%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL013+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 : n016.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 3.84s 11.37s
% Output : CNFRefutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 15
% Syntax : Number of formulae : 98 ( 90 unt; 2 def)
% Number of atoms : 127 ( 105 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 6 |; 2 &)
% ( 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 : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 109 ( 0 sgn 108 !; 1 ?; 61 :)
% 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(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,
! [X0] :
( composition(zero,X0) = zero
& composition(X0,zero) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0] :
( composition(zero,X0) = zero
& composition(X0,zero) = zero ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0] :
( zero != composition(zero,X0)
| zero != composition(X0,zero) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
( zero != composition(zero,sK0)
| zero != composition(sK0,zero) ),
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(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,
( zero != composition(zero,sK0)
| zero != composition(sK0,zero) ),
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_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,
( ( composition(sK0,zero) != zero )
| ( composition(zero,sK0) != zero ) ),
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_106,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_115,definition,
iPr_def_10 = composition(zero,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_116,definition,
iPr_def_11 = composition(sK0,zero),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_117,negated_conjecture,
( ( iPr_def_11 != zero )
| ( iPr_def_10 != zero ) ),
inference(demodulation,[status(thm)],[c_61,c_116,c_115]) ).
tcf(c_195,plain,
! [X0: $i] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(superposition,[status(thm)],[c_106,c_75]) ).
tcf(c_196,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_205,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_245,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_59,c_205]) ).
tcf(c_387,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_212]) ).
tcf(c_406,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_387,c_55]) ).
tcf(c_568,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_406,c_53]) ).
tcf(c_581,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(demodulation,[status(thm)],[c_406,c_568]) ).
tcf(c_646,plain,
join(zero,composition(converse(one),complement(top))) = zero,
inference(superposition,[status(thm)],[c_581,c_195]) ).
tcf(c_649,plain,
join(zero,composition(one,zero)) = zero,
inference(light_normalisation,[status(thm)],[c_646,c_106,c_568]) ).
tcf(c_660,plain,
join(zero,zero) = zero,
inference(demodulation,[status(thm)],[c_649,c_581]) ).
tcf(c_661,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_660,c_50]) ).
tcf(c_700,plain,
! [X0: $i] : join(complement(X0),complement(composition(converse(one),X0))) = complement(X0),
inference(superposition,[status(thm)],[c_581,c_196]) ).
tcf(c_711,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_700,c_568,c_581]) ).
tcf(c_839,plain,
! [X0: $i] : join(complement(join(complement(X0),X0)),complement(complement(X0))) = X0,
inference(superposition,[status(thm)],[c_711,c_74]) ).
tcf(c_841,plain,
! [X0: $i] : join(complement(complement(X0)),complement(join(X0,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_839,c_50,c_49]) ).
tcf(c_842,plain,
! [X0: $i] : join(complement(complement(X0)),zero) = X0,
inference(light_normalisation,[status(thm)],[c_841,c_59,c_106]) ).
tcf(c_843,plain,
! [X0: $i] : join(zero,complement(complement(X0))) = X0,
inference(theory_normalisation,[status(thm)],[c_842,c_50,c_49]) ).
tcf(c_935,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_843,c_661]) ).
tcf(c_937,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_843,c_935]) ).
tcf(c_938,plain,
! [X0: $i] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(demodulation,[status(thm)],[c_195,c_935]) ).
tcf(c_947,plain,
! [X0: $i] : join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_935,c_49]) ).
tcf(c_950,plain,
! [X0: $i] : join(converse(zero),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_935,c_206]) ).
tcf(c_954,plain,
! [X0: $i] : join(converse(zero),X0) = X0,
inference(light_normalisation,[status(thm)],[c_950,c_55]) ).
tcf(c_968,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(superposition,[status(thm)],[c_937,c_711]) ).
tcf(c_994,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_968,c_50]) ).
tcf(c_1059,plain,
converse(zero) = zero,
inference(superposition,[status(thm)],[c_954,c_947]) ).
tcf(c_1075,plain,
! [X0: $i] : composition(converse(X0),zero) = converse(composition(zero,X0)),
inference(superposition,[status(thm)],[c_1059,c_57]) ).
tcf(c_1206,plain,
! [X0: $i] : join(X0,top) = top,
inference(superposition,[status(thm)],[c_59,c_994]) ).
tcf(c_1232,plain,
! [X0: $i] : join(top,X0) = top,
inference(superposition,[status(thm)],[c_1206,c_49]) ).
tcf(c_1248,plain,
converse(top) = top,
inference(superposition,[status(thm)],[c_1232,c_245]) ).
tcf(c_1256,plain,
composition(top,complement(composition(top,top))) = zero,
inference(superposition,[status(thm)],[c_1248,c_938]) ).
tcf(c_1385,plain,
! [X0: $i] : join(composition(X0,complement(composition(top,top))),zero) = composition(join(X0,top),complement(composition(top,top))),
inference(superposition,[status(thm)],[c_1256,c_54]) ).
tcf(c_1389,plain,
! [X0: $i] : join(zero,composition(X0,complement(composition(top,top)))) = composition(join(X0,top),complement(composition(top,top))),
inference(theory_normalisation,[status(thm)],[c_1385,c_50,c_49]) ).
tcf(c_1390,plain,
! [X0: $i] : join(zero,composition(X0,complement(composition(top,top)))) = zero,
inference(light_normalisation,[status(thm)],[c_1389,c_1206,c_1256]) ).
tcf(c_1538,plain,
composition(converse(sK0),zero) = converse(iPr_def_10),
inference(superposition,[status(thm)],[c_115,c_1075]) ).
tcf(c_2894,plain,
! [X0: $i] : composition(X0,complement(composition(top,top))) = zero,
inference(demodulation,[status(thm)],[c_1390,c_935]) ).
tcf(c_2912,plain,
complement(composition(top,top)) = zero,
inference(superposition,[status(thm)],[c_2894,c_581]) ).
tcf(c_2927,plain,
! [X0: $i] : composition(X0,zero) = zero,
inference(demodulation,[status(thm)],[c_2894,c_2912]) ).
tcf(c_2941,plain,
zero = iPr_def_11,
inference(demodulation,[status(thm)],[c_116,c_2927]) ).
tcf(c_2943,plain,
converse(iPr_def_10) = zero,
inference(demodulation,[status(thm)],[c_1538,c_2927]) ).
tcf(c_2950,plain,
converse(iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1059,c_2941]) ).
tcf(c_2958,plain,
( ( iPr_def_11 != iPr_def_11 )
| ( iPr_def_10 != iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_117,c_2941]) ).
tcf(c_2959,plain,
iPr_def_10 != iPr_def_11,
inference(equality_resolution_simp,[status(thm)],[c_2958]) ).
tcf(c_2980,plain,
converse(iPr_def_10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_2943,c_2941]) ).
tcf(c_2988,plain,
converse(iPr_def_11) = iPr_def_10,
inference(superposition,[status(thm)],[c_2980,c_55]) ).
tcf(c_3046,plain,
iPr_def_10 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_2950,c_2988]) ).
tcf(c_3047,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3046,c_2959]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL013+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/10.40 % Computer : n016.cluster.edu
% 0.12/10.40 % Model : x86_64 x86_64
% 0.12/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.40 % Memory : 8046.5625MB
% 0.12/10.40 % OS : Linux 6.8.0-71-generic
% 0.12/10.40 % CPULimit : 300
% 0.12/10.40 % WCLimit : 300
% 0.12/10.40 % DateTime : Thu Sep 24 07:16:39 UTC 2026
% 0.12/10.40 % CPUTime :
% 0.12/10.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/10.44 Running first-order theorem proving
% 0.12/10.45 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
% 0.12/10.46
% 0.12/10.46 % ======== iProver multi-core TPTP/SMT =========
% 0.12/10.46
% 0.12/10.46 % Detected problem language: tptp
% 0.12/10.47 % Proving...
% 3.84/11.37 % SZS status Started for theBenchmark.p
% 3.84/11.37 % SZS status Theorem for theBenchmark.p
% 3.84/11.37
% 3.84/11.37 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.84/11.37
% 3.84/11.37 % ------ iProver source info
% 3.84/11.37
% 3.84/11.37 % git: date: 2026-07-19 20:42:38 +0200
% 3.84/11.37 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.84/11.37 % git: non_committed_changes: false
% 3.84/11.37
% 3.84/11.37 % ------ Parsing...
% 3.84/11.37 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.84/11.37
% 3.84/11.37 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.84/11.37
% 3.84/11.37 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.84/11.37
% 3.84/11.37 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.84/11.37 % ------ Proving...
% 3.84/11.37 % ------ Problem Properties
% 3.84/11.37
% 3.84/11.37 %
% 3.84/11.37 % clauses 15
% 3.84/11.37 % conjectures 1
% 3.84/11.37 % EPR 1
% 3.84/11.37 % Horn 15
% 3.84/11.37 % unary 14
% 3.84/11.37 % binary 1
% 3.84/11.37 % lits 16
% 3.84/11.37 % lits eq 16
% 3.84/11.37 % fd_pure 0
% 3.84/11.37 % fd_pseudo 0
% 3.84/11.37 % fd_cond 0
% 3.84/11.37 % fd_pseudo_cond 0
% 3.84/11.37 % AC symbols 1
% 3.84/11.37
% 3.84/11.37 % ------ Schedule dynamic 5 is on
% 3.84/11.37
% 3.84/11.37 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.84/11.37
% 3.84/11.37
% 3.84/11.37 % ------
% 3.84/11.37 % Current options:
% 3.84/11.37 % ------
% 3.84/11.37
% 3.84/11.37
% 3.84/11.37 %
% 3.84/11.37
% 3.84/11.37 % ------ Proving...
% 3.84/11.37 %
% 3.84/11.37
% 3.84/11.37 % SZS status Theorem for theBenchmark.p
% 3.84/11.37
% 3.84/11.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.84/11.37
% 3.84/11.37
%------------------------------------------------------------------------------