%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL008+4 : 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 02:36:34 PM UTC 2026
% Result : Theorem 219.65s 36.04s
% Output : CNFRefutation 219.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 85 ( 77 unt; 0 def)
% Number of atoms : 93 ( 92 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 6 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 138 ( 0 sgn 135 !; 3 ?; 78 :)
% 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(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(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(f17,conjecture,
! [X0,X1,X2] :
( join(join(composition(X0,X1),composition(X0,X2)),composition(X0,join(X1,X2))) = composition(X0,join(X1,X2))
& join(join(composition(X0,join(X1,X2)),composition(X0,X1)),composition(X0,X2)) = join(composition(X0,X1),composition(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( join(join(composition(X0,X1),composition(X0,X2)),composition(X0,join(X1,X2))) = composition(X0,join(X1,X2))
& join(join(composition(X0,join(X1,X2)),composition(X0,X1)),composition(X0,X2)) = join(composition(X0,X1),composition(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1,X2] :
( composition(X0,join(X1,X2)) != join(join(composition(X0,X1),composition(X0,X2)),composition(X0,join(X1,X2)))
| join(join(composition(X0,join(X1,X2)),composition(X0,X1)),composition(X0,X2)) != join(composition(X0,X1),composition(X0,X2)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
( composition(sK0,join(sK1,sK2)) != join(join(composition(sK0,sK1),composition(sK0,sK2)),composition(sK0,join(sK1,sK2)))
| join(join(composition(sK0,join(sK1,sK2)),composition(sK0,sK1)),composition(sK0,sK2)) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f19]) ).
fof(f21,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f22,plain,
! [X2,X0,X1] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(cnf_transformation,[],[f2]) ).
fof(f23,plain,
! [X0,X1] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f24,plain,
! [X0,X1] : complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(cnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f27,plain,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
fof(f28,plain,
! [X0] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f29,plain,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(cnf_transformation,[],[f9]) ).
fof(f30,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f31,plain,
! [X0,X1] : complement(X1) = join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f32,plain,
! [X0] : top = join(X0,complement(X0)),
inference(cnf_transformation,[],[f12]) ).
fof(f33,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f37,plain,
( composition(sK0,join(sK1,sK2)) != join(join(composition(sK0,sK1),composition(sK0,sK2)),composition(sK0,join(sK1,sK2)))
| join(join(composition(sK0,join(sK1,sK2)),composition(sK0,sK1)),composition(sK0,sK2)) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0] : zero = complement(join(complement(X0),complement(complement(X0)))),
inference(definition_unfolding,[],[f33,f24]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f22]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = X0,
inference(cnf_transformation,[],[f23]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f25]) ).
tcf(c_53,plain,
! [X0: $i] : composition(X0,one) = X0,
inference(cnf_transformation,[],[f26]) ).
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,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f28]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f29]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f30]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(cnf_transformation,[],[f31]) ).
tcf(c_59,plain,
! [X0: $i] : join(X0,complement(X0)) = top,
inference(cnf_transformation,[],[f32]) ).
tcf(c_60,plain,
! [X0: $i] : complement(join(complement(X0),complement(complement(X0)))) = zero,
inference(cnf_transformation,[],[f38]) ).
tcf(c_64,negated_conjecture,
( ( join(join(composition(sK0,sK1),composition(sK0,sK2)),composition(sK0,join(sK1,sK2))) != composition(sK0,join(sK1,sK2)) )
| ( join(join(composition(sK0,join(sK1,sK2)),composition(sK0,sK1)),composition(sK0,sK2)) != join(composition(sK0,sK1),composition(sK0,sK2)) ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_80,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_81,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_84,negated_conjecture,
( ( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2)) )
| ( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != join(composition(sK0,sK1),composition(sK0,sK2)) ) ),
inference(theory_normalisation,[status(thm)],[c_64,c_50,c_49]) ).
tcf(c_123,plain,
complement(top) = zero,
inference(demodulation,[status(thm)],[c_60,c_59]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i] : join(complement(join(complement(join(complement(X0),X1)),join(complement(X0),complement(X1)))),complement(X0)) = join(complement(X0),X1),
inference(superposition,[status(thm)],[c_80,c_80]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(complement(X0),join(complement(X1),complement(join(complement(X0),X1)))))) = join(complement(X0),X1),
inference(theory_normalisation,[status(thm)],[c_229,c_50,c_49]) ).
tcf(c_4850,plain,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X2,X1)) = composition(join(X2,X0),X1),
inference(superposition,[status(thm)],[c_54,c_49]) ).
tcf(c_70321,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_70332,plain,
! [X0: $i] : join(complement(join(complement(X0),complement(X0))),complement(top)) = X0,
inference(superposition,[status(thm)],[c_59,c_80]) ).
tcf(c_70338,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(X0)))) = X0,
inference(theory_normalisation,[status(thm)],[c_70332,c_50,c_49]) ).
tcf(c_70339,plain,
! [X0: $i] : join(zero,complement(join(complement(X0),complement(X0)))) = X0,
inference(demodulation,[status(thm)],[c_70338,c_123]) ).
tcf(c_70345,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_70349,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_59,c_50]) ).
tcf(c_70363,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_55,c_57]) ).
tcf(c_70394,plain,
! [X0: $i,X1: $i,X2: $i] : composition(converse(X0),join(X1,converse(X2))) = converse(composition(join(converse(X1),X2),X0)),
inference(superposition,[status(thm)],[c_70321,c_57]) ).
tcf(c_70616,plain,
! [X0: $i] : join(top,complement(complement(X0))) = join(X0,top),
inference(superposition,[status(thm)],[c_59,c_70349]) ).
tcf(c_70730,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_53,c_70363]) ).
tcf(c_70755,plain,
! [X0: $i,X1: $i,X2: $i] : join(converse(X0),composition(converse(X1),X2)) = converse(join(X0,composition(converse(X2),X1))),
inference(superposition,[status(thm)],[c_70363,c_56]) ).
tcf(c_70758,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(demodulation,[status(thm)],[c_70730,c_55]) ).
tcf(c_70771,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_70758,c_53]) ).
tcf(c_70783,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_70758,c_70345]) ).
tcf(c_70784,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(demodulation,[status(thm)],[c_70783,c_70758]) ).
tcf(c_71010,plain,
! [X0: $i] : join(complement(X0),composition(one,complement(composition(one,X0)))) = complement(X0),
inference(superposition,[status(thm)],[c_70771,c_81]) ).
tcf(c_71019,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = complement(X0),
inference(demodulation,[status(thm)],[c_71010,c_70784]) ).
tcf(c_71026,plain,
! [X0: $i] : join(zero,complement(complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_70339,c_71019]) ).
tcf(c_71074,plain,
! [X0: $i] : join(X0,complement(X0)) = join(top,complement(X0)),
inference(superposition,[status(thm)],[c_71019,c_70349]) ).
tcf(c_71083,plain,
! [X0: $i] : join(top,complement(X0)) = top,
inference(demodulation,[status(thm)],[c_71074,c_59]) ).
tcf(c_71096,plain,
! [X0: $i] : join(X0,top) = top,
inference(demodulation,[status(thm)],[c_70616,c_71083]) ).
tcf(c_71105,plain,
! [X0: $i] : join(top,X0) = top,
inference(superposition,[status(thm)],[c_71096,c_49]) ).
tcf(c_71120,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = top,
inference(demodulation,[status(thm)],[c_70349,c_71105]) ).
tcf(c_71408,plain,
! [X0: $i] : join(complement(X0),complement(X0)) = join(complement(X0),complement(top)),
inference(superposition,[status(thm)],[c_71120,c_235]) ).
tcf(c_71413,plain,
! [X0: $i] : join(zero,complement(X0)) = complement(X0),
inference(demodulation,[status(thm)],[c_71408,c_49,c_123,c_71019]) ).
tcf(c_71427,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_71026,c_71413]) ).
tcf(c_71430,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(superposition,[status(thm)],[c_71427,c_71019]) ).
tcf(c_73187,plain,
! [X0: $i,X1: $i,X2: $i] : join(converse(composition(X0,X1)),composition(X2,converse(X0))) = composition(join(X2,converse(X1)),converse(X0)),
inference(superposition,[status(thm)],[c_57,c_4850]) ).
tcf(c_73270,plain,
! [X0: $i,X1: $i,X2: $i] : join(converse(converse(composition(X0,X1))),composition(converse(converse(X0)),X2)) = converse(composition(join(converse(X2),converse(X1)),converse(X0))),
inference(superposition,[status(thm)],[c_73187,c_70755]) ).
tcf(c_73286,plain,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X0,X2)) = composition(X0,join(X2,X1)),
inference(demodulation,[status(thm)],[c_73270,c_55,c_70394]) ).
tcf(c_73302,plain,
( ( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK2,sK1)) )
| ( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2)) ) ),
inference(demodulation,[status(thm)],[c_84,c_73286]) ).
tcf(c_73303,plain,
join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2)),
inference(theory_normalisation,[status(thm)],[c_73302,c_50,c_49]) ).
tcf(c_73531,plain,
$false,
inference(ground_joinability,[status(thm)],[c_73303,c_49,c_50,c_71430,c_73286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL008+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.38 % Computer : n016.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Thu Sep 24 07:13:19 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.42 Running first-order theorem proving
% 0.16/5.42 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
% 0.16/5.43
% 0.16/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.43
% 0.16/5.43 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 219.65/36.04 % SZS status Started for theBenchmark.p
% 219.65/36.04 % SZS status Theorem for theBenchmark.p
% 219.65/36.04
% 219.65/36.04 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 219.65/36.04
% 219.65/36.04 % ------ iProver source info
% 219.65/36.04
% 219.65/36.04 % git: date: 2026-07-19 20:42:38 +0200
% 219.65/36.04 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 219.65/36.04 % git: non_committed_changes: false
% 219.65/36.04
% 219.65/36.04 % ------ Parsing...
% 219.65/36.04 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 219.65/36.04
% 219.65/36.04 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 219.65/36.04
% 219.65/36.04 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 219.65/36.04
% 219.65/36.04 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 219.65/36.04 % ------ Proving...
% 219.65/36.04 % ------ Problem Properties
% 219.65/36.04
% 219.65/36.04 %
% 219.65/36.04 % clauses 16
% 219.65/36.04 % conjectures 1
% 219.65/36.04 % EPR 0
% 219.65/36.04 % Horn 16
% 219.65/36.04 % unary 15
% 219.65/36.04 % binary 1
% 219.65/36.04 % lits 17
% 219.65/36.04 % lits eq 17
% 219.65/36.04 % fd_pure 0
% 219.65/36.04 % fd_pseudo 0
% 219.65/36.04 % fd_cond 0
% 219.65/36.04 % fd_pseudo_cond 0
% 219.65/36.04 % AC symbols 1
% 219.65/36.04
% 219.65/36.04 % ------ Input Options Time Limit: Unbounded
% 219.65/36.04
% 219.65/36.04
% 219.65/36.04 % ------
% 219.65/36.04 % Current options:
% 219.65/36.04 % ------
% 219.65/36.04
% 219.65/36.04
% 219.65/36.04 %
% 219.65/36.04
% 219.65/36.04 % ------ Proving...
% 219.65/36.04 %
% 219.65/36.04
% 219.65/36.04 % SZS status Theorem for theBenchmark.p
% 219.65/36.04
% 219.65/36.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 219.65/36.04
% 219.65/36.04
%------------------------------------------------------------------------------