%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL048+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 : n006.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 02:37:02 PM UTC 2026
% Result : Theorem 7.04s 2.59s
% Output : CNFRefutation 7.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 95 ( 86 unt; 4 def)
% Number of atoms : 183 ( 107 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 7 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 86 !; 3 ?; 45 :)
% 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(f8,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
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,X1,X2] :
( join(join(X0,X1),X2) = X2
=> ( join(X1,X2) = X2
& join(X0,X2) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] :
( join(join(X0,X1),X2) = X2
=> ( join(X1,X2) = X2
& join(X0,X2) = X2 ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1,X2] :
( join(join(X0,X1),X2) = X2
& ( join(X1,X2) != X2
| join(X0,X2) != X2 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
( sK2 = join(join(sK0,sK1),sK2)
& ( sK2 != join(sK1,sK2)
| sK2 != join(sK0,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[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(f25,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
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,
sK2 = join(join(sK0,sK1),sK2),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
( sK2 != join(sK1,sK2)
| sK2 != join(sK0,sK2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,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_55,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f25]) ).
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,[],[f33]) ).
tcf(c_61,negated_conjecture,
( ( join(sK1,sK2) != sK2 )
| ( join(sK0,sK2) != sK2 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_62,negated_conjecture,
join(join(sK0,sK1),sK2) = sK2,
inference(cnf_transformation,[],[f31]) ).
tcf(c_75,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_76,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_77,negated_conjecture,
( ( join(sK2,sK1) != sK2 )
| ( join(sK2,sK0) != sK2 ) ),
inference(theory_normalisation,[status(thm)],[c_61,c_50,c_49]) ).
tcf(c_78,negated_conjecture,
join(sK2,join(sK0,sK1)) = sK2,
inference(theory_normalisation,[status(thm)],[c_62,c_50,c_49]) ).
tcf(c_111,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_120,definition,
iPr_def_10 = join(sK0,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_121,definition,
iPr_def_11 = join(sK2,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_122,definition,
iPr_def_12 = join(sK2,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_123,definition,
iPr_def_13 = join(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_124,negated_conjecture,
iPr_def_11 = sK2,
inference(demodulation,[status(thm)],[c_78,c_120,c_121]) ).
tcf(c_125,negated_conjecture,
( ( iPr_def_13 != sK2 )
| ( iPr_def_12 != sK2 ) ),
inference(demodulation,[status(thm)],[c_77,c_123,c_122]) ).
tcf(c_202,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_205,plain,
( ( iPr_def_11 != iPr_def_13 )
| ( iPr_def_11 != iPr_def_12 ) ),
inference(light_normalisation,[status(thm)],[c_125,c_124]) ).
tcf(c_208,plain,
join(iPr_def_10,sK2) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_121,c_50,c_49]) ).
tcf(c_209,plain,
join(iPr_def_10,iPr_def_11) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_208,c_124]) ).
tcf(c_210,plain,
join(iPr_def_11,sK0) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_122,c_124]) ).
tcf(c_225,plain,
join(iPr_def_11,sK1) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_123,c_124]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,complement(X1))),complement(join(complement(X1),complement(X0)))) = X1,
inference(superposition,[status(thm)],[c_49,c_75]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_352,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_248]) ).
tcf(c_370,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_352,c_55]) ).
tcf(c_430,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_59,c_50]) ).
tcf(c_435,plain,
! [X0: $i] : join(iPr_def_11,join(sK0,X0)) = join(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_210,c_50]) ).
tcf(c_436,plain,
! [X0: $i] : join(iPr_def_11,join(sK1,X0)) = join(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_225,c_50]) ).
tcf(c_533,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_370,c_53]) ).
tcf(c_537,plain,
! [X0: $i] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_370,c_76]) ).
tcf(c_543,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(demodulation,[status(thm)],[c_370,c_533]) ).
tcf(c_622,plain,
join(iPr_def_11,iPr_def_10) = join(iPr_def_12,sK1),
inference(superposition,[status(thm)],[c_120,c_435]) ).
tcf(c_626,plain,
join(iPr_def_10,iPr_def_11) = join(iPr_def_12,sK1),
inference(theory_normalisation,[status(thm)],[c_622,c_50,c_49]) ).
tcf(c_627,plain,
join(iPr_def_12,sK1) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_626,c_209]) ).
tcf(c_694,plain,
! [X0: $i] : join(iPr_def_11,join(X0,sK0)) = join(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_210,c_202]) ).
tcf(c_695,plain,
! [X0: $i] : join(iPr_def_11,join(X0,sK1)) = join(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_225,c_202]) ).
tcf(c_886,plain,
join(sK1,iPr_def_12) = join(iPr_def_13,sK0),
inference(superposition,[status(thm)],[c_694,c_436]) ).
tcf(c_887,plain,
join(iPr_def_12,sK1) = join(iPr_def_13,sK0),
inference(theory_normalisation,[status(thm)],[c_886,c_50,c_49]) ).
tcf(c_888,plain,
join(iPr_def_13,sK0) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_887,c_627]) ).
tcf(c_948,plain,
! [X0: $i] : join(iPr_def_13,join(X0,sK0)) = join(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_888,c_202]) ).
tcf(c_4630,plain,
! [X0: $i] : join(top,complement(complement(X0))) = join(X0,top),
inference(superposition,[status(thm)],[c_59,c_430]) ).
tcf(c_4678,plain,
join(complement(iPr_def_11),iPr_def_13) = join(top,sK1),
inference(superposition,[status(thm)],[c_430,c_695]) ).
tcf(c_4716,plain,
join(iPr_def_13,complement(iPr_def_11)) = join(sK1,top),
inference(theory_normalisation,[status(thm)],[c_4678,c_50,c_49]) ).
tcf(c_6864,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_537,c_543]) ).
tcf(c_6874,plain,
! [X0: $i] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(superposition,[status(thm)],[c_6864,c_430]) ).
tcf(c_6887,plain,
! [X0: $i] : join(top,complement(X0)) = top,
inference(light_normalisation,[status(thm)],[c_6874,c_59]) ).
tcf(c_6909,plain,
! [X0: $i] : join(X0,top) = top,
inference(demodulation,[status(thm)],[c_4630,c_6887]) ).
tcf(c_6916,plain,
join(iPr_def_13,complement(iPr_def_11)) = top,
inference(demodulation,[status(thm)],[c_4716,c_6909]) ).
tcf(c_6991,plain,
! [X0: $i] : join(top,X0) = top,
inference(superposition,[status(thm)],[c_6909,c_49]) ).
tcf(c_7053,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = top,
inference(demodulation,[status(thm)],[c_430,c_6991]) ).
tcf(c_7525,plain,
join(complement(iPr_def_13),iPr_def_11) = top,
inference(superposition,[status(thm)],[c_7053,c_948]) ).
tcf(c_7531,plain,
join(iPr_def_11,complement(iPr_def_13)) = top,
inference(theory_normalisation,[status(thm)],[c_7525,c_50,c_49]) ).
tcf(c_8430,plain,
join(complement(top),complement(join(complement(iPr_def_11),complement(iPr_def_13)))) = iPr_def_11,
inference(superposition,[status(thm)],[c_6916,c_237]) ).
tcf(c_8439,plain,
join(zero,complement(join(complement(iPr_def_11),complement(iPr_def_13)))) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_8430,c_111]) ).
tcf(c_8929,plain,
join(complement(top),complement(join(complement(iPr_def_13),complement(iPr_def_11)))) = iPr_def_13,
inference(superposition,[status(thm)],[c_7531,c_237]) ).
tcf(c_8936,plain,
join(complement(top),complement(join(complement(iPr_def_11),complement(iPr_def_13)))) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_8929,c_50,c_49]) ).
tcf(c_8937,plain,
iPr_def_11 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_8936,c_111,c_8439]) ).
tcf(c_8938,plain,
iPr_def_11 != iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_205,c_8937]) ).
tcf(c_8961,plain,
join(iPr_def_11,sK0) = iPr_def_11,
inference(demodulation,[status(thm)],[c_888,c_8937]) ).
tcf(c_8966,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_210,c_8961]) ).
tcf(c_8967,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_8966,c_8938]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/1.20 % Computer : n006.cluster.edu
% 0.03/1.20 % Model : x86_64 x86_64
% 0.03/1.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/1.20 % Memory : 8046.5625MB
% 0.03/1.20 % OS : Linux 6.8.0-71-generic
% 0.03/1.20 % CPULimit : 300
% 0.03/1.20 % WCLimit : 300
% 0.03/1.20 % DateTime : Thu Sep 24 07:37:44 UTC 2026
% 0.03/1.20 % CPUTime :
% 0.03/1.20 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/1.24 Running first-order theorem proving
% 0.03/1.24 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
% 0.03/1.25
% 0.03/1.25 % ======== iProver multi-core TPTP/SMT =========
% 0.03/1.25
% 0.03/1.25 % Detected problem language: tptp
% 0.03/1.26 % Proving...
% 7.04/2.59 % SZS status Started for theBenchmark.p
% 7.04/2.59 % SZS status Theorem for theBenchmark.p
% 7.04/2.59
% 7.04/2.59 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.04/2.59
% 7.04/2.59 % ------ iProver source info
% 7.04/2.59
% 7.04/2.59 % git: date: 2026-07-19 20:42:38 +0200
% 7.04/2.59 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.04/2.59 % git: non_committed_changes: false
% 7.04/2.59
% 7.04/2.59 % ------ Parsing...
% 7.04/2.59 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.04/2.59
% 7.04/2.59 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.04/2.59
% 7.04/2.59 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.04/2.59
% 7.04/2.59 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 7.04/2.59 % ------ Proving...
% 7.04/2.59 % ------ Problem Properties
% 7.04/2.59
% 7.04/2.59 %
% 7.04/2.59 % clauses 18
% 7.04/2.59 % conjectures 2
% 7.04/2.59 % EPR 2
% 7.04/2.59 % Horn 18
% 7.04/2.59 % unary 17
% 7.04/2.59 % binary 1
% 7.04/2.59 % lits 19
% 7.04/2.59 % lits eq 19
% 7.04/2.59 % fd_pure 0
% 7.04/2.59 % fd_pseudo 0
% 7.04/2.59 % fd_cond 0
% 7.04/2.59 % fd_pseudo_cond 0
% 7.04/2.59 % AC symbols 1
% 7.04/2.59
% 7.04/2.59 % ------ Schedule dynamic 5 is on
% 7.04/2.59
% 7.04/2.59 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.04/2.59
% 7.04/2.59
% 7.04/2.59 % ------
% 7.04/2.59 % Current options:
% 7.04/2.59 % ------
% 7.04/2.59
% 7.04/2.59
% 7.04/2.59 %
% 7.04/2.59
% 7.04/2.59 % ------ Proving...
% 7.04/2.59 %
% 7.04/2.59
% 7.04/2.59 % SZS status Theorem for theBenchmark.p
% 7.04/2.59
% 7.04/2.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.04/2.59
% 7.04/2.59
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