%------------------------------------------------------------------------------
% 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 : 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 02:36:34 PM UTC 2026
% Result : Unsatisfiable 18.86s 8.63s
% Output : CNFRefutation 18.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 46 ( 40 unt; 4 def)
% Number of atoms : 85 ( 51 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 15 ~; 6 |; 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 : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?; 29 :)
% 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(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(f23,negated_conjecture,
join(sk1,sk2) = sk2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
fof(f24,plain,
sk2 = join(sk1,sk2),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( join(composition(sk3,sk1),composition(sk3,sk2)) != composition(sk3,sk2)
| join(composition(sk1,sk3),composition(sk2,sk3)) != composition(sk2,sk3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_18) ).
fof(f26,plain,
( composition(sk3,sk2) != join(composition(sk3,sk1),composition(sk3,sk2))
| composition(sk2,sk3) != join(composition(sk1,sk3),composition(sk2,sk3)) ),
inference(reorient_equations,[],[f25]) ).
tcf(c_67,negated_conjecture,
join(sk1,sk2) = sk2,
inference(cnf_transformation,[],[f24]) ).
tcf(c_68,negated_conjecture,
( ( join(composition(sk3,sk1),composition(sk3,sk2)) != composition(sk3,sk2) )
| ( join(composition(sk1,sk3),composition(sk2,sk3)) != composition(sk2,sk3) ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_71,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_72,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_79,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_93,negated_conjecture,
join(sk2,sk1) = sk2,
inference(theory_normalisation,[status(thm)],[c_67,c_69,c_70]) ).
tcf(c_94,negated_conjecture,
( ( join(composition(sk3,sk2),composition(sk3,sk1)) != composition(sk3,sk2) )
| ( join(composition(sk2,sk3),composition(sk1,sk3)) != composition(sk2,sk3) ) ),
inference(theory_normalisation,[status(thm)],[c_68,c_69,c_70]) ).
tcf(c_133,plain,
( ( composition(join(sk2,sk1),sk3) != composition(sk2,sk3) )
| ( join(composition(sk3,sk2),composition(sk3,sk1)) != composition(sk3,sk2) ) ),
inference(ac_demodulation,[status(thm)],[c_94,c_71,c_69,c_70]) ).
tcf(c_134,plain,
( ( composition(sk2,sk3) != composition(sk2,sk3) )
| ( join(composition(sk3,sk2),composition(sk3,sk1)) != composition(sk3,sk2) ) ),
inference(light_normalisation,[status(thm)],[c_133,c_93]) ).
tcf(c_135,plain,
join(composition(sk3,sk2),composition(sk3,sk1)) != composition(sk3,sk2),
inference(equality_resolution_simp,[status(thm)],[c_134]) ).
tcf(c_142,definition,
iPr_def_10 = composition(sk3,sk2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_143,definition,
iPr_def_11 = composition(sk3,sk1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_144,definition,
iPr_def_12 = join(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_145,definition,
iPr_def_13 = join(sk2,sk1),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_146,plain,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_135,c_143,c_142,c_144]) ).
tcf(c_147,negated_conjecture,
iPr_def_13 = sk2,
inference(demodulation,[status(thm)],[c_93,c_145]) ).
tcf(c_223,plain,
composition(sk3,iPr_def_13) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_142,c_147]) ).
tcf(c_224,plain,
join(iPr_def_13,sk1) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_145,c_147]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i] : converse(join(converse(X0),X1)) = join(X0,converse(X1)),
inference(superposition,[status(thm)],[c_79,c_78]) ).
tcf(c_375,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_72,c_71]) ).
tcf(c_754,plain,
! [X0: $i,X1: $i] : converse(join(X0,converse(X1))) = join(X1,converse(X0)),
inference(superposition,[status(thm)],[c_70,c_238]) ).
tcf(c_1140,plain,
! [X0: $i,X1: $i,X2: $i] : composition(join(X0,converse(X1)),converse(X2)) = converse(composition(X2,join(X1,converse(X0)))),
inference(superposition,[status(thm)],[c_754,c_72]) ).
tcf(c_18622,plain,
! [X0: $i] : join(converse(iPr_def_10),composition(X0,converse(sk3))) = composition(join(converse(iPr_def_13),X0),converse(sk3)),
inference(superposition,[status(thm)],[c_223,c_375]) ).
tcf(c_18743,plain,
! [X0: $i,X1: $i,X2: $i] : composition(join(converse(X0),converse(X1)),converse(X2)) = converse(composition(X2,join(X1,X0))),
inference(superposition,[status(thm)],[c_79,c_1140]) ).
tcf(c_19100,plain,
! [X0: $i] : composition(join(converse(iPr_def_13),converse(X0)),converse(sk3)) = join(converse(iPr_def_10),converse(composition(sk3,X0))),
inference(superposition,[status(thm)],[c_72,c_18622]) ).
tcf(c_19115,plain,
! [X0: $i] : converse(join(iPr_def_10,composition(sk3,X0))) = converse(composition(sk3,join(X0,iPr_def_13))),
inference(demodulation,[status(thm)],[c_19100,c_78,c_18743]) ).
tcf(c_19120,plain,
converse(composition(sk3,join(sk1,iPr_def_13))) = converse(join(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_143,c_19115]) ).
tcf(c_19182,plain,
converse(composition(sk3,join(iPr_def_13,sk1))) = converse(join(iPr_def_10,iPr_def_11)),
inference(theory_normalisation,[status(thm)],[c_19120,c_69,c_70]) ).
tcf(c_19183,plain,
converse(iPr_def_10) = converse(iPr_def_12),
inference(light_normalisation,[status(thm)],[c_19182,c_144,c_223,c_224]) ).
tcf(c_19269,plain,
converse(converse(iPr_def_10)) = iPr_def_12,
inference(superposition,[status(thm)],[c_19183,c_79]) ).
tcf(c_19393,plain,
iPr_def_10 = iPr_def_12,
inference(demodulation,[status(thm)],[c_19269,c_79]) ).
tcf(c_19435,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_146,c_19393]) ).
tcf(c_19436,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_19435]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL009-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.60 % Computer : n008.cluster.edu
% 0.13/5.60 % Model : x86_64 x86_64
% 0.13/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.60 % Memory : 8046.5625MB
% 0.13/5.60 % OS : Linux 6.8.0-71-generic
% 0.13/5.60 % CPULimit : 300
% 0.13/5.60 % WCLimit : 300
% 0.13/5.60 % DateTime : Thu Sep 24 07:08:18 UTC 2026
% 0.13/5.60 % CPUTime :
% 0.13/5.61 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.66 Running first-order theorem proving
% 0.13/5.66 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
% 0.13/5.67
% 0.13/5.67 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.67
% 0.13/5.68 % Detected problem language: tptp
% 0.13/5.69 % Proving...
% 18.86/8.63 % SZS status Started for theBenchmark.p
% 18.86/8.63 % SZS status Unsatisfiable for theBenchmark.p
% 18.86/8.63
% 18.86/8.63 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.86/8.63
% 18.86/8.63 % ------ iProver source info
% 18.86/8.63
% 18.86/8.63 % git: date: 2026-07-19 20:42:38 +0200
% 18.86/8.63 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.86/8.63 % git: non_committed_changes: false
% 18.86/8.63
% 18.86/8.63 % ------ Parsing...% successful
% 18.86/8.63
% 18.86/8.63
% 18.86/8.63 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.86/8.63
% 18.86/8.63 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 18.86/8.63
% 18.86/8.63 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 18.86/8.63 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.86/8.63
% 18.86/8.63 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 18.86/8.63 % ------ Proving...
% 18.86/8.63 % ------ Problem Properties
% 18.86/8.63
% 18.86/8.63 %
% 18.86/8.63 % clauses 18
% 18.86/8.63 % conjectures 1
% 18.86/8.63 % EPR 2
% 18.86/8.63 % Horn 18
% 18.86/8.63 % unary 18
% 18.86/8.63 % binary 0
% 18.86/8.63 % lits 18
% 18.86/8.63 % lits eq 18
% 18.86/8.63 % fd_pure 0
% 18.86/8.63 % fd_pseudo 0
% 18.86/8.63 % fd_cond 0
% 18.86/8.63 % fd_pseudo_cond 0
% 18.86/8.63 % AC symbols 1
% 18.86/8.63
% 18.86/8.63 % ------ Schedule UEQ
% 18.86/8.63
% 18.86/8.63 % ------ Option_UEQ Time Limit: 10.
% 18.86/8.63
% 18.86/8.63
% 18.86/8.63 % ------
% 18.86/8.63 % Current options:
% 18.86/8.63 % ------
% 18.86/8.63
% 18.86/8.63
% 18.86/8.63 %
% 18.86/8.63
% 18.86/8.63 % ------ Proving...
% 18.86/8.63 %
% 18.86/8.63
% 18.86/8.63 % SZS status Unsatisfiable for theBenchmark.p
% 18.86/8.63
% 18.86/8.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.86/8.63
% 18.86/8.63
%------------------------------------------------------------------------------