%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL012-2 : 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 : n014.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 02:36:36 PM UTC 2026
% Result : Unsatisfiable 50.38s 7.32s
% Output : CNFRefutation 50.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 22
% Syntax : Number of formulae : 154 ( 154 unt; 7 def)
% Number of atoms : 279 ( 153 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 : 11 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 192 ( 0 sgn 192 !; 0 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux1_join_commutativity_1) ).
fof(f2,axiom,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux2_join_associativity_2) ).
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_3) ).
fof(f4,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,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_4) ).
fof(f6,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_associativity_5) ).
fof(f8,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_identity_6) ).
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_multiplicativity_10) ).
fof(f13,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_11) ).
fof(f14,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',def_top_12) ).
fof(f17,axiom,
! [X2,X0,X1] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-1.ax',dedekind_law_14) ).
fof(f18,plain,
! [X2,X0,X1] : composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))) = join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
! [X2,X0,X1] : join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)) = meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-1.ax',modular_law_1_15) ).
fof(f20,plain,
! [X2,X0,X1] : meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2) = join(meet(composition(X0,X1),X2),meet(composition(X0,meet(X1,composition(converse(X0),X2))),X2)),
inference(reorient_equations,[],[f19]) ).
fof(f23,negated_conjecture,
join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) != complement(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
complement(sk1) != join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)),
inference(reorient_equations,[],[f23]) ).
fof(f26,plain,
! [X2,X0,X1] : composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2))))) = join(complement(join(complement(composition(X0,X1)),complement(X2))),composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2)))))),
inference(definition_unfolding,[],[f18,f6,f6,f6,f6,f6]) ).
fof(f27,plain,
! [X2,X0,X1] : complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2))) = join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2)))),
inference(definition_unfolding,[],[f20,f6,f6,f6,f6,f6]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f4]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
tcf(c_70,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f14]) ).
tcf(c_76,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f15]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(composition(X0,X1)),complement(X2))),composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2)))))) = composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2))))),
inference(cnf_transformation,[],[f26]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2)))) = complement(join(complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))),complement(X2))),
inference(cnf_transformation,[],[f27]) ).
tcf(c_81,negated_conjecture,
join(composition(complement(composition(sk1,sk2)),converse(sk2)),complement(sk1)) != complement(sk1),
inference(cnf_transformation,[],[f24]) ).
tcf(c_97,negated_conjecture,
join(complement(sk1),composition(complement(composition(sk1,sk2)),converse(sk2))) != complement(sk1),
inference(theory_normalisation,[status(thm)],[c_81,c_67,c_66]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(theory_normalisation,[status(thm)],[c_68,c_67,c_66]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_75,c_67,c_66]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(X2),complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2))))))))) = complement(join(complement(X2),complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))))),
inference(theory_normalisation,[status(thm)],[c_79,c_67,c_66]) ).
tcf(c_145,definition,
iPr_def_10 = complement(sk1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_146,definition,
iPr_def_11 = composition(sk1,sk2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_147,definition,
iPr_def_12 = complement(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_148,definition,
iPr_def_13 = converse(sk2),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_149,definition,
iPr_def_14 = composition(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_150,definition,
iPr_def_15 = join(iPr_def_10,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_151,definition,
iPr_def_16 = complement(top),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_152,negated_conjecture,
iPr_def_15 != iPr_def_10,
inference(demodulation,[status(thm)],[c_97,c_148,c_146,c_147,c_149,c_145,c_150]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(composition(X0,X1)),complement(X2))),complement(join(complement(X2),complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2))))))))) = complement(join(complement(X2),complement(composition(X0,complement(join(complement(X1),complement(composition(converse(X0),X2)))))))),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(composition(X0,X1)),complement(X2))),composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2)))))) = composition(complement(join(complement(X0),complement(composition(X2,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),X2))))),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_159,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_162,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_164,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(superposition,[status(thm)],[c_166,c_167]) ).
tcf(c_305,plain,
converse(iPr_def_13) = sk2,
inference(superposition,[status(thm)],[c_148,c_162]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X1),complement(composition(X0,complement(join(complement(one),complement(composition(converse(X0),X1))))))))) = complement(join(complement(X1),complement(composition(X0,complement(join(complement(one),complement(composition(converse(X0),X1)))))))),
inference(superposition,[status(thm)],[c_164,c_155]) ).
tcf(c_329,plain,
join(iPr_def_11,iPr_def_12) = top,
inference(superposition,[status(thm)],[c_147,c_159]) ).
tcf(c_332,plain,
join(iPr_def_12,iPr_def_11) = top,
inference(demodulation,[status(thm)],[c_329,c_167]) ).
tcf(c_357,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_162,c_160]) ).
tcf(c_424,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_159,c_157]) ).
tcf(c_428,plain,
! [X0: $i] : join(complement(join(iPr_def_10,X0)),complement(join(iPr_def_10,complement(X0)))) = sk1,
inference(superposition,[status(thm)],[c_145,c_157]) ).
tcf(c_432,plain,
! [X0: $i] : join(complement(join(complement(X0),top)),complement(join(complement(X0),iPr_def_16))) = X0,
inference(superposition,[status(thm)],[c_151,c_157]) ).
tcf(c_436,plain,
! [X0: $i] : join(iPr_def_16,complement(join(complement(X0),complement(X0)))) = X0,
inference(demodulation,[status(thm)],[c_424,c_167,c_151]) ).
tcf(c_438,plain,
! [X0: $i] : join(complement(join(iPr_def_16,complement(X0))),complement(join(top,complement(X0)))) = X0,
inference(demodulation,[status(thm)],[c_432,c_167]) ).
tcf(c_467,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(composition(X0,X1)),iPr_def_10)),composition(complement(join(complement(X0),complement(composition(sk1,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),sk1)))))) = composition(complement(join(complement(X0),complement(composition(sk1,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),sk1))))),
inference(superposition,[status(thm)],[c_145,c_158]) ).
tcf(c_497,plain,
! [X0: $i,X1: $i] : join(complement(join(iPr_def_10,complement(composition(X0,X1)))),composition(complement(join(complement(X0),complement(composition(sk1,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),sk1)))))) = composition(complement(join(complement(X0),complement(composition(sk1,converse(X1))))),complement(join(complement(X1),complement(composition(converse(X0),sk1))))),
inference(demodulation,[status(thm)],[c_467,c_167]) ).
tcf(c_548,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_162,c_161]) ).
tcf(c_552,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(superposition,[status(thm)],[c_162,c_161]) ).
tcf(c_569,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_164,c_165]) ).
tcf(c_596,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_159,c_166]) ).
tcf(c_602,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_14,X0)) = join(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_150,c_166]) ).
tcf(c_603,plain,
! [X0: $i] : join(iPr_def_12,join(iPr_def_11,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_332,c_166]) ).
tcf(c_606,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(join(X0,X1)))) = top,
inference(superposition,[status(thm)],[c_166,c_159]) ).
tcf(c_711,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(X0))) = join(X1,top),
inference(superposition,[status(thm)],[c_159,c_252]) ).
tcf(c_718,plain,
! [X0: $i] : join(iPr_def_12,join(X0,iPr_def_11)) = join(X0,top),
inference(superposition,[status(thm)],[c_332,c_252]) ).
tcf(c_1913,plain,
! [X0: $i] : join(iPr_def_10,join(X0,iPr_def_14)) = join(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_167,c_602]) ).
tcf(c_1930,plain,
! [X0: $i] : join(iPr_def_12,join(X0,iPr_def_11)) = join(top,X0),
inference(superposition,[status(thm)],[c_167,c_603]) ).
tcf(c_2944,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_164,c_357]) ).
tcf(c_2991,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(demodulation,[status(thm)],[c_2944,c_162]) ).
tcf(c_4059,plain,
! [X0: $i,X1: $i] : composition(join(converse(one),X0),X1) = join(X1,composition(X0,X1)),
inference(superposition,[status(thm)],[c_2991,c_163]) ).
tcf(c_4068,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_2991,c_164]) ).
tcf(c_4071,plain,
! [X0: $i,X1: $i] : composition(join(X0,converse(one)),X1) = join(composition(X0,X1),X1),
inference(superposition,[status(thm)],[c_2991,c_163]) ).
tcf(c_4075,plain,
! [X0: $i] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_2991,c_156]) ).
tcf(c_4109,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_2991,c_569]) ).
tcf(c_4110,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(demodulation,[status(thm)],[c_4109,c_2991]) ).
tcf(c_4112,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(demodulation,[status(thm)],[c_4075,c_4110]) ).
tcf(c_4113,plain,
! [X0: $i,X1: $i] : join(composition(X0,X1),X1) = composition(join(X0,one),X1),
inference(demodulation,[status(thm)],[c_4071,c_4068]) ).
tcf(c_4114,plain,
! [X0: $i,X1: $i] : join(X0,composition(X1,X0)) = composition(join(X1,one),X0),
inference(demodulation,[status(thm)],[c_4113,c_167]) ).
tcf(c_4115,plain,
! [X0: $i,X1: $i] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(demodulation,[status(thm)],[c_4059,c_4068]) ).
tcf(c_4270,plain,
! [X0: $i] : join(complement(X0),composition(converse(one),complement(X0))) = complement(X0),
inference(superposition,[status(thm)],[c_4110,c_156]) ).
tcf(c_4295,plain,
! [X0: $i] : composition(join(one,one),complement(X0)) = complement(X0),
inference(demodulation,[status(thm)],[c_4270,c_167,c_4068,c_4114]) ).
tcf(c_4508,plain,
composition(join(one,one),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_145,c_4295]) ).
tcf(c_4509,plain,
composition(join(one,one),iPr_def_16) = iPr_def_16,
inference(superposition,[status(thm)],[c_151,c_4295]) ).
tcf(c_4535,plain,
join(iPr_def_16,iPr_def_16) = iPr_def_16,
inference(demodulation,[status(thm)],[c_4509,c_4115,c_4110]) ).
tcf(c_4536,plain,
join(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_4508,c_4115,c_4110]) ).
tcf(c_5118,plain,
! [X0: $i] : join(iPr_def_16,join(iPr_def_16,X0)) = join(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_4535,c_166]) ).
tcf(c_5123,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_10,X0)) = join(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_4536,c_166]) ).
tcf(c_5167,plain,
join(iPr_def_10,iPr_def_15) = iPr_def_15,
inference(superposition,[status(thm)],[c_150,c_5123]) ).
tcf(c_5181,plain,
join(iPr_def_10,iPr_def_14) = join(iPr_def_15,iPr_def_10),
inference(superposition,[status(thm)],[c_5123,c_1913]) ).
tcf(c_5185,plain,
join(iPr_def_15,iPr_def_10) = iPr_def_15,
inference(demodulation,[status(thm)],[c_5167,c_167]) ).
tcf(c_5189,plain,
join(iPr_def_10,iPr_def_14) = iPr_def_15,
inference(demodulation,[status(thm)],[c_5181,c_5185]) ).
tcf(c_5705,plain,
! [X0: $i] : join(iPr_def_16,complement(complement(X0))) = X0,
inference(light_normalisation,[status(thm)],[c_436,c_4112]) ).
tcf(c_5706,plain,
join(iPr_def_16,complement(iPr_def_10)) = sk1,
inference(superposition,[status(thm)],[c_145,c_5705]) ).
tcf(c_5707,plain,
join(iPr_def_16,complement(iPr_def_16)) = top,
inference(superposition,[status(thm)],[c_151,c_5705]) ).
tcf(c_5708,plain,
join(iPr_def_16,complement(iPr_def_12)) = iPr_def_11,
inference(superposition,[status(thm)],[c_147,c_5705]) ).
tcf(c_5712,plain,
! [X0: $i] : join(iPr_def_16,X0) = X0,
inference(superposition,[status(thm)],[c_5705,c_5118]) ).
tcf(c_5713,plain,
complement(iPr_def_12) = iPr_def_11,
inference(demodulation,[status(thm)],[c_5708,c_5712]) ).
tcf(c_5714,plain,
complement(iPr_def_16) = top,
inference(demodulation,[status(thm)],[c_5707,c_5712]) ).
tcf(c_5715,plain,
complement(iPr_def_10) = sk1,
inference(demodulation,[status(thm)],[c_5706,c_5712]) ).
tcf(c_5720,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_5705,c_5712]) ).
tcf(c_5746,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_159,c_548]) ).
tcf(c_7038,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(converse(X1),X0),
inference(superposition,[status(thm)],[c_167,c_552]) ).
tcf(c_7286,plain,
! [X0: $i,X1: $i] : join(top,complement(join(complement(X0),complement(X1)))) = join(join(complement(X0),X1),X0),
inference(superposition,[status(thm)],[c_157,c_596]) ).
tcf(c_7361,plain,
! [X0: $i,X1: $i] : join(top,complement(join(complement(X0),complement(X1)))) = join(complement(X0),join(X1,X0)),
inference(demodulation,[status(thm)],[c_7286,c_166]) ).
tcf(c_7362,plain,
! [X0: $i,X1: $i] : join(top,complement(join(complement(X0),complement(X1)))) = join(X0,join(X1,complement(X0))),
inference(theory_normalisation,[status(thm)],[c_7361,c_166,c_167]) ).
tcf(c_7363,plain,
! [X0: $i,X1: $i] : join(top,complement(join(complement(X0),complement(X1)))) = join(X1,top),
inference(demodulation,[status(thm)],[c_7362,c_711]) ).
tcf(c_7956,plain,
! [X0: $i] : join(X0,iPr_def_16) = X0,
inference(superposition,[status(thm)],[c_5712,c_167]) ).
tcf(c_7963,plain,
! [X0: $i] : join(converse(iPr_def_16),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_5712,c_552]) ).
tcf(c_7988,plain,
! [X0: $i] : join(converse(iPr_def_16),X0) = X0,
inference(demodulation,[status(thm)],[c_7963,c_162]) ).
tcf(c_7996,plain,
complement(iPr_def_11) = iPr_def_12,
inference(superposition,[status(thm)],[c_5713,c_5720]) ).
tcf(c_7997,plain,
complement(sk1) = iPr_def_10,
inference(superposition,[status(thm)],[c_5715,c_5720]) ).
tcf(c_7998,plain,
complement(top) = iPr_def_16,
inference(superposition,[status(thm)],[c_5714,c_5720]) ).
tcf(c_8273,plain,
! [X0: $i,X1: $i] : join(join(complement(X0),complement(composition(X1,complement(join(complement(one),complement(composition(converse(X1),X0))))))),complement(join(complement(X0),complement(composition(X1,complement(join(complement(one),complement(composition(converse(X1),X0))))))))) = join(complement(join(complement(X1),complement(X0))),top),
inference(superposition,[status(thm)],[c_318,c_711]) ).
tcf(c_8341,plain,
! [X0: $i] : join(X0,top) = top,
inference(demodulation,[status(thm)],[c_8273,c_167,c_166,c_606,c_7363]) ).
tcf(c_8366,plain,
! [X0: $i] : join(iPr_def_12,join(X0,iPr_def_11)) = top,
inference(demodulation,[status(thm)],[c_718,c_8341]) ).
tcf(c_8369,plain,
! [X0: $i] : join(top,X0) = top,
inference(demodulation,[status(thm)],[c_1930,c_8366]) ).
tcf(c_9705,plain,
! [X0: $i] : join(converse(top),X0) = converse(top),
inference(superposition,[status(thm)],[c_8341,c_7038]) ).
tcf(c_10399,plain,
converse(top) = top,
inference(superposition,[status(thm)],[c_8369,c_5746]) ).
tcf(c_13418,plain,
converse(iPr_def_16) = iPr_def_16,
inference(superposition,[status(thm)],[c_7988,c_7956]) ).
tcf(c_15431,plain,
! [X0: $i] : join(X0,composition(complement(one),X0)) = composition(top,X0),
inference(superposition,[status(thm)],[c_159,c_4115]) ).
tcf(c_15705,plain,
composition(top,top) = top,
inference(superposition,[status(thm)],[c_15431,c_8369]) ).
tcf(c_17214,plain,
join(complement(top),composition(converse(top),complement(top))) = complement(top),
inference(superposition,[status(thm)],[c_15705,c_156]) ).
tcf(c_17220,plain,
composition(top,iPr_def_16) = iPr_def_16,
inference(demodulation,[status(thm)],[c_17214,c_4114,c_9705,c_10399,c_7998]) ).
tcf(c_17288,plain,
! [X0: $i] : composition(join(X0,top),iPr_def_16) = join(composition(X0,iPr_def_16),iPr_def_16),
inference(superposition,[status(thm)],[c_17220,c_163]) ).
tcf(c_17297,plain,
! [X0: $i] : composition(X0,iPr_def_16) = iPr_def_16,
inference(demodulation,[status(thm)],[c_17288,c_8341,c_7956,c_17220]) ).
tcf(c_19064,plain,
! [X0: $i] : composition(converse(iPr_def_16),X0) = converse(iPr_def_16),
inference(superposition,[status(thm)],[c_17297,c_357]) ).
tcf(c_19101,plain,
! [X0: $i] : composition(iPr_def_16,X0) = iPr_def_16,
inference(demodulation,[status(thm)],[c_19064,c_13418]) ).
tcf(c_21966,plain,
join(complement(join(iPr_def_10,complement(iPr_def_14))),composition(complement(join(complement(iPr_def_12),complement(composition(sk1,converse(iPr_def_13))))),complement(join(complement(iPr_def_13),complement(composition(converse(iPr_def_12),sk1)))))) = composition(complement(join(complement(iPr_def_12),complement(composition(sk1,converse(iPr_def_13))))),complement(join(complement(iPr_def_13),complement(composition(converse(iPr_def_12),sk1))))),
inference(superposition,[status(thm)],[c_149,c_497]) ).
tcf(c_22070,plain,
complement(join(iPr_def_10,complement(iPr_def_14))) = iPr_def_16,
inference(demodulation,[status(thm)],[c_21966,c_167,c_146,c_305,c_332,c_5713,c_7956,c_7996,c_7998,c_19101]) ).
tcf(c_29768,plain,
join(complement(join(iPr_def_10,iPr_def_14)),iPr_def_16) = sk1,
inference(superposition,[status(thm)],[c_22070,c_428]) ).
tcf(c_29772,plain,
complement(iPr_def_15) = sk1,
inference(demodulation,[status(thm)],[c_29768,c_5189,c_7956]) ).
tcf(c_29989,plain,
join(complement(join(iPr_def_16,sk1)),complement(join(top,sk1))) = iPr_def_15,
inference(superposition,[status(thm)],[c_29772,c_438]) ).
tcf(c_30094,plain,
iPr_def_10 = iPr_def_15,
inference(demodulation,[status(thm)],[c_29989,c_5712,c_8369,c_7956,c_7997,c_7998]) ).
tcf(c_30202,plain,
iPr_def_15 != iPr_def_15,
inference(demodulation,[status(thm)],[c_152,c_30094]) ).
tcf(c_30203,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_30202]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL012-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 07:11:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running UEQ theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 50.38/7.32 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 50.38/7.32 % SZS status Started for theBenchmark.p
% 50.38/7.32 % SZS status Unsatisfiable for theBenchmark.p
% 50.38/7.32
% 50.38/7.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 50.38/7.32
% 50.38/7.32 % ------ iProver source info
% 50.38/7.32
% 50.38/7.32 % git: date: 2026-07-19 20:42:38 +0200
% 50.38/7.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 50.38/7.32 % git: non_committed_changes: false
% 50.38/7.32
% 50.38/7.32 % ------ Parsing...% successful
% 50.38/7.32
% 50.38/7.32
% 50.38/7.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 50.38/7.32
% 50.38/7.32 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 50.38/7.32
% 50.38/7.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 50.38/7.32
% 50.38/7.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 50.38/7.32 % ------ Proving...
% 50.38/7.32 % ------ Problem Properties
% 50.38/7.32
% 50.38/7.32 %
% 50.38/7.32 % clauses 23
% 50.38/7.32 % conjectures 1
% 50.38/7.32 % EPR 2
% 50.38/7.32 % Horn 23
% 50.38/7.32 % unary 23
% 50.38/7.32 % binary 0
% 50.38/7.32 % lits 23
% 50.38/7.32 % lits eq 23
% 50.38/7.32 % fd_pure 0
% 50.38/7.32 % fd_pseudo 0
% 50.38/7.32 % fd_cond 0
% 50.38/7.32 % fd_pseudo_cond 0
% 50.38/7.32 % AC symbols 1
% 50.38/7.32
% 50.38/7.32 % ------ Input Options Time Limit: Unbounded
% 50.38/7.32
% 50.38/7.32
% 50.38/7.32 % ------
% 50.38/7.32 % Current options:
% 50.38/7.32 % ------
% 50.38/7.32
% 50.38/7.32
% 50.38/7.32 %
% 50.38/7.32
% 50.38/7.32 % ------ Proving...
% 50.38/7.32 %
% 50.38/7.32
% 50.38/7.32 % SZS status Unsatisfiable for theBenchmark.p
% 50.38/7.32
% 50.38/7.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 50.38/7.32
% 50.38/7.32
%------------------------------------------------------------------------------