%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL008-2 : 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 : 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 02:36:33 PM UTC 2026
% Result : Unsatisfiable 225.84s 52.09s
% Output : CNFRefutation 225.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 86 ( 81 unt; 0 def)
% Number of atoms : 91 ( 90 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 11 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 9 ( 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 : 130 ( 0 sgn 130 !; 0 ?; 98 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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(f7,axiom,
! [X2,X0,X1] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_associativity_5) ).
fof(f8,axiom,
! [X0] : composition(X0,one) = X0,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/REL001-0.ax',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/REL001-0.ax',def_top_12) ).
fof(f16,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',def_zero_13) ).
fof(f17,negated_conjecture,
( join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
( join(composition(sk1,sk2),composition(sk1,sk3)) != join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3))
| composition(sk1,join(sk2,sk3)) != join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) ),
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_66,plain,
! [X0: $i,X1: $i,X2: $i] : composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
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,
( ( join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3)) )
| ( join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3)) ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_88,negated_conjecture,
( ( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3)) )
| ( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != join(composition(sk1,sk2),composition(sk1,sk3)) ) ),
inference(theory_normalisation,[status(thm)],[c_75,c_64,c_63]) ).
tcf(c_89,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_90,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_121,plain,
complement(top) = zero,
inference(demodulation,[status(thm)],[c_74,c_73]) ).
tcf(c_221,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_89,c_89]) ).
tcf(c_227,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_221,c_64,c_63]) ).
tcf(c_978,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(superposition,[status(thm)],[c_64,c_63]) ).
tcf(c_979,plain,
join(top,zero) = top,
inference(superposition,[status(thm)],[c_121,c_73]) ).
tcf(c_1007,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = join(top,X1),
inference(superposition,[status(thm)],[c_73,c_64]) ).
tcf(c_1009,plain,
! [X0: $i] : join(top,join(zero,X0)) = join(top,X0),
inference(superposition,[status(thm)],[c_979,c_64]) ).
tcf(c_1012,plain,
! [X0: $i,X1: $i] : composition(X0,composition(one,X1)) = composition(X0,X1),
inference(superposition,[status(thm)],[c_67,c_66]) ).
tcf(c_1015,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_69,c_71]) ).
tcf(c_1028,plain,
! [X0: $i] : join(top,join(X0,zero)) = join(top,X0),
inference(superposition,[status(thm)],[c_63,c_1009]) ).
tcf(c_1154,plain,
! [X0: $i] : join(top,join(X0,zero)) = join(X0,top),
inference(superposition,[status(thm)],[c_979,c_978]) ).
tcf(c_1402,plain,
! [X0: $i] : join(top,complement(complement(X0))) = join(X0,top),
inference(superposition,[status(thm)],[c_73,c_1007]) ).
tcf(c_1404,plain,
! [X0: $i,X1: $i] : join(top,composition(converse(X0),complement(composition(X0,X1)))) = join(X1,complement(X1)),
inference(superposition,[status(thm)],[c_90,c_1007]) ).
tcf(c_1430,plain,
! [X0: $i,X1: $i] : join(top,composition(converse(X0),complement(composition(X0,X1)))) = top,
inference(demodulation,[status(thm)],[c_1404,c_73]) ).
tcf(c_2850,plain,
! [X0: $i] : composition(converse(one),X0) = converse(converse(X0)),
inference(superposition,[status(thm)],[c_67,c_1015]) ).
tcf(c_2879,plain,
! [X0: $i] : composition(converse(one),X0) = X0,
inference(demodulation,[status(thm)],[c_2850,c_69]) ).
tcf(c_2973,plain,
converse(one) = one,
inference(superposition,[status(thm)],[c_2879,c_67]) ).
tcf(c_2981,plain,
! [X0: $i] : composition(converse(one),X0) = composition(one,X0),
inference(superposition,[status(thm)],[c_2879,c_1012]) ).
tcf(c_2985,plain,
! [X0: $i] : composition(one,X0) = X0,
inference(demodulation,[status(thm)],[c_2981,c_2879]) ).
tcf(c_3114,plain,
! [X0: $i] : join(top,composition(converse(one),complement(X0))) = top,
inference(superposition,[status(thm)],[c_2985,c_1430]) ).
tcf(c_3121,plain,
! [X0: $i] : join(top,complement(X0)) = top,
inference(demodulation,[status(thm)],[c_3114,c_2973,c_2985]) ).
tcf(c_3123,plain,
! [X0: $i] : join(X0,top) = top,
inference(demodulation,[status(thm)],[c_1402,c_3121]) ).
tcf(c_3126,plain,
! [X0: $i] : join(top,join(X0,zero)) = top,
inference(demodulation,[status(thm)],[c_1154,c_3123]) ).
tcf(c_3127,plain,
! [X0: $i] : join(top,X0) = top,
inference(demodulation,[status(thm)],[c_1028,c_3126]) ).
tcf(c_3130,plain,
! [X0: $i,X1: $i] : join(X0,join(complement(X0),X1)) = top,
inference(demodulation,[status(thm)],[c_1007,c_3127]) ).
tcf(c_4775,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(converse(X0),X1),
inference(superposition,[status(thm)],[c_69,c_70]) ).
tcf(c_11764,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(converse(X1),X0),
inference(superposition,[status(thm)],[c_63,c_4775]) ).
tcf(c_68455,plain,
! [X0: $i] : join(X0,top) = top,
inference(superposition,[status(thm)],[c_3130,c_3130]) ).
tcf(c_68518,plain,
! [X0: $i] : join(complement(top),complement(join(complement(X0),complement(top)))) = X0,
inference(superposition,[status(thm)],[c_68455,c_89]) ).
tcf(c_68520,plain,
! [X0: $i] : join(zero,complement(join(zero,complement(X0)))) = X0,
inference(demodulation,[status(thm)],[c_68518,c_63,c_121]) ).
tcf(c_68564,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(complement(X0),join(complement(composition(converse(X1),complement(composition(X1,X0)))),complement(complement(X0)))))) = complement(X0),
inference(superposition,[status(thm)],[c_90,c_227]) ).
tcf(c_68587,plain,
! [X0: $i,X1: $i] : join(complement(X0),complement(join(complement(X0),join(complement(complement(X0)),complement(composition(converse(X1),complement(composition(X1,X0)))))))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_68564,c_64,c_63]) ).
tcf(c_68588,plain,
! [X0: $i] : join(zero,complement(X0)) = complement(X0),
inference(demodulation,[status(thm)],[c_68587,c_63,c_121,c_3130]) ).
tcf(c_68594,plain,
! [X0: $i] : join(zero,complement(complement(X0))) = X0,
inference(demodulation,[status(thm)],[c_68520,c_68588]) ).
tcf(c_68596,plain,
! [X0: $i,X1: $i] : converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c_69,c_71]) ).
tcf(c_68597,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_71,c_68]) ).
tcf(c_68656,plain,
! [X0: $i] : complement(complement(X0)) = X0,
inference(demodulation,[status(thm)],[c_68594,c_68588]) ).
tcf(c_68659,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_68656,c_68588]) ).
tcf(c_68663,plain,
! [X0: $i,X1: $i] : join(complement(join(X0,X1)),complement(join(X0,complement(X1)))) = complement(X0),
inference(superposition,[status(thm)],[c_68656,c_89]) ).
tcf(c_68715,plain,
! [X0: $i,X1: $i,X2: $i] : composition(converse(X0),join(converse(X1),X2)) = converse(composition(join(converse(X2),X1),X0)),
inference(superposition,[status(thm)],[c_11764,c_71]) ).
tcf(c_68766,plain,
! [X0: $i] : join(complement(join(X0,X0)),complement(top)) = complement(X0),
inference(superposition,[status(thm)],[c_73,c_68663]) ).
tcf(c_68781,plain,
! [X0: $i] : join(complement(top),complement(join(X0,X0))) = complement(X0),
inference(theory_normalisation,[status(thm)],[c_68766,c_64,c_63]) ).
tcf(c_68782,plain,
! [X0: $i] : complement(join(X0,X0)) = complement(X0),
inference(demodulation,[status(thm)],[c_68781,c_121,c_68659]) ).
tcf(c_69303,plain,
! [X0: $i] : join(X0,X0) = complement(complement(X0)),
inference(superposition,[status(thm)],[c_68782,c_68656]) ).
tcf(c_69311,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_69303,c_68656]) ).
tcf(c_74322,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_68596,c_70]) ).
tcf(c_74881,plain,
! [X0: $i,X1: $i,X2: $i] : join(converse(converse(composition(X0,X1))),composition(converse(converse(X0)),X2)) = converse(composition(join(converse(X1),converse(X2)),converse(X0))),
inference(superposition,[status(thm)],[c_68597,c_74322]) ).
tcf(c_74952,plain,
! [X0: $i,X1: $i,X2: $i] : join(composition(X0,X1),composition(X0,X2)) = composition(X0,join(X2,X1)),
inference(demodulation,[status(thm)],[c_74881,c_69,c_68715]) ).
tcf(c_74977,plain,
( ( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk3,sk2)) )
| ( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3)) ) ),
inference(demodulation,[status(thm)],[c_88,c_74952]) ).
tcf(c_74978,plain,
join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3)),
inference(theory_normalisation,[status(thm)],[c_74977,c_64,c_63]) ).
tcf(c_74979,plain,
$false,
inference(ground_joinability,[status(thm)],[c_74978,c_63,c_64,c_69311,c_74952]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL008-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/20.41 % Computer : n016.cluster.edu
% 0.10/20.41 % Model : x86_64 x86_64
% 0.10/20.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/20.41 % Memory : 8046.5625MB
% 0.10/20.41 % OS : Linux 6.8.0-71-generic
% 0.10/20.41 % CPULimit : 300
% 0.10/20.41 % WCLimit : 300
% 0.10/20.41 % DateTime : Thu Sep 24 07:14:18 UTC 2026
% 0.10/20.42 % CPUTime :
% 0.10/20.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/20.46 Running first-order theorem proving
% 0.10/20.46 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
% 0.10/20.47
% 0.10/20.47 % ======== iProver multi-core TPTP/SMT =========
% 0.10/20.47
% 0.10/20.47 % Detected problem language: tptp
% 0.10/20.48 % Proving...
% 225.84/52.09 % SZS status Started for theBenchmark.p
% 225.84/52.09 % SZS status Unsatisfiable for theBenchmark.p
% 225.84/52.09
% 225.84/52.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 225.84/52.09
% 225.84/52.09 % ------ iProver source info
% 225.84/52.09
% 225.84/52.09 % git: date: 2026-07-19 20:42:38 +0200
% 225.84/52.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 225.84/52.09 % git: non_committed_changes: false
% 225.84/52.09
% 225.84/52.09 % ------ Parsing...% successful
% 225.84/52.09
% 225.84/52.09
% 225.84/52.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 225.84/52.09
% 225.84/52.09 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 225.84/52.09
% 225.84/52.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 225.84/52.09
% 225.84/52.09 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 225.84/52.09 % ------ Proving...
% 225.84/52.09 % ------ Problem Properties
% 225.84/52.09
% 225.84/52.09 %
% 225.84/52.09 % clauses 13
% 225.84/52.09 % conjectures 1
% 225.84/52.09 % EPR 0
% 225.84/52.09 % Horn 13
% 225.84/52.09 % unary 12
% 225.84/52.09 % binary 1
% 225.84/52.09 % lits 14
% 225.84/52.09 % lits eq 14
% 225.84/52.09 % fd_pure 0
% 225.84/52.09 % fd_pseudo 0
% 225.84/52.09 % fd_cond 0
% 225.84/52.09 % fd_pseudo_cond 0
% 225.84/52.09 % AC symbols 1
% 225.84/52.09
% 225.84/52.09 % ------ Input Options Time Limit: Unbounded
% 225.84/52.09
% 225.84/52.09
% 225.84/52.09 % ------
% 225.84/52.09 % Current options:
% 225.84/52.09 % ------
% 225.84/52.09
% 225.84/52.09
% 225.84/52.09 %
% 225.84/52.09
% 225.84/52.09 % ------ Proving...
% 225.84/52.09 %
% 225.84/52.09
% 225.84/52.09 % SZS status Unsatisfiable for theBenchmark.p
% 225.84/52.09
% 225.84/52.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 225.84/52.09
% 225.84/52.09
%------------------------------------------------------------------------------