%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL009+2 : 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 : n010.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 02:36:34 PM UTC 2026
% Result : Theorem 44.07s 8.18s
% Output : CNFRefutation 44.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 43 unt; 4 def)
% Number of atoms : 94 ( 64 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 18 ~; 7 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 59 !; 3 ?; 27 :)
% 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(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(f17,conjecture,
! [X0,X1,X2] :
( join(X0,X1) = X1
=> ( join(composition(X2,X0),composition(X2,X1)) = composition(X2,X1)
& join(composition(X0,X2),composition(X1,X2)) = composition(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( join(X0,X1) = X1
=> ( join(composition(X2,X0),composition(X2,X1)) = composition(X2,X1)
& join(composition(X0,X2),composition(X1,X2)) = composition(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] :
( join(X0,X1) = X1
& ( composition(X2,X1) != join(composition(X2,X0),composition(X2,X1))
| composition(X1,X2) != join(composition(X0,X2),composition(X1,X2)) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
( sK1 = join(sK0,sK1)
& ( composition(sK2,sK1) != join(composition(sK2,sK0),composition(sK2,sK1))
| composition(sK1,sK2) != join(composition(sK0,sK2),composition(sK1,sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f19]) ).
fof(f21,plain,
sK1 = join(sK0,sK1),
inference(cnf_transformation,[],[f20]) ).
fof(f22,plain,
( composition(sK2,sK1) != join(composition(sK2,sK0),composition(sK2,sK1))
| composition(sK1,sK2) != join(composition(sK0,sK2),composition(sK1,sK2)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f23,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f24,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f25,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f26,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f32,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f33,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_49,negated_conjecture,
( ( join(composition(sK0,sK2),composition(sK1,sK2)) != composition(sK1,sK2) )
| ( join(composition(sK2,sK0),composition(sK2,sK1)) != composition(sK2,sK1) ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_50,negated_conjecture,
join(sK0,sK1) = sK1,
inference(cnf_transformation,[],[f21]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f23]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X2,X1)) = composition(join(X0,X2),X1),
inference(cnf_transformation,[],[f25]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_61,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f33]) ).
tcf(c_75,negated_conjecture,
( ( join(composition(sK2,sK1),composition(sK2,sK0)) != composition(sK2,sK1) )
| ( join(composition(sK1,sK2),composition(sK0,sK2)) != composition(sK1,sK2) ) ),
inference(theory_normalisation,[status(thm)],[c_49,c_51,c_52]) ).
tcf(c_76,negated_conjecture,
join(sK1,sK0) = sK1,
inference(theory_normalisation,[status(thm)],[c_50,c_51,c_52]) ).
tcf(c_115,plain,
( ( composition(join(sK1,sK0),sK2) != composition(sK1,sK2) )
| ( join(composition(sK2,sK1),composition(sK2,sK0)) != composition(sK2,sK1) ) ),
inference(ac_demodulation,[status(thm)],[c_75,c_53,c_51,c_52]) ).
tcf(c_116,plain,
( ( composition(sK1,sK2) != composition(sK1,sK2) )
| ( join(composition(sK2,sK1),composition(sK2,sK0)) != composition(sK2,sK1) ) ),
inference(light_normalisation,[status(thm)],[c_115,c_76]) ).
tcf(c_117,plain,
join(composition(sK2,sK1),composition(sK2,sK0)) != composition(sK2,sK1),
inference(equality_resolution_simp,[status(thm)],[c_116]) ).
tcf(c_124,definition,
iPr_def_10 = composition(sK2,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_125,definition,
iPr_def_11 = composition(sK2,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_126,definition,
iPr_def_12 = join(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_127,definition,
iPr_def_13 = join(sK1,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_128,plain,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_117,c_125,c_124,c_126]) ).
tcf(c_129,negated_conjecture,
iPr_def_13 = sK1,
inference(demodulation,[status(thm)],[c_76,c_127]) ).
tcf(c_205,plain,
composition(sK2,iPr_def_13) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_124,c_129]) ).
tcf(c_206,plain,
join(iPr_def_13,sK0) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_127,c_129]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i] : converse(composition(X0,converse(X1))) = composition(X1,converse(X0)),
inference(superposition,[status(thm)],[c_61,c_54]) ).
tcf(c_335,plain,
! [X0: $i,X1: $i,X2: $i] : join(converse(composition(X0,X1)),composition(X2,converse(X0))) = composition(join(converse(X1),X2),converse(X0)),
inference(superposition,[status(thm)],[c_54,c_53]) ).
tcf(c_434,plain,
! [X0: $i,X1: $i,X2: $i] : join(converse(X0),composition(X1,converse(X2))) = converse(join(X0,composition(X2,converse(X1)))),
inference(superposition,[status(thm)],[c_214,c_60]) ).
tcf(c_37609,plain,
! [X0: $i,X1: $i,X2: $i] : join(converse(X0),composition(converse(X1),converse(X2))) = converse(join(X0,composition(X2,X1))),
inference(superposition,[status(thm)],[c_61,c_434]) ).
tcf(c_69282,plain,
! [X0: $i] : composition(join(converse(iPr_def_13),X0),converse(sK2)) = join(converse(iPr_def_10),composition(X0,converse(sK2))),
inference(superposition,[status(thm)],[c_205,c_335]) ).
tcf(c_70615,plain,
! [X0: $i] : join(converse(iPr_def_10),composition(converse(X0),converse(sK2))) = composition(converse(join(iPr_def_13,X0)),converse(sK2)),
inference(superposition,[status(thm)],[c_60,c_69282]) ).
tcf(c_71036,plain,
! [X0: $i] : converse(composition(sK2,join(iPr_def_13,X0))) = converse(join(iPr_def_10,composition(sK2,X0))),
inference(demodulation,[status(thm)],[c_70615,c_54,c_37609]) ).
tcf(c_71042,plain,
converse(join(iPr_def_10,composition(sK2,sK0))) = converse(composition(sK2,iPr_def_13)),
inference(superposition,[status(thm)],[c_206,c_71036]) ).
tcf(c_71510,plain,
converse(iPr_def_10) = converse(iPr_def_12),
inference(light_normalisation,[status(thm)],[c_71042,c_125,c_126,c_205]) ).
tcf(c_71978,plain,
converse(converse(iPr_def_10)) = iPr_def_12,
inference(superposition,[status(thm)],[c_71510,c_61]) ).
tcf(c_72582,plain,
iPr_def_10 = iPr_def_12,
inference(demodulation,[status(thm)],[c_71978,c_61]) ).
tcf(c_72668,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_128,c_72582]) ).
tcf(c_72669,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_72668]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL009+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.60 % Computer : n010.cluster.edu
% 0.12/0.60 % Model : x86_64 x86_64
% 0.12/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.60 % Memory : 8046.5625MB
% 0.12/0.60 % OS : Linux 6.8.0-71-generic
% 0.12/0.60 % CPULimit : 300
% 0.12/0.60 % WCLimit : 300
% 0.12/0.60 % DateTime : Thu Sep 24 07:08:03 UTC 2026
% 0.12/0.60 % CPUTime :
% 0.12/0.60 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.64 Running first-order theorem proving
% 0.16/0.64 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
% 0.16/0.65
% 0.16/0.65 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.65
% 0.16/0.65 % Detected problem language: tptp
% 0.16/0.67 % Proving...
% 44.07/8.18 % SZS status Started for theBenchmark.p
% 44.07/8.18 % SZS status Theorem for theBenchmark.p
% 44.07/8.18
% 44.07/8.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 44.07/8.18
% 44.07/8.18 % ------ iProver source info
% 44.07/8.18
% 44.07/8.18 % git: date: 2026-07-19 20:42:38 +0200
% 44.07/8.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 44.07/8.18 % git: non_committed_changes: false
% 44.07/8.18
% 44.07/8.18 % ------ Parsing...
% 44.07/8.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 44.07/8.18
% 44.07/8.18 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 44.07/8.18
% 44.07/8.18 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 44.07/8.18 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 44.07/8.18
% 44.07/8.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 44.07/8.18 % ------ Proving...
% 44.07/8.18 % ------ Problem Properties
% 44.07/8.18
% 44.07/8.18 %
% 44.07/8.18 % clauses 18
% 44.07/8.18 % conjectures 1
% 44.07/8.18 % EPR 2
% 44.07/8.18 % Horn 18
% 44.07/8.18 % unary 18
% 44.07/8.18 % binary 0
% 44.07/8.18 % lits 18
% 44.07/8.18 % lits eq 18
% 44.07/8.18 % fd_pure 0
% 44.07/8.18 % fd_pseudo 0
% 44.07/8.18 % fd_cond 0
% 44.07/8.18 % fd_pseudo_cond 0
% 44.07/8.18 % AC symbols 1
% 44.07/8.18
% 44.07/8.18 % ------ Schedule UEQ
% 44.07/8.18
% 44.07/8.18 % ------ Option_UEQ Time Limit: 10.
% 44.07/8.18
% 44.07/8.18
% 44.07/8.18 % ------
% 44.07/8.18 % Current options:
% 44.07/8.18 % ------
% 44.07/8.18
% 44.07/8.18
% 44.07/8.18 %
% 44.07/8.18
% 44.07/8.18 % ------ Proving...
% 44.07/8.18 %
% 44.07/8.18
% 44.07/8.18 % SZS status Theorem for theBenchmark.p
% 44.07/8.18
% 44.07/8.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 44.07/8.18
% 44.07/8.18
%------------------------------------------------------------------------------