%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL015+1 : 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 : n008.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 : Theorem 3.64s 1.20s
% Output : CNFRefutation 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 15
% Syntax : Number of formulae : 91 ( 91 unt; 1 def)
% Number of atoms : 108 ( 90 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 : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 110 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(f2,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(f3,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
fof(f4,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
fof(f5,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(f6,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(f7,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(f9,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(f10,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(f11,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(f12,axiom,
! [X0] : top = join(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(f13,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(f14,conjecture,
composition(top,top) = top,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
composition(top,top) != top,
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
top != composition(top,top),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f18,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f19,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f20,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f21,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f23,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f24,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f25,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f26,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f27,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f28,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f29,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f30,plain,
top != composition(top,top),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f29,f20]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f17]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f18]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f19]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f21]) ).
tcf(c_53,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f22]) ).
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,[],[f23]) ).
tcf(c_55,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f24]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f25]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f27]) ).
tcf(c_59,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f28]) ).
tcf(c_60,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f31]) ).
tcf(c_61,negated_conjecture,
composition(top,top) != top,
inference(cnf_transformation,[],[f30]) ).
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_104,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_111,definition,
iPr_def_10 = composition(top,top),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_112,negated_conjecture,
iPr_def_10 != top,
inference(demodulation,[status(thm)],[c_61,c_111]) ).
tcf(c_181,plain,
! [X0: $i] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(superposition,[status(thm)],[c_104,c_75]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(X1,complement(composition(converse(X1),X0)))) = complement(X0),
inference(superposition,[status(thm)],[c_55,c_75]) ).
tcf(c_184,plain,
join(complement(top),composition(converse(top),complement(iPr_def_10))) = complement(top),
inference(superposition,[status(thm)],[c_111,c_75]) ).
tcf(c_185,plain,
join(zero,composition(converse(top),complement(iPr_def_10))) = zero,
inference(light_normalisation,[status(thm)],[c_184,c_104]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_249,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_59,c_188]) ).
tcf(c_376,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_193]) ).
tcf(c_397,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_376,c_55]) ).
tcf(c_407,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_397,c_53]) ).
tcf(c_416,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_397,c_202]) ).
tcf(c_418,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_416,c_397]) ).
tcf(c_445,plain,
join(zero,composition(converse(one),complement(top))) = zero,
inference(superposition,[status(thm)],[c_418,c_181]) ).
tcf(c_448,plain,
join(zero,composition(one,zero)) = zero,
inference(light_normalisation,[status(thm)],[c_445,c_104,c_407]) ).
tcf(c_454,plain,
join(zero,zero) = zero,
inference(demodulation,[status(thm)],[c_448,c_418]) ).
tcf(c_455,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_454,c_50]) ).
tcf(c_464,plain,
! [X0: $i] : join(complement(X0),complement(composition(converse(one),X0))) = complement(X0),
inference(superposition,[status(thm)],[c_418,c_182]) ).
tcf(c_475,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_464,c_407,c_418]) ).
tcf(c_552,plain,
! [X0: $i] : join(complement(join(complement(X0),X0)),complement(complement(X0))) = X0,
inference(superposition,[status(thm)],[c_475,c_74]) ).
tcf(c_554,plain,
! [X0: $i] : join(complement(complement(X0)),complement(join(X0,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_552,c_50,c_49]) ).
tcf(c_555,plain,
! [X0: $i] : join(complement(complement(X0)),zero) = X0,
inference(light_normalisation,[status(thm)],[c_554,c_59,c_104]) ).
tcf(c_556,plain,
! [X0: $i] : join(zero,complement(complement(X0))) = X0,
inference(theory_normalisation,[status(thm)],[c_555,c_50,c_49]) ).
tcf(c_560,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_556,c_455]) ).
tcf(c_563,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_556,c_560]) ).
tcf(c_565,plain,
composition(converse(top),complement(iPr_def_10)) = zero,
inference(demodulation,[status(thm)],[c_185,c_560]) ).
tcf(c_575,plain,
complement(zero) = top,
inference(superposition,[status(thm)],[c_560,c_59]) ).
tcf(c_594,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(superposition,[status(thm)],[c_563,c_475]) ).
tcf(c_616,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_594,c_50]) ).
tcf(c_736,plain,
! [X0: $i] : join(X0,top) = top,
inference(superposition,[status(thm)],[c_59,c_616]) ).
tcf(c_757,plain,
! [X0: $i] : join(top,X0) = top,
inference(superposition,[status(thm)],[c_736,c_49]) ).
tcf(c_773,plain,
converse(top) = top,
inference(superposition,[status(thm)],[c_757,c_249]) ).
tcf(c_776,plain,
composition(top,complement(iPr_def_10)) = zero,
inference(demodulation,[status(thm)],[c_565,c_773]) ).
tcf(c_803,plain,
! [X0: $i] : join(composition(X0,complement(iPr_def_10)),zero) = composition(join(X0,top),complement(iPr_def_10)),
inference(superposition,[status(thm)],[c_776,c_54]) ).
tcf(c_808,plain,
! [X0: $i] : join(zero,composition(X0,complement(iPr_def_10))) = composition(join(X0,top),complement(iPr_def_10)),
inference(theory_normalisation,[status(thm)],[c_803,c_50,c_49]) ).
tcf(c_809,plain,
! [X0: $i] : join(zero,composition(X0,complement(iPr_def_10))) = zero,
inference(light_normalisation,[status(thm)],[c_808,c_736,c_776]) ).
tcf(c_865,plain,
! [X0: $i] : composition(X0,complement(iPr_def_10)) = zero,
inference(demodulation,[status(thm)],[c_809,c_560]) ).
tcf(c_879,plain,
complement(iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_865,c_418]) ).
tcf(c_895,plain,
complement(zero) = iPr_def_10,
inference(superposition,[status(thm)],[c_879,c_563]) ).
tcf(c_899,plain,
top = iPr_def_10,
inference(demodulation,[status(thm)],[c_575,c_895]) ).
tcf(c_910,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_112,c_899]) ).
tcf(c_911,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_910]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL015+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n008.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 07:13:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 3.64/1.20 % SZS status Started for theBenchmark.p
% 3.64/1.20 % SZS status Theorem for theBenchmark.p
% 3.64/1.20
% 3.64/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.64/1.20
% 3.64/1.20 % ------ iProver source info
% 3.64/1.20
% 3.64/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.64/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.64/1.20 % git: non_committed_changes: false
% 3.64/1.20
% 3.64/1.20 % ------ Parsing...
% 3.64/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 3.64/1.20 %
% 3.64/1.20
% 3.64/1.20 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.64/1.20
% 3.64/1.20 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.64/1.20 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.64/1.20
% 3.64/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.64/1.20 % ------ Proving...
% 3.64/1.20 % ------ Problem Properties
% 3.64/1.20
% 3.64/1.20 %
% 3.64/1.20 % clauses 14
% 3.64/1.20 % conjectures 1
% 3.64/1.20 % EPR 1
% 3.64/1.20 % Horn 14
% 3.64/1.20 % unary 14
% 3.64/1.20 % binary 0
% 3.64/1.20 % lits 14
% 3.64/1.20 % lits eq 14
% 3.64/1.20 % fd_pure 0
% 3.64/1.20 % fd_pseudo 0
% 3.64/1.20 % fd_cond 0
% 3.64/1.20 % fd_pseudo_cond 0
% 3.64/1.20 % AC symbols 1
% 3.64/1.20
% 3.64/1.20 % ------ Schedule UEQ
% 3.64/1.20
% 3.64/1.20 % ------ Option_UEQ Time Limit: 10.
% 3.64/1.20
% 3.64/1.20
% 3.64/1.20 % ------
% 3.64/1.20 % Current options:
% 3.64/1.20 % ------
% 3.64/1.20
% 3.64/1.20
% 3.64/1.20 %
% 3.64/1.20
% 3.64/1.20 % ------ Proving...
% 3.64/1.20 %
% 3.64/1.20
% 3.64/1.20 % SZS status Theorem for theBenchmark.p
% 3.64/1.20
% 3.64/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.28/1.20
% 4.28/1.20
%------------------------------------------------------------------------------