%------------------------------------------------------------------------------
% 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/sandbox/benchmark/theBenchmark.p THM
% Computer : n001.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 : Unsatisfiable 3.59s 1.20s
% Output : CNFRefutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 15
% Syntax : Number of formulae : 91 ( 86 unt; 2 def)
% Number of atoms : 117 ( 95 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 11 ~; 5 |; 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 : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 95 !; 0 ?; 66 :)
% 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(f17,negated_conjecture,
( composition(zero,sk1) != zero
| composition(sk1,zero) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
( zero != composition(zero,sk1)
| zero != composition(sk1,zero) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f16,f6]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f4]) ).
tcf(c_67,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_68,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_69,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f14]) ).
tcf(c_73,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f15]) ).
tcf(c_74,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f19]) ).
tcf(c_75,negated_conjecture,
( ( composition(zero,sk1) != zero )
| ( composition(sk1,zero) != zero ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = X0,
inference(theory_normalisation,[status(thm)],[c_65,c_64,c_63]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(converse(X1),complement(composition(X1,X0)))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_72,c_64,c_63]) ).
tcf(c_120,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_74,c_73,c_64,c_63]) ).
tcf(c_129,definition,
iPr_def_10 = composition(sk1,zero),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_130,definition,
iPr_def_11 = composition(zero,sk1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_131,negated_conjecture,
( ( iPr_def_11 != zero )
| ( iPr_def_10 != zero ) ),
inference(demodulation,[status(thm)],[c_75,c_130,c_129]) ).
tcf(c_209,plain,
! [X0: $i] : join(zero,composition(converse(X0),complement(composition(X0,top)))) = zero,
inference(superposition,[status(thm)],[c_120,c_89]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] : join(complement(X0),composition(X1,complement(composition(converse(X1),X0)))) = complement(X0),
inference(superposition,[status(thm)],[c_69,c_89]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_69,c_70]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(superposition,[status(thm)],[c_69,c_70]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(superposition,[status(thm)],[c_69,c_71]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_69,c_71]) ).
tcf(c_259,plain,
! [X0: $i] : join(X0,converse(complement(converse(X0)))) = converse(top),
inference(superposition,[status(thm)],[c_73,c_219]) ).
tcf(c_401,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_67,c_226]) ).
tcf(c_420,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_401,c_69]) ).
tcf(c_582,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_420,c_67]) ).
tcf(c_595,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(demodulation,[status(thm)],[c_420,c_582]) ).
tcf(c_660,plain,
join(zero,composition(converse(one),complement(top))) = zero,
inference(superposition,[status(thm)],[c_595,c_209]) ).
tcf(c_663,plain,
join(zero,composition(one,zero)) = zero,
inference(light_normalisation,[status(thm)],[c_660,c_120,c_582]) ).
tcf(c_674,plain,
join(zero,zero) = zero,
inference(demodulation,[status(thm)],[c_663,c_595]) ).
tcf(c_675,plain,
! [X0: $i] : join(zero,join(zero,X0)) = join(zero,X0),
inference(superposition,[status(thm)],[c_674,c_64]) ).
tcf(c_740,plain,
! [X0: $i] : join(complement(X0),complement(composition(converse(one),X0))) = complement(X0),
inference(superposition,[status(thm)],[c_595,c_210]) ).
tcf(c_751,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_740,c_582,c_595]) ).
tcf(c_853,plain,
! [X0: $i] : join(complement(join(complement(X0),X0)),complement(complement(X0))) = X0,
inference(superposition,[status(thm)],[c_751,c_88]) ).
tcf(c_855,plain,
! [X0: $i] : join(complement(complement(X0)),complement(join(X0,complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_853,c_64,c_63]) ).
tcf(c_856,plain,
! [X0: $i] : join(complement(complement(X0)),zero) = X0,
inference(light_normalisation,[status(thm)],[c_855,c_73,c_120]) ).
tcf(c_857,plain,
! [X0: $i] : join(zero,complement(complement(X0))) = X0,
inference(theory_normalisation,[status(thm)],[c_856,c_64,c_63]) ).
tcf(c_949,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_857,c_675]) ).
tcf(c_951,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_857,c_949]) ).
tcf(c_952,plain,
! [X0: $i] : composition(converse(X0),complement(composition(X0,top))) = zero,
inference(demodulation,[status(thm)],[c_209,c_949]) ).
tcf(c_961,plain,
! [X0: $i] : join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_949,c_63]) ).
tcf(c_964,plain,
! [X0: $i] : join(converse(zero),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_949,c_220]) ).
tcf(c_968,plain,
! [X0: $i] : join(converse(zero),X0) = X0,
inference(light_normalisation,[status(thm)],[c_964,c_69]) ).
tcf(c_982,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(superposition,[status(thm)],[c_951,c_751]) ).
tcf(c_1008,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_982,c_64]) ).
tcf(c_1041,plain,
converse(zero) = zero,
inference(superposition,[status(thm)],[c_968,c_961]) ).
tcf(c_1054,plain,
! [X0: $i] : composition(zero,converse(X0)) = converse(composition(X0,zero)),
inference(superposition,[status(thm)],[c_1041,c_225]) ).
tcf(c_1056,plain,
! [X0: $i] : composition(converse(X0),zero) = converse(composition(zero,X0)),
inference(superposition,[status(thm)],[c_1041,c_71]) ).
tcf(c_1150,plain,
! [X0: $i] : join(X0,top) = top,
inference(superposition,[status(thm)],[c_73,c_1008]) ).
tcf(c_1227,plain,
! [X0: $i] : join(top,X0) = top,
inference(superposition,[status(thm)],[c_1150,c_63]) ).
tcf(c_1243,plain,
converse(top) = top,
inference(superposition,[status(thm)],[c_1227,c_259]) ).
tcf(c_1251,plain,
composition(top,complement(composition(top,top))) = zero,
inference(superposition,[status(thm)],[c_1243,c_952]) ).
tcf(c_1358,plain,
! [X0: $i] : composition(join(X0,top),complement(composition(top,top))) = join(composition(X0,complement(composition(top,top))),zero),
inference(superposition,[status(thm)],[c_1251,c_68]) ).
tcf(c_1362,plain,
! [X0: $i] : composition(join(X0,top),complement(composition(top,top))) = join(zero,composition(X0,complement(composition(top,top)))),
inference(theory_normalisation,[status(thm)],[c_1358,c_64,c_63]) ).
tcf(c_1363,plain,
! [X0: $i] : join(zero,composition(X0,complement(composition(top,top)))) = zero,
inference(light_normalisation,[status(thm)],[c_1362,c_1150,c_1251]) ).
tcf(c_1368,plain,
composition(zero,converse(sk1)) = converse(iPr_def_10),
inference(superposition,[status(thm)],[c_129,c_1054]) ).
tcf(c_1530,plain,
composition(converse(sk1),zero) = converse(iPr_def_11),
inference(superposition,[status(thm)],[c_130,c_1056]) ).
tcf(c_2908,plain,
! [X0: $i] : composition(X0,complement(composition(top,top))) = zero,
inference(demodulation,[status(thm)],[c_1363,c_949]) ).
tcf(c_2926,plain,
complement(composition(top,top)) = zero,
inference(superposition,[status(thm)],[c_2908,c_595]) ).
tcf(c_2941,plain,
! [X0: $i] : composition(X0,zero) = zero,
inference(demodulation,[status(thm)],[c_2908,c_2926]) ).
tcf(c_2953,plain,
zero = iPr_def_10,
inference(demodulation,[status(thm)],[c_129,c_2941]) ).
tcf(c_2954,plain,
! [X0: $i] : composition(zero,converse(X0)) = converse(zero),
inference(demodulation,[status(thm)],[c_1054,c_2941]) ).
tcf(c_2957,plain,
converse(iPr_def_11) = zero,
inference(demodulation,[status(thm)],[c_1530,c_2941]) ).
tcf(c_2959,plain,
! [X0: $i] : composition(zero,converse(X0)) = zero,
inference(light_normalisation,[status(thm)],[c_2954,c_1041]) ).
tcf(c_2960,plain,
converse(iPr_def_10) = zero,
inference(demodulation,[status(thm)],[c_1368,c_2959]) ).
tcf(c_2974,plain,
( ( iPr_def_10 != iPr_def_11 )
| ( iPr_def_10 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_131,c_2953]) ).
tcf(c_2975,plain,
iPr_def_10 != iPr_def_11,
inference(equality_resolution_simp,[status(thm)],[c_2974]) ).
tcf(c_2995,plain,
converse(iPr_def_11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_2957,c_2953]) ).
tcf(c_3003,plain,
converse(iPr_def_10) = iPr_def_11,
inference(superposition,[status(thm)],[c_2995,c_69]) ).
tcf(c_3061,plain,
iPr_def_10 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_2960,c_2953,c_3003]) ).
tcf(c_3062,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3061,c_2975]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 07:18:37 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.59/1.20 % SZS status Started for theBenchmark.p
% 3.59/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 3.59/1.20
% 3.59/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.59/1.20
% 3.59/1.20 % ------ iProver source info
% 3.59/1.20
% 3.59/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.59/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.59/1.20 % git: non_committed_changes: false
% 3.59/1.20
% 3.59/1.20 % ------ Parsing...% successful
% 3.59/1.20
% 3.59/1.20
% 3.59/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.59/1.20
% 3.59/1.20 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.59/1.20
% 3.59/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.59/1.20
% 3.59/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.59/1.20 % ------ Proving...
% 3.59/1.20 % ------ Problem Properties
% 3.59/1.20
% 3.59/1.20 %
% 3.59/1.20 % clauses 15
% 3.59/1.20 % conjectures 1
% 3.59/1.20 % EPR 1
% 3.59/1.20 % Horn 15
% 3.59/1.20 % unary 14
% 3.59/1.20 % binary 1
% 3.59/1.20 % lits 16
% 3.59/1.20 % lits eq 16
% 3.59/1.20 % fd_pure 0
% 3.59/1.20 % fd_pseudo 0
% 3.59/1.20 % fd_cond 0
% 3.59/1.20 % fd_pseudo_cond 0
% 3.59/1.20 % AC symbols 1
% 3.59/1.20
% 3.59/1.20 % ------ Schedule dynamic 5 is on
% 3.59/1.20
% 3.59/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.59/1.20
% 3.59/1.20
% 3.59/1.20 % ------
% 3.59/1.20 % Current options:
% 3.59/1.20 % ------
% 3.59/1.20
% 3.59/1.20
% 3.59/1.20 %
% 3.59/1.20
% 3.59/1.20 % ------ Proving...
% 3.59/1.20 %
% 3.59/1.20
% 3.59/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 3.59/1.20
% 3.59/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.59/1.20
% 3.59/1.20
%------------------------------------------------------------------------------