%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL050+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 : n020.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 02:37:03 PM UTC 2026
% Result : Theorem 10.69s 2.74s
% Output : CNFRefutation 10.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 18
% Syntax : Number of formulae : 157 ( 148 unt; 4 def)
% Number of atoms : 255 ( 165 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 : 153 ( 0 sgn 152 !; 1 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(f14,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/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f15,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)],[f14]) ).
fof(f16,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,[],[f15]) ).
fof(f17,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)],[f16]) ).
fof(f18,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f19,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f20,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f22,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f23,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f24,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f25,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f27,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f29,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f30,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f31,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,[],[f17]) ).
fof(f32,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f30,f21]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f18]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f19]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f20]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f22]) ).
tcf(c_53,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f23]) ).
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,[],[f24]) ).
tcf(c_55,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f25]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f28]) ).
tcf(c_59,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f29]) ).
tcf(c_60,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f32]) ).
tcf(c_61,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,[],[f31]) ).
tcf(c_74,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_75,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_76,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_61,c_50,c_49]) ).
tcf(c_107,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_116,definition,
iPr_def_10 = composition(sK0,top),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_117,definition,
iPr_def_11 = complement(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_118,definition,
iPr_def_12 = composition(iPr_def_11,top),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_119,definition,
iPr_def_13 = join(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_120,negated_conjecture,
( ( iPr_def_13 != iPr_def_12 )
| ( iPr_def_13 != iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_76,c_118,c_116,c_117,c_119]) ).
tcf(c_195,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_220,plain,
join(top,zero) = top,
inference(superposition,[status(thm)],[c_107,c_59]) ).
tcf(c_222,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_59,c_74]) ).
tcf(c_224,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_222,c_50,c_49]) ).
tcf(c_225,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_224,c_107]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_253,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_59,c_236]) ).
tcf(c_307,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_237,c_57]) ).
tcf(c_364,plain,
! [X0: $i] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(superposition,[status(thm)],[c_107,c_75]) ).
tcf(c_365,plain,
! [X0: $i] : join(iPr_def_11,composition(converse(X0),complement(composition(X0,iPr_def_10)))) = iPr_def_11,
inference(superposition,[status(thm)],[c_117,c_75]) ).
tcf(c_372,plain,
join(complement(top),composition(converse(sK0),complement(iPr_def_10))) = complement(top),
inference(superposition,[status(thm)],[c_116,c_75]) ).
tcf(c_376,plain,
join(zero,composition(converse(sK0),iPr_def_11)) = zero,
inference(light_normalisation,[status(thm)],[c_372,c_107,c_117]) ).
tcf(c_409,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_59,c_50]) ).
tcf(c_413,plain,
! [X0: $i] : join(top,join(zero,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_220,c_50]) ).
tcf(c_453,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_456,plain,
! [X0: $i] : composition(iPr_def_11,composition(top,X0)) = composition(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_118,c_52]) ).
tcf(c_555,plain,
! [X0: $i] : join(top,join(X0,zero)) = join(top,X0),
inference(superposition,[status(thm)],[c_49,c_413]) ).
tcf(c_707,plain,
! [X0: $i,X1: $i] : join(X0,join(X1,complement(X0))) = join(X1,top),
inference(superposition,[status(thm)],[c_59,c_195]) ).
tcf(c_711,plain,
! [X0: $i] : join(top,join(X0,zero)) = join(X0,top),
inference(superposition,[status(thm)],[c_220,c_195]) ).
tcf(c_1041,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_243]) ).
tcf(c_1061,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_1041,c_55]) ).
tcf(c_1095,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_1061,c_53]) ).
tcf(c_1099,plain,
! [X0: $i] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_1061,c_75]) ).
tcf(c_1102,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_1061,c_453]) ).
tcf(c_1104,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_1102,c_1061]) ).
tcf(c_1138,plain,
join(one,converse(complement(one))) = converse(top),
inference(superposition,[status(thm)],[c_1095,c_253]) ).
tcf(c_1156,plain,
! [X0: $i,X1: $i] : join(X0,composition(X1,X0)) = composition(join(one,X1),X0),
inference(superposition,[status(thm)],[c_1104,c_54]) ).
tcf(c_1573,plain,
! [X0: $i] : join(top,complement(complement(X0))) = join(X0,top),
inference(superposition,[status(thm)],[c_59,c_409]) ).
tcf(c_2587,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_1099,c_1104]) ).
tcf(c_2588,plain,
! [X0: $i] : join(zero,complement(complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_225,c_2587]) ).
tcf(c_2592,plain,
join(zero,zero) = zero,
inference(superposition,[status(thm)],[c_107,c_2587]) ).
tcf(c_2603,plain,
! [X0: $i] : join(X0,complement(X0)) = join(complement(X0),top),
inference(superposition,[status(thm)],[c_2587,c_707]) ).
tcf(c_2604,plain,
! [X0: $i] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(theory_normalisation,[status(thm)],[c_2603,c_50,c_49]) ).
tcf(c_2605,plain,
! [X0: $i] : join(top,complement(X0)) = top,
inference(light_normalisation,[status(thm)],[c_2604,c_59]) ).
tcf(c_2614,plain,
! [X0: $i] : join(X0,top) = top,
inference(demodulation,[status(thm)],[c_1573,c_2605]) ).
tcf(c_2621,plain,
! [X0: $i] : join(top,join(X0,zero)) = top,
inference(demodulation,[status(thm)],[c_711,c_2614]) ).
tcf(c_2626,plain,
! [X0: $i] : join(top,X0) = top,
inference(demodulation,[status(thm)],[c_555,c_2621]) ).
tcf(c_2643,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_2592,c_50]) ).
tcf(c_2745,plain,
converse(top) = top,
inference(superposition,[status(thm)],[c_2626,c_253]) ).
tcf(c_2752,plain,
join(one,converse(complement(one))) = top,
inference(demodulation,[status(thm)],[c_1138,c_2745]) ).
tcf(c_2762,plain,
! [X0: $i] : composition(top,converse(X0)) = converse(composition(X0,top)),
inference(superposition,[status(thm)],[c_2745,c_242]) ).
tcf(c_2764,plain,
! [X0: $i] : composition(converse(X0),top) = converse(composition(top,X0)),
inference(superposition,[status(thm)],[c_2745,c_57]) ).
tcf(c_2937,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_2588,c_2643]) ).
tcf(c_2950,plain,
composition(converse(sK0),iPr_def_11) = zero,
inference(demodulation,[status(thm)],[c_376,c_2937]) ).
tcf(c_3033,plain,
! [X0: $i] : join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_2937,c_49]) ).
tcf(c_3038,plain,
complement(zero) = top,
inference(superposition,[status(thm)],[c_2937,c_59]) ).
tcf(c_3041,plain,
! [X0: $i] : join(converse(zero),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_2937,c_237]) ).
tcf(c_3053,plain,
! [X0: $i] : join(converse(zero),X0) = X0,
inference(light_normalisation,[status(thm)],[c_3041,c_55]) ).
tcf(c_3200,plain,
! [X0: $i] : composition(converse(sK0),composition(iPr_def_11,X0)) = composition(zero,X0),
inference(superposition,[status(thm)],[c_2950,c_52]) ).
tcf(c_3203,plain,
composition(converse(iPr_def_11),sK0) = converse(zero),
inference(superposition,[status(thm)],[c_2950,c_243]) ).
tcf(c_3342,plain,
converse(zero) = zero,
inference(superposition,[status(thm)],[c_3053,c_3033]) ).
tcf(c_3380,plain,
! [X0: $i] : composition(converse(X0),zero) = converse(composition(zero,X0)),
inference(superposition,[status(thm)],[c_3342,c_57]) ).
tcf(c_3673,plain,
composition(converse(iPr_def_11),sK0) = zero,
inference(light_normalisation,[status(thm)],[c_3203,c_3342]) ).
tcf(c_3675,plain,
! [X0: $i] : composition(converse(iPr_def_11),composition(sK0,X0)) = composition(zero,X0),
inference(superposition,[status(thm)],[c_3673,c_52]) ).
tcf(c_4270,plain,
composition(top,converse(iPr_def_11)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_118,c_2762]) ).
tcf(c_4323,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_4270,c_54]) ).
tcf(c_4331,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_4323,c_50,c_49]) ).
tcf(c_4332,plain,
! [X0: $i] : join(converse(iPr_def_12),composition(X0,converse(iPr_def_11))) = converse(iPr_def_12),
inference(light_normalisation,[status(thm)],[c_4331,c_2614,c_4270]) ).
tcf(c_4811,plain,
composition(converse(sK0),iPr_def_12) = composition(zero,top),
inference(superposition,[status(thm)],[c_118,c_3200]) ).
tcf(c_4831,plain,
composition(converse(iPr_def_12),sK0) = converse(composition(zero,top)),
inference(superposition,[status(thm)],[c_4811,c_243]) ).
tcf(c_5497,plain,
composition(converse(iPr_def_11),iPr_def_10) = composition(zero,top),
inference(superposition,[status(thm)],[c_116,c_3675]) ).
tcf(c_5546,plain,
composition(converse(iPr_def_10),iPr_def_11) = converse(composition(zero,top)),
inference(superposition,[status(thm)],[c_5497,c_243]) ).
tcf(c_7151,plain,
composition(converse(iPr_def_10),iPr_def_11) = composition(converse(iPr_def_12),sK0),
inference(light_normalisation,[status(thm)],[c_4831,c_5546]) ).
tcf(c_7202,plain,
composition(converse(iPr_def_10),iPr_def_11) = composition(top,zero),
inference(demodulation,[status(thm)],[c_5546,c_2745,c_3380]) ).
tcf(c_7203,plain,
composition(converse(iPr_def_12),sK0) = composition(top,zero),
inference(demodulation,[status(thm)],[c_7151,c_7202]) ).
tcf(c_7586,plain,
! [X0: $i] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(demodulation,[status(thm)],[c_364,c_2937]) ).
tcf(c_7588,plain,
composition(top,complement(composition(top,top))) = zero,
inference(superposition,[status(thm)],[c_2745,c_7586]) ).
tcf(c_7614,plain,
! [X0: $i] : composition(converse(complement(composition(X0,top))),X0) = converse(zero),
inference(superposition,[status(thm)],[c_7586,c_243]) ).
tcf(c_7619,plain,
! [X0: $i] : composition(converse(complement(composition(X0,top))),X0) = zero,
inference(light_normalisation,[status(thm)],[c_7614,c_3342]) ).
tcf(c_8955,plain,
! [X0: $i] : composition(join(one,X0),zero) = composition(X0,zero),
inference(superposition,[status(thm)],[c_1156,c_2937]) ).
tcf(c_8969,plain,
! [X0: $i] : composition(join(one,X0),top) = top,
inference(superposition,[status(thm)],[c_1156,c_2626]) ).
tcf(c_9308,plain,
composition(top,top) = top,
inference(superposition,[status(thm)],[c_2752,c_8969]) ).
tcf(c_9326,plain,
! [X0: $i] : composition(converse(complement(top)),join(one,X0)) = zero,
inference(superposition,[status(thm)],[c_8969,c_7619]) ).
tcf(c_9331,plain,
! [X0: $i] : composition(zero,join(one,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_9326,c_107,c_3342]) ).
tcf(c_9339,plain,
composition(top,complement(top)) = zero,
inference(demodulation,[status(thm)],[c_7588,c_9308]) ).
tcf(c_9340,plain,
composition(top,zero) = zero,
inference(light_normalisation,[status(thm)],[c_9339,c_107]) ).
tcf(c_9342,plain,
composition(converse(iPr_def_12),sK0) = zero,
inference(demodulation,[status(thm)],[c_7203,c_9340]) ).
tcf(c_9381,plain,
composition(iPr_def_11,top) = composition(iPr_def_12,top),
inference(superposition,[status(thm)],[c_9308,c_456]) ).
tcf(c_9384,plain,
composition(iPr_def_12,top) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_9381,c_118]) ).
tcf(c_9552,plain,
composition(top,converse(iPr_def_12)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_9384,c_2762]) ).
tcf(c_9610,plain,
! [X0: $i] : composition(converse(iPr_def_12),composition(sK0,X0)) = composition(zero,X0),
inference(superposition,[status(thm)],[c_9342,c_52]) ).
tcf(c_10295,plain,
! [X0: $i] : composition(join(converse(one),X0),converse(zero)) = converse(zero),
inference(superposition,[status(thm)],[c_9331,c_307]) ).
tcf(c_10298,plain,
! [X0: $i] : composition(X0,zero) = zero,
inference(light_normalisation,[status(thm)],[c_10295,c_1095,c_3342,c_8955]) ).
tcf(c_10443,plain,
! [X0: $i] : composition(converse(zero),X0) = converse(zero),
inference(superposition,[status(thm)],[c_10298,c_243]) ).
tcf(c_10452,plain,
! [X0: $i] : composition(zero,X0) = zero,
inference(light_normalisation,[status(thm)],[c_10443,c_3342]) ).
tcf(c_10627,plain,
composition(converse(converse(iPr_def_12)),top) = converse(converse(iPr_def_12)),
inference(superposition,[status(thm)],[c_9552,c_2764]) ).
tcf(c_12274,plain,
! [X0: $i] : composition(converse(iPr_def_12),composition(sK0,X0)) = zero,
inference(light_normalisation,[status(thm)],[c_9610,c_10452]) ).
tcf(c_12276,plain,
composition(converse(iPr_def_12),iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_116,c_12274]) ).
tcf(c_12305,plain,
join(iPr_def_11,composition(converse(converse(iPr_def_12)),complement(zero))) = iPr_def_11,
inference(superposition,[status(thm)],[c_12276,c_365]) ).
tcf(c_12307,plain,
join(iPr_def_11,converse(converse(iPr_def_12))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_12305,c_3038,c_10627]) ).
tcf(c_12344,plain,
iPr_def_11 = iPr_def_13,
inference(demodulation,[status(thm)],[c_12307,c_55,c_119]) ).
tcf(c_12381,plain,
join(iPr_def_11,iPr_def_12) = iPr_def_11,
inference(demodulation,[status(thm)],[c_119,c_12344]) ).
tcf(c_12382,plain,
( ( iPr_def_11 != iPr_def_12 )
| ( iPr_def_11 != iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_120,c_12344]) ).
tcf(c_12384,plain,
iPr_def_11 != iPr_def_12,
inference(equality_resolution_simp,[status(thm)],[c_12382]) ).
tcf(c_24570,plain,
join(converse(iPr_def_12),converse(iPr_def_11)) = converse(iPr_def_12),
inference(superposition,[status(thm)],[c_1104,c_4332]) ).
tcf(c_24590,plain,
join(converse(iPr_def_11),converse(iPr_def_12)) = converse(iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_24570,c_50,c_49]) ).
tcf(c_24604,plain,
converse(iPr_def_11) = converse(iPr_def_12),
inference(demodulation,[status(thm)],[c_24590,c_56,c_12381]) ).
tcf(c_24645,plain,
converse(converse(iPr_def_11)) = iPr_def_12,
inference(superposition,[status(thm)],[c_24604,c_55]) ).
tcf(c_24758,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_24645,c_55]) ).
tcf(c_24759,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_24758,c_12384]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL050+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n020.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 07:39:18 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 10.69/2.74 % SZS status Started for theBenchmark.p
% 10.69/2.74 % SZS status Theorem for theBenchmark.p
% 10.69/2.74
% 10.69/2.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.69/2.74
% 10.69/2.74 % ------ iProver source info
% 10.69/2.74
% 10.69/2.74 % git: date: 2026-07-19 20:42:38 +0200
% 10.69/2.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.69/2.74 % git: non_committed_changes: false
% 10.69/2.74
% 10.69/2.74 % ------ Parsing...
% 10.69/2.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.69/2.74
% 10.69/2.74 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.69/2.74
% 10.69/2.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.69/2.74
% 10.69/2.74 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.69/2.74 % ------ Proving...
% 10.69/2.74 % ------ Problem Properties
% 10.69/2.74
% 10.69/2.74 %
% 10.69/2.74 % clauses 17
% 10.69/2.74 % conjectures 1
% 10.69/2.74 % EPR 1
% 10.69/2.74 % Horn 17
% 10.69/2.74 % unary 16
% 10.69/2.74 % binary 1
% 10.69/2.74 % lits 18
% 10.69/2.74 % lits eq 18
% 10.69/2.74 % fd_pure 0
% 10.69/2.74 % fd_pseudo 0
% 10.69/2.74 % fd_cond 0
% 10.69/2.74 % fd_pseudo_cond 0
% 10.69/2.74 % AC symbols 1
% 10.69/2.74
% 10.69/2.74 % ------ Schedule dynamic 5 is on
% 10.69/2.74
% 10.69/2.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.69/2.74
% 10.69/2.74
% 10.69/2.74 % ------
% 10.69/2.74 % Current options:
% 10.69/2.74 % ------
% 10.69/2.74
% 10.69/2.74
% 10.69/2.74 %
% 10.69/2.74
% 10.69/2.74 % ------ Proving...
% 10.69/2.74 %
% 10.69/2.74
% 10.69/2.74 % SZS status Theorem for theBenchmark.p
% 10.69/2.74
% 10.69/2.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.69/2.75
% 10.69/2.75
%------------------------------------------------------------------------------