1: $i] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(superposition,[status(thm)],[c_1215,c_54]) ).
tcf(c_1397,plain,
! [X0: $i] : join(top,join(X0,zero)) = join(X0,top),
inference(superposition,[status(thm)],[c_242,c_217]) ).
tcf(c_2180,plain,
! [X0: $i] : join(top,complement(complement(X0))) = join(X0,top),
inference(superposition,[status(thm)],[c_59,c_411]) ).
tcf(c_2630,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_1210,c_1215]) ).
tcf(c_2631,plain,
! [X0: $i] : join(zero,complement(complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_247,c_2630]) ).
tcf(c_2635,plain,
join(zero,zero) = zero,
inference(superposition,[status(thm)],[c_123,c_2630]) ).
tcf(c_2641,plain,
! [X0: $i] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(superposition,[status(thm)],[c_2630,c_411]) ).
tcf(c_2651,plain,
! [X0: $i] : join(top,complement(X0)) = top,
inference(light_normalisation,[status(thm)],[c_2641,c_59]) ).
tcf(c_2664,plain,
! [X0: $i] : join(X0,top) = top,
inference(demodulation,[status(thm)],[c_2180,c_2651]) ).
tcf(c_2670,plain,
! [X0: $i] : join(top,join(X0,zero)) = top,
inference(demodulation,[status(thm)],[c_1397,c_2664]) ).
tcf(c_2674,plain,
! [X0: $i] : join(top,X0) = top,
inference(demodulation,[status(thm)],[c_670,c_2670]) ).
tcf(c_2678,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = top,
inference(demodulation,[status(thm)],[c_411,c_2674]) ).
tcf(c_2695,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_2635,c_50]) ).
tcf(c_2781,plain,
converse(top) = top,
inference(superposition,[status(thm)],[c_2674,c_275]) ).
tcf(c_2986,plain,
! [X0: $i] : composition(top,converse(X0)) = converse(composition(X0,top)),
inference(superposition,[status(thm)],[c_2781,c_264]) ).
tcf(c_2988,plain,
! [X0: $i] : composition(converse(X0),top) = converse(composition(top,X0)),
inference(superposition,[status(thm)],[c_2781,c_57]) ).
tcf(c_3088,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_2631,c_2695]) ).
tcf(c_3094,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_2631,c_3088]) ).
tcf(c_3096,plain,
composition(converse(sK0),iPr_def_11) = zero,
inference(demodulation,[status(thm)],[c_386,c_3088]) ).
tcf(c_3159,plain,
! [X0: $i] : join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_3088,c_49]) ).
tcf(c_3164,plain,
complement(zero) = top,
inference(superposition,[status(thm)],[c_3088,c_59]) ).
tcf(c_3167,plain,
! [X0: $i] : join(converse(zero),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_3088,c_259]) ).
tcf(c_3178,plain,
! [X0: $i] : join(converse(zero),X0) = X0,
inference(light_normalisation,[status(thm)],[c_3167,c_55]) ).
tcf(c_3376,plain,
! [X0: $i] : composition(converse(sK0),composition(iPr_def_11,X0)) = composition(zero,X0),
inference(superposition,[status(thm)],[c_3096,c_52]) ).
tcf(c_3381,plain,
composition(converse(iPr_def_11),sK0) = converse(zero),
inference(superposition,[status(thm)],[c_3096,c_265]) ).
tcf(c_3475,plain,
converse(zero) = zero,
inference(superposition,[status(thm)],[c_3178,c_3159]) ).
tcf(c_3505,plain,
! [X0: $i] : composition(converse(X0),zero) = converse(composition(zero,X0)),
inference(superposition,[status(thm)],[c_3475,c_57]) ).
tcf(c_3906,plain,
composition(converse(iPr_def_11),sK0) = zero,
inference(light_normalisation,[status(thm)],[c_3381,c_3475]) ).
tcf(c_3911,plain,
! [X0: $i] : composition(converse(iPr_def_11),composition(sK0,X0)) = composition(zero,X0),
inference(superposition,[status(thm)],[c_3906,c_52]) ).
tcf(c_4172,plain,
! [X0: $i,X1: $i] : join(complement(X0),join(X0,X1)) = top,
inference(superposition,[status(thm)],[c_3094,c_2678]) ).
tcf(c_4208,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(X0))) = top,
inference(theory_normalisation,[status(thm)],[c_4172,c_50,c_49]) ).
tcf(c_4517,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,join(X2,complement(X0)))) = top,
inference(superposition,[status(thm)],[c_50,c_4208]) ).
tcf(c_4700,plain,
composition(top,converse(iPr_def_11)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_134,c_2986]) ).
tcf(c_4814,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_4700,c_54]) ).
tcf(c_4824,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_4814,c_50,c_49]) ).
tcf(c_4825,plain,
! [X0: $i] : join(converse(iPr_def_12),composition(X0,converse(iPr_def_11))) = converse(iPr_def_12),
inference(light_normalisation,[status(thm)],[c_4824,c_2664,c_4700]) ).
tcf(c_5159,plain,
composition(converse(sK0),iPr_def_12) = composition(zero,top),
inference(superposition,[status(thm)],[c_134,c_3376]) ).
tcf(c_5203,plain,
composition(converse(iPr_def_12),sK0) = converse(composition(zero,top)),
inference(superposition,[status(thm)],[c_5159,c_265]) ).
tcf(c_5649,plain,
composition(converse(iPr_def_11),iPr_def_10) = composition(zero,top),
inference(superposition,[status(thm)],[c_132,c_3911]) ).
tcf(c_5746,plain,
composition(converse(iPr_def_10),iPr_def_11) = converse(composition(zero,top)),
inference(superposition,[status(thm)],[c_5649,c_265]) ).
tcf(c_6665,plain,
composition(converse(iPr_def_10),iPr_def_11) = composition(converse(iPr_def_12),sK0),
inference(light_normalisation,[status(thm)],[c_5203,c_5746]) ).
tcf(c_6874,plain,
composition(converse(iPr_def_10),iPr_def_11) = composition(top,zero),
inference(demodulation,[status(thm)],[c_5746,c_2781,c_3505]) ).
tcf(c_6875,plain,
composition(converse(iPr_def_12),sK0) = composition(top,zero),
inference(demodulation,[status(thm)],[c_6665,c_6874]) ).
tcf(c_8262,plain,
! [X0: $i] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(demodulation,[status(thm)],[c_374,c_3088]) ).
tcf(c_8264,plain,
composition(top,complement(composition(top,top))) = zero,
inference(superposition,[status(thm)],[c_2781,c_8262]) ).
tcf(c_8295,plain,
! [X0: $i] : composition(converse(complement(composition(X0,top))),X0) = converse(zero),
inference(superposition,[status(thm)],[c_8262,c_265]) ).
tcf(c_8300,plain,
! [X0: $i] : composition(converse(complement(composition(X0,top))),X0) = zero,
inference(light_normalisation,[status(thm)],[c_8295,c_3475]) ).
tcf(c_9747,plain,
! [X0: $i] : composition(join(one,X0),zero) = composition(X0,zero),
inference(superposition,[status(thm)],[c_1298,c_3088]) ).
tcf(c_9761,plain,
! [X0: $i] : composition(join(one,X0),top) = top,
inference(superposition,[status(thm)],[c_1298,c_2674]) ).
tcf(c_10223,plain,
composition(top,top) = top,
inference(superposition,[status(thm)],[c_4517,c_9761]) ).
tcf(c_10239,plain,
! [X0: $i] : composition(converse(complement(top)),join(one,X0)) = zero,
inference(superposition,[status(thm)],[c_9761,c_8300]) ).
tcf(c_10244,plain,
! [X0: $i] : composition(zero,join(one,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_10239,c_123,c_3475]) ).
tcf(c_10255,plain,
composition(top,complement(top)) = zero,
inference(demodulation,[status(thm)],[c_8264,c_10223]) ).
tcf(c_10256,plain,
composition(top,zero) = zero,
inference(light_normalisation,[status(thm)],[c_10255,c_123]) ).
tcf(c_10258,plain,
composition(converse(iPr_def_12),sK0) = zero,
inference(demodulation,[status(thm)],[c_6875,c_10256]) ).
tcf(c_10328,plain,
composition(iPr_def_11,top) = composition(iPr_def_12,top),
inference(superposition,[status(thm)],[c_10223,c_464]) ).
tcf(c_10331,plain,
composition(iPr_def_12,top) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_10328,c_134]) ).
tcf(c_10531,plain,
composition(top,converse(iPr_def_12)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_10331,c_2986]) ).
tcf(c_10623,plain,
! [X0: $i] : composition(converse(iPr_def_12),composition(sK0,X0)) = composition(zero,X0),
inference(superposition,[status(thm)],[c_10258,c_52]) ).
tcf(c_11258,plain,
! [X0: $i] : composition(join(converse(one),X0),converse(zero)) = converse(zero),
inference(superposition,[status(thm)],[c_10244,c_329]) ).
tcf(c_11318,plain,
! [X0: $i] : composition(X0,zero) = zero,
inference(light_normalisation,[status(thm)],[c_11258,c_1201,c_3475,c_9747]) ).
tcf(c_11763,plain,
! [X0: $i] : composition(converse(zero),X0) = converse(zero),
inference(superposition,[status(thm)],[c_11318,c_265]) ).
tcf(c_11771,plain,
! [X0: $i] : composition(zero,X0) = zero,
inference(light_normalisation,[status(thm)],[c_11763,c_3475]) ).
tcf(c_12090,plain,
composition(converse(converse(iPr_def_12)),top) = converse(converse(iPr_def_12)),
inference(superposition,[status(thm)],[c_10531,c_2988]) ).
tcf(c_14298,plain,
! [X0: $i] : composition(converse(iPr_def_12),composition(sK0,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_10623,c_11771]) ).
tcf(c_14300,plain,
composition(converse(iPr_def_12),iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_132,c_14298]) ).
tcf(c_14404,plain,
join(iPr_def_11,composition(converse(converse(iPr_def_12)),complement(zero))) = iPr_def_11,
inference(superposition,[status(thm)],[c_14300,c_375]) ).
tcf(c_14406,plain,
join(iPr_def_11,converse(converse(iPr_def_12))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_14404,c_3164,c_12090]) ).
tcf(c_14559,plain,
iPr_def_11 = iPr_def_13,
inference(demodulation,[status(thm)],[c_14406,c_55,c_135]) ).
tcf(c_14596,plain,
join(iPr_def_11,iPr_def_12) = iPr_def_11,
inference(demodulation,[status(thm)],[c_135,c_14559]) ).
tcf(c_14597,plain,
( ( iPr_def_11 != iPr_def_12 )
| ( iPr_def_11 != iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_136,c_14559]) ).
tcf(c_14599,plain,
iPr_def_11 != iPr_def_12,
inference(equality_resolution_simp,[status(thm)],[c_14597]) ).
tcf(c_27396,plain,
join(converse(iPr_def_12),converse(iPr_def_11)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_1215,c_4825]) ).
tcf(c_27416,plain,
join(converse(iPr_def_11),converse(iPr_def_12)) = converse(iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_27396,c_50,c_49]) ).
tcf(c_27479,plain,
converse(iPr_def_11) = converse(iPr_def_12),
inference(demodulation,[status(thm)],[c_27416,c_56,c_14596]) ).
tcf(c_27521,plain,
converse(converse(iPr_def_11)) = iPr_def_12,
inference(superposition,[status(thm)],[c_27479,c_55]) ).
tcf(c_27626,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_27521,c_55]) ).
tcf(c_27627,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_27626,c_14599]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL050+4 : 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 : n011.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 07:38:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 0.15/0.42
% 0.15/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.42
% 0.15/0.42 % Detected problem language: tptp
% 0.15/0.43 % Proving...
% 18.54/3.27 % SZS status Started for theBenchmark.p
% 18.54/3.27 % SZS status Theorem for theBenchmark.p
% 18.54/3.27
% 18.54/3.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.54/3.27
% 18.54/3.27 % ------ iProver source info
% 18.54/3.27
% 18.54/3.27 % git: date: 2026-07-19 20:42:38 +0200
% 18.54/3.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.54/3.27 % git: non_committed_changes: false
% 18.54/3.27
% 18.54/3.27 % ------ Parsing...
% 18.54/3.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.54/3.27
% 18.54/3.27 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 18.54/3.27
% 18.54/3.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.54/3.27
% 18.54/3.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 18.54/3.27 % ------ Proving...
% 18.54/3.27 % ------ Problem Properties
% 18.54/3.27
% 18.54/3.27 %
% 18.54/3.27 % clauses 20
% 18.54/3.27 % conjectures 1
% 18.54/3.27 % EPR 1
% 18.54/3.27 % Horn 20
% 18.54/3.27 % unary 19
% 18.54/3.27 % binary 1
% 18.54/3.27 % lits 21
% 18.54/3.27 % lits eq 21
% 18.54/3.27 % fd_pure 0
% 18.54/3.27 % fd_pseudo 0
% 18.54/3.27 % fd_cond 0
% 18.54/3.27 % fd_pseudo_cond 0
% 18.54/3.27 % AC symbols 1
% 18.54/3.27
% 18.54/3.27 % ------ Schedule dynamic 5 is on
% 18.54/3.27
% 18.54/3.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 18.54/3.27
% 18.54/3.27
% 18.54/3.27 % ------
% 18.54/3.27 % Current options:
% 18.54/3.27 % ------
% 18.54/3.27
% 18.54/3.27
% 18.54/3.27 %
% 18.54/3.27
% 18.54/3.27 % ------ Proving...
% 18.54/3.27 %
% 18.54/3.27
% 18.54/3.27 % SZS status Theorem for theBenchmark.p
% 18.54/3.27
% 18.54/3.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.54/3.27
% 18.54/3.27
%------------------------------------------------------------------------------