%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : REL009-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 10.72s 7.30s
% Output : CNFRefutation 10.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 41 ( 35 unt; 4 def)
% Number of atoms : 76 ( 46 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 : 4 ( 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 : 32 ( 0 sgn 32 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/REL001-0.ax',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/REL001-0.ax',converse_multiplicativity_10) ).
fof(f17,negated_conjecture,
join(sk1,sk2) = sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(f18,plain,
sk2 = join(sk1,sk2),
inference(reorient_equations,[],[f17]) ).
fof(f19,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/sandbox/benchmark/theBenchmark.p',goals_15) ).
fof(f20,plain,
( composition(sk3,sk2) != join(composition(sk3,sk1),composition(sk3,sk2))
| composition(sk2,sk3) != join(composition(sk1,sk3),composition(sk2,sk3)) ),
inference(reorient_equations,[],[f19]) ).
tcf(c_64,negated_conjecture,
join(sk1,sk2) = sk2,
inference(cnf_transformation,[],[f18]) ).
tcf(c_65,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,[],[f20]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : composition(converse(X0),converse(X1)) = converse(composition(X1,X0)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_70,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_73,plain,
! [X0: $i,X1: $i] : join(converse(X0),converse(X1)) = converse(join(X0,X1)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_74,plain,
! [X0: $i] : converse(converse(X0)) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_84,negated_conjecture,
join(sk2,sk1) = sk2,
inference(theory_normalisation,[status(thm)],[c_64,c_66,c_67]) ).
tcf(c_85,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_65,c_66,c_67]) ).
tcf(c_114,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_85,c_70,c_66,c_67]) ).
tcf(c_115,plain,
( ( composition(sk2,sk3) != composition(sk2,sk3) )
| ( join(composition(sk3,sk2),composition(sk3,sk1)) != composition(sk3,sk2) ) ),
inference(light_normalisation,[status(thm)],[c_114,c_84]) ).
tcf(c_116,plain,
join(composition(sk3,sk2),composition(sk3,sk1)) != composition(sk3,sk2),
inference(equality_resolution_simp,[status(thm)],[c_115]) ).
tcf(c_123,definition,
iPr_def_10 = composition(sk3,sk2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_124,definition,
iPr_def_11 = composition(sk3,sk1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_125,definition,
iPr_def_12 = join(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_126,definition,
iPr_def_13 = join(sk2,sk1),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_127,plain,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_116,c_124,c_123,c_125]) ).
tcf(c_128,negated_conjecture,
iPr_def_13 = sk2,
inference(demodulation,[status(thm)],[c_84,c_126]) ).
tcf(c_198,plain,
composition(sk3,iPr_def_13) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_123,c_128]) ).
tcf(c_199,plain,
join(iPr_def_13,sk1) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_126,c_128]) ).
tcf(c_350,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_69,c_70]) ).
tcf(c_15559,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_198,c_350]) ).
tcf(c_16070,plain,
! [X0: $i] : join(converse(iPr_def_10),composition(converse(X0),converse(sk3))) = composition(converse(join(iPr_def_13,X0)),converse(sk3)),
inference(superposition,[status(thm)],[c_73,c_15559]) ).
tcf(c_16198,plain,
! [X0: $i] : converse(join(iPr_def_10,composition(sk3,X0))) = converse(composition(sk3,join(iPr_def_13,X0))),
inference(demodulation,[status(thm)],[c_16070,c_73,c_69]) ).
tcf(c_16203,plain,
converse(join(iPr_def_10,composition(sk3,sk1))) = converse(composition(sk3,iPr_def_13)),
inference(superposition,[status(thm)],[c_199,c_16198]) ).
tcf(c_16279,plain,
converse(iPr_def_10) = converse(iPr_def_12),
inference(light_normalisation,[status(thm)],[c_16203,c_124,c_125,c_198]) ).
tcf(c_16351,plain,
converse(converse(iPr_def_10)) = iPr_def_12,
inference(superposition,[status(thm)],[c_16279,c_74]) ).
tcf(c_16433,plain,
iPr_def_10 = iPr_def_12,
inference(demodulation,[status(thm)],[c_16351,c_74]) ).
tcf(c_16453,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_127,c_16433]) ).
tcf(c_16454,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_16453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL009-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.39 % Computer : n026.cluster.edu
% 0.09/5.39 % Model : x86_64 x86_64
% 0.09/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.39 % Memory : 8046.5625MB
% 0.09/5.39 % OS : Linux 6.8.0-71-generic
% 0.09/5.39 % CPULimit : 300
% 0.09/5.39 % WCLimit : 300
% 0.09/5.39 % DateTime : Thu Sep 24 07:10:45 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 10.72/7.30 % SZS status Started for theBenchmark.p
% 10.72/7.30 % SZS status Unsatisfiable for theBenchmark.p
% 10.72/7.30
% 10.72/7.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.72/7.30
% 10.72/7.30 % ------ iProver source info
% 10.72/7.30
% 10.72/7.30 % git: date: 2026-07-19 20:42:38 +0200
% 10.72/7.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.72/7.30 % git: non_committed_changes: false
% 10.72/7.30
% 10.72/7.30 % ------ Parsing...% successful
% 10.72/7.30
% 10.72/7.30
% 10.72/7.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.72/7.30
% 10.72/7.30 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.72/7.30
% 10.72/7.30 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 10.72/7.30 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.72/7.30
% 10.72/7.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.72/7.30 % ------ Proving...
% 10.72/7.30 % ------ Problem Properties
% 10.72/7.30
% 10.72/7.30 %
% 10.72/7.30 % clauses 15
% 10.72/7.30 % conjectures 1
% 10.72/7.30 % EPR 2
% 10.72/7.30 % Horn 15
% 10.72/7.30 % unary 15
% 10.72/7.30 % binary 0
% 10.72/7.30 % lits 15
% 10.72/7.30 % lits eq 15
% 10.72/7.30 % fd_pure 0
% 10.72/7.30 % fd_pseudo 0
% 10.72/7.30 % fd_cond 0
% 10.72/7.30 % fd_pseudo_cond 0
% 10.72/7.30 % AC symbols 1
% 10.72/7.30
% 10.72/7.30 % ------ Schedule UEQ
% 10.72/7.30
% 10.72/7.30 % ------ Option_UEQ Time Limit: 10.
% 10.72/7.30
% 10.72/7.30
% 10.72/7.30 % ------
% 10.72/7.30 % Current options:
% 10.72/7.30 % ------
% 10.72/7.30
% 10.72/7.30
% 10.72/7.30 %
% 10.72/7.30
% 10.72/7.30 % ------ Proving...
% 10.72/7.30 %
% 10.72/7.30
% 10.72/7.30 % SZS status Unsatisfiable for theBenchmark.p
% 10.72/7.30
% 10.72/7.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.72/7.31
% 10.72/7.31
%------------------------------------------------------------------------------