%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL002+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 02:36:29 PM UTC 2026
% Result : Theorem 3.06s 1.27s
% Output : CNFRefutation 3.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 69 ( 69 unt; 1 def)
% Number of atoms : 80 ( 68 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 84 !; 1 ?; 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(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(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] : join(X0,top) = top,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0] : join(X0,top) = top,
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0] : top != join(X0,top),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
top != join(sK0,top),
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(f21,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f22,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
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,
top != join(sK0,top),
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_52,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f22]) ).
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,[],[f32]) ).
tcf(c_61,negated_conjecture,
join(sK0,top) != top,
inference(cnf_transformation,[],[f31]) ).
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_76,negated_conjecture,
join(top,sK0) != top,
inference(theory_normalisation,[status(thm)],[c_61,c_50,c_49]) ).
tcf(c_105,plain,
complement(top) = zero,
inference(ac_demodulation,[status(thm)],[c_60,c_59,c_50,c_49]) ).
tcf(c_112,definition,
iPr_def_10 = join(top,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_113,negated_conjecture,
iPr_def_10 != top,
inference(demodulation,[status(thm)],[c_76,c_112]) ).
tcf(c_180,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_181,plain,
join(top,zero) = top,
inference(superposition,[status(thm)],[c_105,c_59]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_59,c_50]) ).
tcf(c_213,plain,
! [X0: $i] : join(top,join(sK0,X0)) = join(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_112,c_50]) ).
tcf(c_214,plain,
! [X0: $i] : join(top,join(zero,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_181,c_50]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_221,plain,
! [X0: $i] : join(top,join(X0,sK0)) = join(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_49,c_213]) ).
tcf(c_229,plain,
! [X0: $i] : join(top,join(X0,zero)) = join(top,X0),
inference(superposition,[status(thm)],[c_49,c_214]) ).
tcf(c_248,plain,
join(top,sK0) = join(iPr_def_10,zero),
inference(superposition,[status(thm)],[c_221,c_214]) ).
tcf(c_249,plain,
join(iPr_def_10,zero) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_248,c_112]) ).
tcf(c_385,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_208]) ).
tcf(c_405,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(light_normalisation,[status(thm)],[c_385,c_55]) ).
tcf(c_419,plain,
! [X0: $i] : join(complement(X0),complement(composition(one,X0))) = complement(X0),
inference(superposition,[status(thm)],[c_405,c_75]) ).
tcf(c_422,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_405,c_217]) ).
tcf(c_424,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(light_normalisation,[status(thm)],[c_422,c_405]) ).
tcf(c_489,plain,
! [X0: $i] : join(top,join(X0,zero)) = join(X0,top),
inference(superposition,[status(thm)],[c_181,c_180]) ).
tcf(c_756,plain,
! [X0: $i] : join(top,complement(complement(X0))) = join(X0,top),
inference(superposition,[status(thm)],[c_59,c_211]) ).
tcf(c_1151,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(light_normalisation,[status(thm)],[c_419,c_424]) ).
tcf(c_1159,plain,
! [X0: $i] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(superposition,[status(thm)],[c_1151,c_211]) ).
tcf(c_1164,plain,
! [X0: $i] : join(top,complement(X0)) = top,
inference(light_normalisation,[status(thm)],[c_1159,c_59]) ).
tcf(c_1174,plain,
! [X0: $i] : join(X0,top) = top,
inference(demodulation,[status(thm)],[c_756,c_1164]) ).
tcf(c_1178,plain,
! [X0: $i] : join(top,join(X0,zero)) = top,
inference(demodulation,[status(thm)],[c_489,c_1174]) ).
tcf(c_1180,plain,
! [X0: $i] : join(top,X0) = top,
inference(demodulation,[status(thm)],[c_229,c_1178]) ).
tcf(c_1187,plain,
! [X0: $i] : join(iPr_def_10,X0) = top,
inference(demodulation,[status(thm)],[c_221,c_1180]) ).
tcf(c_1190,plain,
top = iPr_def_10,
inference(demodulation,[status(thm)],[c_249,c_1187]) ).
tcf(c_1198,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_113,c_1190]) ).
tcf(c_1199,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_1198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL002+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.43 % Computer : n008.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Thu Sep 24 07:06:40 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.49 Running first-order theorem proving
% 0.17/0.49 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
% 0.24/0.51
% 0.24/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.51
% 0.24/0.51 % Detected problem language: tptp
% 0.24/0.52 % Proving...
% 3.06/1.27 % SZS status Started for theBenchmark.p
% 3.06/1.27 % SZS status Theorem for theBenchmark.p
% 3.06/1.27
% 3.06/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.06/1.27
% 3.06/1.27 % ------ iProver source info
% 3.06/1.27
% 3.06/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.06/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.06/1.27 % git: non_committed_changes: false
% 3.06/1.27
% 3.06/1.27 % ------ Parsing...
% 3.06/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_UEQ
% 3.06/1.27 %
% 3.06/1.27
% 3.06/1.27 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.06/1.27
% 3.06/1.27 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.06/1.27 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.06/1.27
% 3.06/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.06/1.27 % ------ Proving...
% 3.06/1.27 % ------ Problem Properties
% 3.06/1.27
% 3.06/1.27 %
% 3.06/1.27 % clauses 14
% 3.06/1.27 % conjectures 1
% 3.06/1.27 % EPR 1
% 3.06/1.27 % Horn 14
% 3.06/1.27 % unary 14
% 3.06/1.27 % binary 0
% 3.06/1.27 % lits 14
% 3.06/1.27 % lits eq 14
% 3.06/1.27 % fd_pure 0
% 3.06/1.27 % fd_pseudo 0
% 3.06/1.27 % fd_cond 0
% 3.06/1.27 % fd_pseudo_cond 0
% 3.06/1.27 % AC symbols 1
% 3.06/1.27
% 3.06/1.27 % ------ Schedule UEQ
% 3.06/1.27
% 3.06/1.27 % ------ Option_UEQ Time Limit: 10.
% 3.06/1.27
% 3.06/1.27
% 3.06/1.27 % ------
% 3.06/1.27 % Current options:
% 3.06/1.27 % ------
% 3.06/1.27
% 3.06/1.27
% 3.06/1.27 %
% 3.06/1.27
% 3.06/1.27 % ------ Proving...
% 3.06/1.27 %
% 3.06/1.27
% 3.06/1.27 % SZS status Theorem for theBenchmark.p
% 3.06/1.27
% 3.06/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.06/1.27
% 3.06/1.27
%------------------------------------------------------------------------------