%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL010-2 : 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 : n005.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 02:36:35 PM UTC 2026
% Result : Unsatisfiable 49.07s 8.69s
% Output : CNFRefutation 49.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 15
% Syntax : Number of formulae : 130 ( 130 unt; 0 def)
% Number of atoms : 130 ( 129 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 141 ( 0 sgn 141 !; 0 ?; 103 :)
% 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(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(f16,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_zero_13) ).
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/sandbox/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,
meet(composition(sk1,sk2),sk3) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
zero = meet(composition(sk1,sk2),sk3),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
meet(sk2,composition(converse(sk1),sk3)) != zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
fof(f26,plain,
zero != meet(sk2,composition(converse(sk1),sk3)),
inference(reorient_equations,[],[f25]) ).
fof(f27,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
fof(f29,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]) ).
fof(f31,plain,
zero = complement(join(complement(composition(sk1,sk2)),complement(sk3))),
inference(definition_unfolding,[],[f24,f6]) ).
fof(f32,plain,
zero != complement(join(complement(sk2),complement(composition(converse(sk1),sk3)))),
inference(definition_unfolding,[],[f26,f6]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f4]) ).
tcf(c_71,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_72,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_73,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f14]) ).
tcf(c_77,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f15]) ).
tcf(c_78,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f27]) ).
tcf(c_80,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,[],[f29]) ).
tcf(c_82,negated_conjecture,
complement(join(complement(composition(sk1,sk2)),complement(sk3))) = zero,
inference(cnf_transformation,[],[f31]) ).
tcf(c_83,negated_conjecture,
complement(join(complement(sk2),complement(composition(converse(sk1),sk3)))) != zero,
inference(cnf_transformation,[],[f32]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(theory_normalisation,[status(thm)],[c_69,c_68,c_67]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_76,c_68,c_67]) ).
tcf(c_101,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_80,c_68,c_67]) ).
tcf(c_103,negated_conjecture,
complement(join(complement(sk3),complement(composition(sk1,sk2)))) = zero,
inference(theory_normalisation,[status(thm)],[c_82,c_68,c_67]) ).
tcf(c_142,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_78,c_77,c_68,c_67]) ).
tcf(c_552,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_77,c_99]) ).
tcf(c_560,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_552,c_68,c_67]) ).
tcf(c_561,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_560,c_142]) ).
tcf(c_1044,plain,
join(complement(sk3),complement(composition(sk1,sk2))) = join(zero,complement(join(zero,zero))),
inference(superposition,[status(thm)],[c_103,c_561]) ).
tcf(c_5538,plain,
complement(join(zero,complement(join(zero,zero)))) = zero,
inference(light_normalisation,[status(thm)],[c_103,c_1044]) ).
tcf(c_5553,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_77,c_68]) ).
tcf(c_5557,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(join(X0,X1)))) = top,
inference(superposition,[status(thm)],[c_68,c_77]) ).
tcf(c_5742,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(superposition,[status(thm)],[c_77,c_99]) ).
tcf(c_5758,plain,
! [X0: $i] : join(complement(join(complement(X0),top)),complement(join(complement(X0),zero))) = X0,
inference(superposition,[status(thm)],[c_142,c_99]) ).
tcf(c_5759,plain,
! [X0: $i] : join(complement(join(complement(X0),join(zero,complement(join(zero,zero))))),complement(join(complement(X0),zero))) = X0,
inference(superposition,[status(thm)],[c_5538,c_99]) ).
tcf(c_5765,plain,
! [X0: $i] : join(complement(join(zero,complement(X0))),complement(join(top,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_5758,c_68,c_67]) ).
tcf(c_5766,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(complement(complement(X0)))))) = X0,
inference(light_normalisation,[status(thm)],[c_5742,c_142]) ).
tcf(c_5769,plain,
! [X0: $i] : join(complement(join(zero,complement(X0))),complement(join(zero,join(complement(X0),complement(join(zero,zero)))))) = X0,
inference(theory_normalisation,[status(thm)],[c_5759,c_68,c_67]) ).
tcf(c_5778,plain,
join(zero,complement(join(top,complement(join(zero,zero))))) = join(zero,zero),
inference(superposition,[status(thm)],[c_5538,c_5765]) ).
tcf(c_5782,plain,
join(complement(join(zero,complement(top))),complement(top)) = top,
inference(superposition,[status(thm)],[c_77,c_5765]) ).
tcf(c_5789,plain,
join(complement(top),complement(join(zero,complement(top)))) = top,
inference(theory_normalisation,[status(thm)],[c_5782,c_68,c_67]) ).
tcf(c_5790,plain,
join(zero,complement(join(zero,zero))) = top,
inference(light_normalisation,[status(thm)],[c_5789,c_142]) ).
tcf(c_7801,plain,
join(zero,join(complement(join(top,complement(join(zero,zero)))),complement(join(zero,zero)))) = top,
inference(superposition,[status(thm)],[c_5778,c_5557]) ).
tcf(c_7840,plain,
join(zero,join(complement(join(zero,zero)),complement(join(top,complement(join(zero,zero)))))) = top,
inference(theory_normalisation,[status(thm)],[c_7801,c_68,c_67]) ).
tcf(c_9488,plain,
join(complement(join(zero,zero)),complement(join(zero,join(complement(join(top,complement(join(zero,zero)))),complement(join(zero,zero)))))) = join(top,complement(join(zero,zero))),
inference(superposition,[status(thm)],[c_5778,c_5769]) ).
tcf(c_9490,plain,
join(complement(join(zero,complement(zero))),complement(join(top,complement(join(zero,zero))))) = zero,
inference(superposition,[status(thm)],[c_5553,c_5769]) ).
tcf(c_9516,plain,
join(complement(join(zero,zero)),complement(join(zero,join(complement(join(zero,zero)),complement(join(top,complement(join(zero,zero)))))))) = join(top,complement(join(zero,zero))),
inference(theory_normalisation,[status(thm)],[c_9488,c_68,c_67]) ).
tcf(c_9517,plain,
join(complement(join(zero,zero)),zero) = join(top,complement(join(zero,zero))),
inference(light_normalisation,[status(thm)],[c_9516,c_142,c_7840]) ).
tcf(c_9518,plain,
join(zero,complement(join(zero,zero))) = join(top,complement(join(zero,zero))),
inference(theory_normalisation,[status(thm)],[c_9517,c_68,c_67]) ).
tcf(c_9519,plain,
join(top,complement(join(zero,zero))) = top,
inference(light_normalisation,[status(thm)],[c_9518,c_5790]) ).
tcf(c_13526,plain,
join(complement(join(zero,complement(zero))),zero) = zero,
inference(light_normalisation,[status(thm)],[c_9490,c_142,c_9519]) ).
tcf(c_13527,plain,
join(zero,zero) = zero,
inference(demodulation,[status(thm)],[c_13526,c_67,c_77,c_142]) ).
tcf(c_13537,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_13527,c_68]) ).
tcf(c_20699,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_5766,c_13537]) ).
tcf(c_84785,plain,
join(complement(sk3),complement(composition(sk1,sk2))) = complement(zero),
inference(demodulation,[status(thm)],[c_1044,c_20699]) ).
tcf(c_84795,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(join(X0,X1)))) = top,
inference(superposition,[status(thm)],[c_77,c_68]) ).
tcf(c_84796,plain,
complement(zero) = top,
inference(superposition,[status(thm)],[c_77,c_20699]) ).
tcf(c_84800,plain,
join(complement(sk3),complement(composition(sk1,sk2))) = top,
inference(demodulation,[status(thm)],[c_84785,c_84796]) ).
tcf(c_84814,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_73,c_75]) ).
tcf(c_84819,plain,
! [X0: $i] : join(complement(sk3),join(complement(composition(sk1,sk2)),X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_84800,c_68]) ).
tcf(c_84821,plain,
! [X0: $i] : join(complement(sk3),join(X0,complement(composition(sk1,sk2)))) = join(top,X0),
inference(superposition,[status(thm)],[c_67,c_84819]) ).
tcf(c_84829,plain,
! [X0: $i,X1: $i] : join(complement(sk3),join(X0,join(X1,complement(composition(sk1,sk2))))) = join(top,join(X0,X1)),
inference(superposition,[status(thm)],[c_68,c_84821]) ).
tcf(c_84851,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(sk3),join(X0,join(X1,join(X2,complement(composition(sk1,sk2)))))) = join(top,join(X0,join(X1,X2))),
inference(superposition,[status(thm)],[c_68,c_84829]) ).
tcf(c_84968,plain,
! [X0: $i] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(superposition,[status(thm)],[c_142,c_100]) ).
tcf(c_84975,plain,
! [X0: $i] : join(top,composition(converse(X0),complement(composition(X0,composition(sk1,sk2))))) = join(complement(sk3),complement(composition(sk1,sk2))),
inference(superposition,[status(thm)],[c_100,c_84819]) ).
tcf(c_84977,plain,
! [X0: $i] : join(top,composition(converse(X0),complement(composition(X0,composition(sk1,sk2))))) = top,
inference(light_normalisation,[status(thm)],[c_84975,c_84800]) ).
tcf(c_84996,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_77,c_99]) ).
tcf(c_85008,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_84996,c_68,c_67]) ).
tcf(c_85009,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_85008,c_142]) ).
tcf(c_85033,plain,
! [X0: $i] : complement(join(complement(X0),complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_85009,c_20699]) ).
tcf(c_85038,plain,
complement(join(top,top)) = zero,
inference(superposition,[status(thm)],[c_84796,c_85033]) ).
tcf(c_85041,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(join(X0,X0)),
inference(superposition,[status(thm)],[c_85033,c_85033]) ).
tcf(c_85045,plain,
! [X0: $i] : join(join(complement(X0),complement(X0)),X0) = top,
inference(superposition,[status(thm)],[c_85033,c_77]) ).
tcf(c_85051,plain,
! [X0: $i] : join(X0,join(complement(X0),complement(X0))) = top,
inference(theory_normalisation,[status(thm)],[c_85045,c_68,c_67]) ).
tcf(c_85062,plain,
! [X0: $i] : join(top,composition(X0,complement(composition(converse(X0),composition(sk1,sk2))))) = top,
inference(superposition,[status(thm)],[c_73,c_84977]) ).
tcf(c_85071,plain,
! [X0: $i,X1: $i] : join(top,join(composition(X0,complement(composition(converse(X0),composition(sk1,sk2)))),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_85062,c_68]) ).
tcf(c_85143,plain,
join(join(top,top),zero) = top,
inference(superposition,[status(thm)],[c_85038,c_77]) ).
tcf(c_85145,plain,
join(zero,join(top,top)) = top,
inference(theory_normalisation,[status(thm)],[c_85143,c_68,c_67]) ).
tcf(c_85173,plain,
! [X0: $i,X1: $i,X2: $i] : join(complement(join(complement(composition(converse(X0),X1)),complement(X2))),complement(join(complement(X2),complement(composition(converse(X0),complement(join(complement(X1),complement(composition(X0,X2))))))))) = complement(join(complement(X2),complement(composition(converse(X0),complement(join(complement(X1),complement(composition(X0,X2)))))))),
inference(superposition,[status(thm)],[c_73,c_101]) ).
tcf(c_85299,plain,
join(top,top) = top,
inference(demodulation,[status(thm)],[c_85145,c_20699]) ).
tcf(c_85301,plain,
! [X0: $i] : join(top,join(top,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_85299,c_68]) ).
tcf(c_85391,plain,
! [X0: $i,X1: $i] : join(top,join(top,join(composition(X0,complement(composition(converse(X0),composition(sk1,sk2)))),X1))) = join(complement(sk3),join(top,join(X1,complement(composition(sk1,sk2))))),
inference(superposition,[status(thm)],[c_85071,c_84851]) ).
tcf(c_85399,plain,
! [X0: $i,X1: $i] : join(top,join(top,join(composition(X0,complement(composition(converse(X0),composition(sk1,sk2)))),X1))) = join(top,join(X1,join(complement(sk3),complement(composition(sk1,sk2))))),
inference(theory_normalisation,[status(thm)],[c_85391,c_68,c_67]) ).
tcf(c_85400,plain,
! [X0: $i] : join(top,join(X0,top)) = join(top,join(top,X0)),
inference(light_normalisation,[status(thm)],[c_85399,c_84800,c_85071]) ).
tcf(c_85401,plain,
! [X0: $i] : join(top,join(X0,top)) = join(top,X0),
inference(light_normalisation,[status(thm)],[c_85400,c_85301]) ).
tcf(c_85594,plain,
! [X0: $i] : join(X0,complement(join(X0,X0))) = top,
inference(light_normalisation,[status(thm)],[c_85051,c_85041]) ).
tcf(c_86642,plain,
! [X0: $i] : join(X0,top) = top,
inference(superposition,[status(thm)],[c_85594,c_84795]) ).
tcf(c_86851,plain,
! [X0: $i] : join(top,X0) = join(top,top),
inference(demodulation,[status(thm)],[c_85401,c_86642]) ).
tcf(c_87110,plain,
! [X0: $i] : join(top,X0) = top,
inference(demodulation,[status(thm)],[c_86851,c_86642]) ).
tcf(c_87329,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_71,c_84814]) ).
tcf(c_87354,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_87329,c_73]) ).
tcf(c_87367,plain,
! [X0: $i,X1: $i] : composition(join(converse(one),X0),X1) = join(X1,composition(X0,X1)),
inference(superposition,[status(thm)],[c_87354,c_72]) ).
tcf(c_87373,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_87354,c_71]) ).
tcf(c_87374,plain,
! [X0: $i,X1: $i] : composition(join(X0,converse(one)),X1) = join(composition(X0,X1),X1),
inference(superposition,[status(thm)],[c_87354,c_72]) ).
tcf(c_87386,plain,
! [X0: $i,X1: $i] : composition(join(X0,converse(one)),X1) = join(X1,composition(X0,X1)),
inference(theory_normalisation,[status(thm)],[c_87374,c_68,c_67]) ).
tcf(c_87580,plain,
! [X0: $i] : converse(join(X0,one)) = join(converse(X0),one),
inference(superposition,[status(thm)],[c_87373,c_74]) ).
tcf(c_87591,plain,
! [X0: $i] : converse(join(X0,one)) = join(one,converse(X0)),
inference(theory_normalisation,[status(thm)],[c_87580,c_68,c_67]) ).
tcf(c_88963,plain,
! [X0: $i,X1: $i] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(light_normalisation,[status(thm)],[c_87367,c_87373]) ).
tcf(c_88980,plain,
! [X0: $i] : composition(join(one,X0),top) = top,
inference(superposition,[status(thm)],[c_88963,c_87110]) ).
tcf(c_89748,plain,
! [X0: $i] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(demodulation,[status(thm)],[c_84968,c_20699]) ).
tcf(c_89749,plain,
! [X0: $i] : composition(X0,complement(composition(converse(X0),top))) = zero,
inference(superposition,[status(thm)],[c_73,c_89748]) ).
tcf(c_89830,plain,
! [X0: $i] : composition(join(X0,one),complement(composition(join(one,converse(X0)),top))) = zero,
inference(superposition,[status(thm)],[c_87591,c_89749]) ).
tcf(c_89949,plain,
! [X0: $i,X1: $i] : join(X0,composition(X1,X0)) = composition(join(X1,one),X0),
inference(light_normalisation,[status(thm)],[c_87386,c_87373]) ).
tcf(c_89968,plain,
! [X0: $i] : composition(join(X0,one),zero) = composition(X0,zero),
inference(superposition,[status(thm)],[c_89949,c_20699]) ).
tcf(c_90951,plain,
! [X0: $i] : composition(X0,zero) = zero,
inference(demodulation,[status(thm)],[c_89830,c_142,c_88980,c_89968]) ).
tcf(c_92331,plain,
join(complement(join(complement(composition(converse(sk1),sk3)),complement(sk2))),complement(join(complement(sk2),complement(composition(converse(sk1),complement(top)))))) = complement(join(complement(sk2),complement(composition(converse(sk1),complement(top))))),
inference(superposition,[status(thm)],[c_84800,c_85173]) ).
tcf(c_92364,plain,
join(complement(join(complement(sk2),complement(composition(converse(sk1),sk3)))),complement(join(complement(sk2),complement(composition(converse(sk1),complement(top)))))) = complement(join(complement(sk2),complement(composition(converse(sk1),complement(top))))),
inference(theory_normalisation,[status(thm)],[c_92331,c_68,c_67]) ).
tcf(c_92365,plain,
join(complement(join(complement(sk2),complement(composition(converse(sk1),sk3)))),complement(join(complement(sk2),complement(composition(converse(sk1),zero))))) = complement(join(complement(sk2),complement(composition(converse(sk1),zero)))),
inference(light_normalisation,[status(thm)],[c_92364,c_142]) ).
tcf(c_92366,plain,
join(complement(join(complement(sk2),complement(composition(converse(sk1),zero)))),complement(join(complement(sk2),complement(composition(converse(sk1),sk3))))) = complement(join(complement(sk2),complement(composition(converse(sk1),zero)))),
inference(theory_normalisation,[status(thm)],[c_92365,c_68,c_67]) ).
tcf(c_92782,plain,
complement(join(complement(sk2),complement(composition(converse(sk1),sk3)))) = zero,
inference(demodulation,[status(thm)],[c_92366,c_142,c_86642,c_20699,c_84796,c_90951]) ).
tcf(c_92783,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_92782,c_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL010-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n005.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 07:07:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running UEQ theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 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...
% 49.07/8.69 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 49.07/8.69 % SZS status Started for theBenchmark.p
% 49.07/8.69 % SZS status Unsatisfiable for theBenchmark.p
% 49.07/8.69
% 49.07/8.69 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 49.07/8.69
% 49.07/8.69 % ------ iProver source info
% 49.07/8.69
% 49.07/8.69 % git: date: 2026-07-19 20:42:38 +0200
% 49.07/8.69 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 49.07/8.69 % git: non_committed_changes: false
% 49.07/8.69
% 49.07/8.69 % ------ Parsing...% successful
% 49.07/8.69
% 49.07/8.69
% 49.07/8.69 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 49.07/8.69
% 49.07/8.69 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 49.07/8.69
% 49.07/8.69 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 49.07/8.69
% 49.07/8.69 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 49.07/8.69 % ------ Proving...
% 49.07/8.69 % ------ Problem Properties
% 49.07/8.69
% 49.07/8.69 %
% 49.07/8.69 % clauses 17
% 49.07/8.69 % conjectures 2
% 49.07/8.69 % EPR 0
% 49.07/8.69 % Horn 17
% 49.07/8.69 % unary 17
% 49.07/8.69 % binary 0
% 49.07/8.69 % lits 17
% 49.07/8.69 % lits eq 17
% 49.07/8.69 % fd_pure 0
% 49.07/8.69 % fd_pseudo 0
% 49.07/8.69 % fd_cond 0
% 49.07/8.69 % fd_pseudo_cond 0
% 49.07/8.69 % AC symbols 1
% 49.07/8.69
% 49.07/8.69 % ------ Input Options Time Limit: Unbounded
% 49.07/8.69
% 49.07/8.69
% 49.07/8.69 % ------
% 49.07/8.69 % Current options:
% 49.07/8.69 % ------
% 49.07/8.69
% 49.07/8.69
% 49.07/8.69 %
% 49.07/8.69
% 49.07/8.69 % ------ Proving...
% 49.07/8.69 %
% 49.07/8.69
% 49.07/8.69 % SZS status Unsatisfiable for theBenchmark.p
% 49.07/8.69
% 49.07/8.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 49.07/8.69
% 49.07/8.69
%------------------------------------------------------------------------------