%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL035-1 : 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 : n019.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 02:36:58 PM UTC 2026
% Result : Unsatisfiable 40.94s 20.87s
% Output : CNFRefutation 40.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 27
% Syntax : Number of formulae : 194 ( 194 unt; 13 def)
% Number of atoms : 476 ( 193 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 156 ( 0 sgn 156 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/REL001-0.ax',composition_associativity_5) ).
fof(f8,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/REL001-0.ax',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/REL001-0.ax',def_top_12) ).
fof(f17,negated_conjecture,
composition(sk1,top) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
sk1 = composition(sk1,top),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
composition(meet(sk2,converse(sk1)),meet(sk1,sk3)) != composition(sk2,meet(sk1,sk3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_15) ).
fof(f21,plain,
composition(complement(join(complement(sk2),complement(converse(sk1)))),complement(join(complement(sk1),complement(sk3)))) != composition(sk2,complement(join(complement(sk1),complement(sk3)))),
inference(definition_unfolding,[],[f19,f6,f6,f6]) ).
tcf(c_64,negated_conjecture,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_65,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_66,negated_conjecture,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f4]) ).
tcf(c_67,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
tcf(c_68,negated_conjecture,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_69,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(cnf_transformation,[],[f9]) ).
tcf(c_70,negated_conjecture,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_71,negated_conjecture,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_72,negated_conjecture,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_73,negated_conjecture,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f14]) ).
tcf(c_74,negated_conjecture,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f15]) ).
tcf(c_76,negated_conjecture,
composition(sk1,top) = sk1,
inference(cnf_transformation,[],[f18]) ).
tcf(c_77,negated_conjecture,
composition(complement(join(complement(sk2),complement(converse(sk1)))),complement(join(complement(sk1),complement(sk3)))) != composition(sk2,complement(join(complement(sk1),complement(sk3)))),
inference(cnf_transformation,[],[f21]) ).
tcf(c_90,negated_conjecture,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(theory_normalisation,[status(thm)],[c_66,c_65,c_64]) ).
tcf(c_91,negated_conjecture,
! [X0: $i,X1: $i] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_73,c_65,c_64]) ).
tcf(c_129,definition,
iPr_def_10 = complement(top),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_130,definition,
iPr_def_11 = complement(sk2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_131,definition,
iPr_def_12 = converse(sk1),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_132,definition,
iPr_def_13 = complement(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_133,definition,
iPr_def_14 = join(iPr_def_11,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_134,definition,
iPr_def_15 = complement(iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_135,definition,
iPr_def_16 = complement(sk1),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_136,definition,
iPr_def_17 = complement(sk3),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_137,definition,
iPr_def_18 = join(iPr_def_16,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_138,definition,
iPr_def_19 = complement(iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_139,definition,
iPr_def_20 = composition(iPr_def_15,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_140,definition,
iPr_def_21 = composition(sk2,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_141,definition,
iPr_def_22 = composition(sk1,top),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_143,negated_conjecture,
! [X0: $i,X1: $i] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_144,negated_conjecture,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_145,negated_conjecture,
iPr_def_20 != iPr_def_21,
inference(demodulation,[status(thm)],[c_77,c_140,c_136,c_135,c_137,c_138,c_131,c_132,c_130,c_133,c_134,c_139]) ).
tcf(c_146,negated_conjecture,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_147,negated_conjecture,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_148,negated_conjecture,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_149,negated_conjecture,
! [X0: $i] : converse(converse(X0)) = X0,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_150,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_151,negated_conjecture,
! [X0: $i] : composition(X0,one) = X0,
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_152,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_153,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_154,negated_conjecture,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_155,negated_conjecture,
iPr_def_22 = sk1,
inference(demodulation,[status(thm)],[c_76,c_141]) ).
tcf(c_2171,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_151,c_152]) ).
tcf(c_2274,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_149,c_147]) ).
tcf(c_2330,plain,
! [X0: $i] : join(iPr_def_10,composition(converse(X0),complement(composition(X0,top)))) = iPr_def_10,
inference(superposition,[status(thm)],[c_129,c_143]) ).
tcf(c_2674,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_146,c_144]) ).
tcf(c_2695,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_2674,c_153,c_154]) ).
tcf(c_2696,plain,
! [X0: $i] : join(iPr_def_10,complement(join(complement(X0),complement(X0)))) = X0,
inference(demodulation,[status(thm)],[c_2695,c_129]) ).
tcf(c_11359,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_151,c_2274]) ).
tcf(c_11361,plain,
! [X0: $i,X1: $i] : composition(converse(composition(one,X0)),X1) = converse(composition(converse(X1),X0)),
inference(superposition,[status(thm)],[c_2171,c_2274]) ).
tcf(c_11414,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(demodulation,[status(thm)],[c_11359,c_149]) ).
tcf(c_11418,plain,
! [X0: $i,X1: $i] : composition(converse(composition(one,X0)),X1) = composition(converse(X0),X1),
inference(demodulation,[status(thm)],[c_11361,c_2274]) ).
tcf(c_11456,plain,
! [X0: $i] : composition(converse(X0),one) = converse(composition(one,X0)),
inference(superposition,[status(thm)],[c_11418,c_151]) ).
tcf(c_11483,plain,
! [X0: $i] : converse(composition(one,X0)) = converse(X0),
inference(demodulation,[status(thm)],[c_11456,c_151]) ).
tcf(c_11719,plain,
! [X0: $i] : composition(one,X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_11483,c_149]) ).
tcf(c_11731,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(demodulation,[status(thm)],[c_11719,c_149]) ).
tcf(c_12040,plain,
! [X0: $i] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_11414,c_143]) ).
tcf(c_12052,plain,
join(iPr_def_10,complement(composition(one,top))) = iPr_def_10,
inference(superposition,[status(thm)],[c_11414,c_2330]) ).
tcf(c_12064,plain,
join(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_12052,c_129,c_11731]) ).
tcf(c_12078,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(demodulation,[status(thm)],[c_12040,c_11731]) ).
tcf(c_12085,plain,
! [X0: $i] : join(iPr_def_10,complement(complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_2696,c_12078]) ).
tcf(c_12266,plain,
! [X0: $i,X1: $i] : join(complement(X0),join(complement(X0),X1)) = join(complement(X0),X1),
inference(superposition,[status(thm)],[c_12078,c_153]) ).
tcf(c_14315,plain,
! [X0: $i] : join(iPr_def_10,join(iPr_def_10,X0)) = join(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_12064,c_153]) ).
tcf(c_14637,plain,
! [X0: $i] : join(iPr_def_10,X0) = X0,
inference(superposition,[status(thm)],[c_12085,c_14315]) ).
tcf(c_14647,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_12085,c_14637]) ).
tcf(c_22398,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_14647,c_12266]) ).
tcf(c_22409,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,X1)),complement(join(X0,complement(X1)))) = complement(X0),
inference(superposition,[status(thm)],[c_14647,c_144]) ).
tcf(c_53598,plain,
converse(iPr_def_22) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_131,c_155]) ).
tcf(c_53618,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,X1)),complement(X0)) = complement(X0),
inference(superposition,[status(thm)],[c_22409,c_22398]) ).
tcf(c_53620,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(X0,X1))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_53618,c_153,c_154]) ).
tcf(c_53632,plain,
complement(iPr_def_22) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_135,c_155]) ).
tcf(c_53648,plain,
join(iPr_def_11,iPr_def_14) = iPr_def_14,
inference(superposition,[status(thm)],[c_133,c_22398]) ).
tcf(c_53651,plain,
join(iPr_def_16,iPr_def_18) = iPr_def_18,
inference(superposition,[status(thm)],[c_137,c_22398]) ).
tcf(c_53659,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,X1)),complement(join(X1,complement(X0)))) = complement(X1),
inference(superposition,[status(thm)],[c_154,c_22409]) ).
tcf(c_53660,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,X0)) = join(X1,X0),
inference(superposition,[status(thm)],[c_154,c_22398]) ).
tcf(c_53683,plain,
composition(iPr_def_22,top) = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_141,c_155]) ).
tcf(c_53685,plain,
converse(iPr_def_12) = iPr_def_22,
inference(superposition,[status(thm)],[c_53598,c_149]) ).
tcf(c_53693,plain,
join(iPr_def_12,iPr_def_13) = top,
inference(superposition,[status(thm)],[c_132,c_146]) ).
tcf(c_53695,plain,
join(iPr_def_18,iPr_def_19) = top,
inference(superposition,[status(thm)],[c_138,c_146]) ).
tcf(c_53699,plain,
! [X0: $i] : join(X0,top) = top,
inference(superposition,[status(thm)],[c_146,c_22398]) ).
tcf(c_53716,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_149,c_147]) ).
tcf(c_53721,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_149,c_148]) ).
tcf(c_53722,plain,
! [X0: $i] : converse(join(iPr_def_22,X0)) = join(iPr_def_12,converse(X0)),
inference(superposition,[status(thm)],[c_53598,c_148]) ).
tcf(c_53723,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(superposition,[status(thm)],[c_149,c_148]) ).
tcf(c_53724,plain,
! [X0: $i] : converse(join(X0,iPr_def_22)) = join(converse(X0),iPr_def_12),
inference(superposition,[status(thm)],[c_53598,c_148]) ).
tcf(c_53730,plain,
! [X0: $i] : converse(join(X0,iPr_def_22)) = join(iPr_def_12,converse(X0)),
inference(theory_normalisation,[status(thm)],[c_53724,c_153,c_154]) ).
tcf(c_53741,plain,
! [X0: $i] : join(top,X0) = top,
inference(superposition,[status(thm)],[c_53699,c_154]) ).
tcf(c_53917,plain,
! [X0: $i] : converse(join(iPr_def_12,X0)) = join(iPr_def_22,converse(X0)),
inference(superposition,[status(thm)],[c_53685,c_148]) ).
tcf(c_53938,plain,
join(complement(top),composition(converse(iPr_def_22),complement(iPr_def_22))) = complement(top),
inference(superposition,[status(thm)],[c_53683,c_143]) ).
tcf(c_53941,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(superposition,[status(thm)],[c_143,c_22398]) ).
tcf(c_53942,plain,
join(iPr_def_10,composition(iPr_def_12,iPr_def_16)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_53938,c_129,c_53598,c_53632]) ).
tcf(c_53956,plain,
! [X0: $i] : composition(join(X0,iPr_def_15),iPr_def_19) = join(composition(X0,iPr_def_19),iPr_def_20),
inference(superposition,[status(thm)],[c_139,c_150]) ).
tcf(c_53957,plain,
! [X0: $i] : composition(join(X0,sk2),iPr_def_19) = join(composition(X0,iPr_def_19),iPr_def_21),
inference(superposition,[status(thm)],[c_140,c_150]) ).
tcf(c_53965,plain,
! [X0: $i] : composition(join(X0,sk2),iPr_def_19) = join(iPr_def_21,composition(X0,iPr_def_19)),
inference(theory_normalisation,[status(thm)],[c_53957,c_153,c_154]) ).
tcf(c_53966,plain,
! [X0: $i] : composition(join(X0,iPr_def_15),iPr_def_19) = join(iPr_def_20,composition(X0,iPr_def_19)),
inference(theory_normalisation,[status(thm)],[c_53956,c_153,c_154]) ).
tcf(c_53992,plain,
! [X0: $i] : join(complement(join(iPr_def_11,X0)),complement(join(iPr_def_11,complement(X0)))) = sk2,
inference(superposition,[status(thm)],[c_130,c_144]) ).
tcf(c_53994,plain,
! [X0: $i] : join(complement(join(iPr_def_10,X0)),complement(join(iPr_def_10,complement(X0)))) = top,
inference(superposition,[status(thm)],[c_129,c_144]) ).
tcf(c_53995,plain,
! [X0: $i] : join(complement(join(iPr_def_13,X0)),complement(join(iPr_def_13,complement(X0)))) = iPr_def_12,
inference(superposition,[status(thm)],[c_132,c_144]) ).
tcf(c_53996,plain,
! [X0: $i] : join(complement(join(iPr_def_15,X0)),complement(join(iPr_def_15,complement(X0)))) = iPr_def_14,
inference(superposition,[status(thm)],[c_134,c_144]) ).
tcf(c_53998,plain,
! [X0: $i] : join(complement(join(iPr_def_16,X0)),complement(join(iPr_def_16,complement(X0)))) = iPr_def_22,
inference(superposition,[status(thm)],[c_53632,c_144]) ).
tcf(c_54012,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(superposition,[status(thm)],[c_144,c_22409]) ).
tcf(c_54017,plain,
complement(iPr_def_16) = iPr_def_22,
inference(demodulation,[status(thm)],[c_53998,c_22409]) ).
tcf(c_54019,plain,
complement(iPr_def_15) = iPr_def_14,
inference(demodulation,[status(thm)],[c_53996,c_22409]) ).
tcf(c_54020,plain,
complement(iPr_def_13) = iPr_def_12,
inference(demodulation,[status(thm)],[c_53995,c_22409]) ).
tcf(c_54021,plain,
complement(iPr_def_10) = top,
inference(demodulation,[status(thm)],[c_53994,c_22409]) ).
tcf(c_54023,plain,
complement(iPr_def_11) = sk2,
inference(demodulation,[status(thm)],[c_53992,c_22409]) ).
tcf(c_54346,plain,
! [X0: $i] : join(iPr_def_18,join(iPr_def_19,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_53695,c_153]) ).
tcf(c_54349,plain,
! [X0: $i] : join(iPr_def_18,join(iPr_def_19,X0)) = top,
inference(demodulation,[status(thm)],[c_54346,c_53741]) ).
tcf(c_54360,plain,
join(complement(iPr_def_14),complement(join(iPr_def_13,complement(iPr_def_11)))) = complement(iPr_def_13),
inference(superposition,[status(thm)],[c_133,c_53659]) ).
tcf(c_54389,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,X1)),complement(X1)) = complement(X1),
inference(superposition,[status(thm)],[c_53659,c_22398]) ).
tcf(c_54395,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(X1,X0))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_54389,c_153,c_154]) ).
tcf(c_54404,plain,
join(iPr_def_15,complement(join(iPr_def_13,complement(iPr_def_11)))) = complement(iPr_def_13),
inference(demodulation,[status(thm)],[c_54360,c_134]) ).
tcf(c_55269,plain,
join(complement(iPr_def_10),complement(join(composition(iPr_def_12,iPr_def_16),complement(iPr_def_10)))) = complement(composition(iPr_def_12,iPr_def_16)),
inference(superposition,[status(thm)],[c_53942,c_53659]) ).
tcf(c_55274,plain,
join(complement(iPr_def_10),complement(join(complement(iPr_def_10),composition(iPr_def_12,iPr_def_16)))) = complement(composition(iPr_def_12,iPr_def_16)),
inference(theory_normalisation,[status(thm)],[c_55269,c_153,c_154]) ).
tcf(c_55275,plain,
complement(composition(iPr_def_12,iPr_def_16)) = top,
inference(demodulation,[status(thm)],[c_55274,c_129,c_54021,c_53741]) ).
tcf(c_55279,plain,
join(complement(iPr_def_14),complement(join(iPr_def_11,complement(iPr_def_14)))) = complement(iPr_def_11),
inference(superposition,[status(thm)],[c_53648,c_22409]) ).
tcf(c_55280,plain,
join(iPr_def_15,complement(join(iPr_def_11,iPr_def_15))) = sk2,
inference(demodulation,[status(thm)],[c_55279,c_134,c_54023]) ).
tcf(c_55350,plain,
join(complement(iPr_def_18),complement(join(iPr_def_16,complement(iPr_def_18)))) = complement(iPr_def_16),
inference(superposition,[status(thm)],[c_53651,c_22409]) ).
tcf(c_55351,plain,
join(iPr_def_19,complement(join(iPr_def_16,iPr_def_19))) = iPr_def_22,
inference(demodulation,[status(thm)],[c_55350,c_138,c_54017]) ).
tcf(c_55363,plain,
complement(iPr_def_12) = iPr_def_13,
inference(superposition,[status(thm)],[c_54020,c_54012]) ).
tcf(c_55365,plain,
complement(iPr_def_14) = iPr_def_15,
inference(superposition,[status(thm)],[c_54019,c_54012]) ).
tcf(c_55367,plain,
complement(top) = iPr_def_10,
inference(superposition,[status(thm)],[c_54021,c_54012]) ).
tcf(c_55608,plain,
composition(iPr_def_12,iPr_def_16) = complement(top),
inference(superposition,[status(thm)],[c_55275,c_54012]) ).
tcf(c_55617,plain,
composition(iPr_def_12,iPr_def_16) = iPr_def_10,
inference(demodulation,[status(thm)],[c_55608,c_55367]) ).
tcf(c_56414,plain,
! [X0: $i] : composition(join(iPr_def_12,X0),iPr_def_16) = join(iPr_def_10,composition(X0,iPr_def_16)),
inference(superposition,[status(thm)],[c_55617,c_150]) ).
tcf(c_56639,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(superposition,[status(thm)],[c_54012,c_53941]) ).
tcf(c_58209,plain,
join(iPr_def_15,sk2) = sk2,
inference(superposition,[status(thm)],[c_55280,c_22398]) ).
tcf(c_58257,plain,
! [X0: $i] : join(complement(join(complement(X0),X0)),complement(complement(X0))) = X0,
inference(superposition,[status(thm)],[c_56639,c_144]) ).
tcf(c_58291,plain,
! [X0: $i] : join(complement(complement(X0)),complement(join(X0,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_58257,c_153,c_154]) ).
tcf(c_58292,plain,
! [X0: $i] : join(X0,iPr_def_10) = X0,
inference(demodulation,[status(thm)],[c_58291,c_146,c_54012,c_55367]) ).
tcf(c_58562,plain,
! [X0: $i] : join(iPr_def_10,X0) = X0,
inference(superposition,[status(thm)],[c_58292,c_53660]) ).
tcf(c_58679,plain,
join(iPr_def_19,iPr_def_22) = iPr_def_22,
inference(superposition,[status(thm)],[c_55351,c_22398]) ).
tcf(c_58682,plain,
join(iPr_def_18,iPr_def_22) = top,
inference(superposition,[status(thm)],[c_55351,c_54349]) ).
tcf(c_58709,plain,
! [X0: $i] : join(iPr_def_18,join(iPr_def_22,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_58682,c_153]) ).
tcf(c_58713,plain,
! [X0: $i] : join(iPr_def_18,join(iPr_def_22,X0)) = top,
inference(demodulation,[status(thm)],[c_58709,c_53741]) ).
tcf(c_58958,plain,
join(iPr_def_12,converse(complement(iPr_def_22))) = converse(top),
inference(superposition,[status(thm)],[c_146,c_53722]) ).
tcf(c_58971,plain,
join(iPr_def_12,converse(iPr_def_16)) = converse(top),
inference(demodulation,[status(thm)],[c_58958,c_53632]) ).
tcf(c_59102,plain,
join(iPr_def_12,converse(iPr_def_19)) = converse(iPr_def_22),
inference(superposition,[status(thm)],[c_58679,c_53730]) ).
tcf(c_59109,plain,
join(iPr_def_12,converse(iPr_def_19)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_59102,c_53598]) ).
tcf(c_59147,plain,
join(iPr_def_22,converse(iPr_def_13)) = converse(top),
inference(superposition,[status(thm)],[c_53693,c_53917]) ).
tcf(c_59187,plain,
join(iPr_def_18,converse(top)) = top,
inference(superposition,[status(thm)],[c_59147,c_58713]) ).
tcf(c_83020,plain,
! [X0: $i] : join(X0,converse(top)) = converse(top),
inference(superposition,[status(thm)],[c_53699,c_53721]) ).
tcf(c_83021,plain,
! [X0: $i] : join(X0,converse(iPr_def_10)) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_58292,c_53721]) ).
tcf(c_83067,plain,
! [X0: $i] : join(X0,converse(iPr_def_10)) = X0,
inference(demodulation,[status(thm)],[c_83021,c_149]) ).
tcf(c_83101,plain,
converse(top) = top,
inference(demodulation,[status(thm)],[c_59187,c_83020]) ).
tcf(c_83122,plain,
join(iPr_def_22,converse(iPr_def_13)) = top,
inference(demodulation,[status(thm)],[c_59147,c_83101]) ).
tcf(c_83123,plain,
join(iPr_def_12,converse(iPr_def_16)) = top,
inference(demodulation,[status(thm)],[c_58971,c_83101]) ).
tcf(c_85845,plain,
converse(iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_83067,c_58562]) ).
tcf(c_90369,plain,
join(complement(top),complement(join(iPr_def_22,complement(converse(iPr_def_13))))) = complement(iPr_def_22),
inference(superposition,[status(thm)],[c_83122,c_22409]) ).
tcf(c_90393,plain,
complement(join(iPr_def_22,complement(converse(iPr_def_13)))) = iPr_def_16,
inference(demodulation,[status(thm)],[c_90369,c_53632,c_58562,c_55367]) ).
tcf(c_93505,plain,
join(iPr_def_15,complement(join(iPr_def_13,sk2))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_54404,c_54020,c_54023]) ).
tcf(c_93524,plain,
join(complement(join(iPr_def_15,join(iPr_def_13,sk2))),complement(iPr_def_12)) = complement(iPr_def_15),
inference(superposition,[status(thm)],[c_93505,c_22409]) ).
tcf(c_93536,plain,
join(complement(iPr_def_12),complement(join(iPr_def_13,join(iPr_def_15,sk2)))) = complement(iPr_def_15),
inference(theory_normalisation,[status(thm)],[c_93524,c_153,c_154]) ).
tcf(c_93537,plain,
join(iPr_def_13,complement(join(iPr_def_13,sk2))) = iPr_def_14,
inference(demodulation,[status(thm)],[c_93536,c_54019,c_55363,c_58209]) ).
tcf(c_144401,plain,
join(iPr_def_10,composition(converse(iPr_def_19),iPr_def_16)) = composition(iPr_def_12,iPr_def_16),
inference(superposition,[status(thm)],[c_59109,c_56414]) ).
tcf(c_144438,plain,
composition(converse(iPr_def_19),iPr_def_16) = iPr_def_10,
inference(demodulation,[status(thm)],[c_144401,c_58562,c_55617]) ).
tcf(c_145529,plain,
composition(converse(iPr_def_16),iPr_def_19) = converse(iPr_def_10),
inference(superposition,[status(thm)],[c_144438,c_53716]) ).
tcf(c_145531,plain,
composition(converse(iPr_def_16),iPr_def_19) = iPr_def_10,
inference(demodulation,[status(thm)],[c_145529,c_85845]) ).
tcf(c_162506,plain,
join(complement(complement(converse(iPr_def_13))),iPr_def_16) = complement(complement(converse(iPr_def_13))),
inference(superposition,[status(thm)],[c_90393,c_54395]) ).
tcf(c_162521,plain,
join(iPr_def_16,complement(complement(converse(iPr_def_13)))) = complement(complement(converse(iPr_def_13))),
inference(theory_normalisation,[status(thm)],[c_162506,c_153,c_154]) ).
tcf(c_162522,plain,
join(iPr_def_16,converse(iPr_def_13)) = converse(iPr_def_13),
inference(demodulation,[status(thm)],[c_162521,c_54012]) ).
tcf(c_166151,plain,
join(converse(iPr_def_16),iPr_def_13) = converse(converse(iPr_def_13)),
inference(superposition,[status(thm)],[c_162522,c_53723]) ).
tcf(c_166161,plain,
join(iPr_def_13,converse(iPr_def_16)) = converse(converse(iPr_def_13)),
inference(theory_normalisation,[status(thm)],[c_166151,c_153,c_154]) ).
tcf(c_166162,plain,
join(iPr_def_13,converse(iPr_def_16)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_166161,c_149]) ).
tcf(c_166207,plain,
join(complement(iPr_def_13),complement(join(converse(iPr_def_16),complement(iPr_def_13)))) = complement(converse(iPr_def_16)),
inference(superposition,[status(thm)],[c_166162,c_53659]) ).
tcf(c_166247,plain,
join(complement(iPr_def_13),complement(join(complement(iPr_def_13),converse(iPr_def_16)))) = complement(converse(iPr_def_16)),
inference(theory_normalisation,[status(thm)],[c_166207,c_153,c_154]) ).
tcf(c_166248,plain,
complement(converse(iPr_def_16)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_166247,c_54020,c_58292,c_55367,c_83123]) ).
tcf(c_168210,plain,
converse(iPr_def_16) = complement(iPr_def_12),
inference(superposition,[status(thm)],[c_166248,c_54012]) ).
tcf(c_168225,plain,
converse(iPr_def_16) = iPr_def_13,
inference(demodulation,[status(thm)],[c_168210,c_55363]) ).
tcf(c_168260,plain,
composition(iPr_def_13,iPr_def_19) = iPr_def_10,
inference(demodulation,[status(thm)],[c_145531,c_168225]) ).
tcf(c_232795,plain,
join(complement(iPr_def_14),complement(join(complement(join(iPr_def_13,sk2)),complement(iPr_def_13)))) = complement(complement(join(iPr_def_13,sk2))),
inference(superposition,[status(thm)],[c_93537,c_53659]) ).
tcf(c_232853,plain,
join(complement(iPr_def_14),complement(join(complement(iPr_def_13),complement(join(iPr_def_13,sk2))))) = complement(complement(join(iPr_def_13,sk2))),
inference(theory_normalisation,[status(thm)],[c_232795,c_153,c_154]) ).
tcf(c_232854,plain,
join(iPr_def_13,sk2) = join(iPr_def_13,iPr_def_15),
inference(demodulation,[status(thm)],[c_232853,c_154,c_54012,c_54020,c_55363,c_55365,c_53620]) ).
tcf(c_237658,plain,
composition(join(iPr_def_13,iPr_def_15),iPr_def_19) = join(iPr_def_21,composition(iPr_def_13,iPr_def_19)),
inference(superposition,[status(thm)],[c_232854,c_53965]) ).
tcf(c_237678,plain,
iPr_def_20 = iPr_def_21,
inference(demodulation,[status(thm)],[c_237658,c_53966,c_58292,c_168260]) ).
tcf(c_237679,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_237678,c_145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL035-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n019.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 07:30:10 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.40 Running UEQ theorem proving
% 0.14/5.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.42
% 0.14/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42
% 0.14/5.42 % Detected problem language: tptp
% 0.14/5.43 % Proving...
% 40.94/20.87 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 40.94/20.87 % SZS status Started for theBenchmark.p
% 40.94/20.87 % SZS status Unsatisfiable for theBenchmark.p
% 40.94/20.87
% 40.94/20.87 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 40.94/20.87
% 40.94/20.87 % ------ iProver source info
% 40.94/20.87
% 40.94/20.87 % git: date: 2026-07-19 20:42:38 +0200
% 40.94/20.87 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 40.94/20.87 % git: non_committed_changes: false
% 40.94/20.87
% 40.94/20.87 % ------ Parsing...% successful
% 40.94/20.87
% 40.94/20.87
% 40.94/20.87 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 40.94/20.87
% 40.94/20.87 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 40.94/20.87
% 40.94/20.87 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 40.94/20.87
% 40.94/20.87 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 40.94/20.87 % ------ Proving...
% 40.94/20.87 % ------ Problem Properties
% 40.94/20.87
% 40.94/20.87 %
% 40.94/20.87 % clauses 27
% 40.94/20.87 % conjectures 13
% 40.94/20.87 % EPR 3
% 40.94/20.87 % Horn 27
% 40.94/20.87 % unary 27
% 40.94/20.87 % binary 0
% 40.94/20.87 % lits 27
% 40.94/20.87 % lits eq 27
% 40.94/20.87 % fd_pure 0
% 40.94/20.87 % fd_pseudo 0
% 40.94/20.87 % fd_cond 0
% 40.94/20.87 % fd_pseudo_cond 0
% 40.94/20.87 % AC symbols 1
% 40.94/20.87
% 40.94/20.87 % ------ Input Options Time Limit: Unbounded
% 40.94/20.87
% 40.94/20.87
% 40.94/20.87 % ------
% 40.94/20.87 % Current options:
% 40.94/20.87 % ------
% 40.94/20.87
% 40.94/20.87
% 40.94/20.87 %
% 40.94/20.87
% 40.94/20.87 % ------ Proving...
% 40.94/20.87 %
% 40.94/20.87
% 40.94/20.87 % SZS status Unsatisfiable for theBenchmark.p
% 40.94/20.87
% 40.94/20.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 40.94/20.88
% 40.94/20.88
%------------------------------------------------------------------------------