%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL048+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 : Thu Sep 24 02:04:10 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 54 unt; 0 def)
% Number of atoms : 67 ( 66 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 3 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% 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 : 77 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(maddux4_definiton_of_meet,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
fof(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
fof(goals,conjecture,
! [X1,X2,X3] :
( join(join(X1,X2),X3) = X3
=> ( join(X2,X3) = X3
& join(X1,X3) = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(c_0_11,plain,
! [X23,X24] : converse(composition(X23,X24)) = composition(converse(X24),converse(X23)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_12,plain,
! [X20] : converse(converse(X20)) = X20,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_13,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,plain,
! [X16] : composition(X16,one) = X16,
inference(variable_rename,[status(thm)],[composition_identity]) ).
cnf(c_0_16,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X25,X26] : join(composition(converse(X25),complement(composition(X25,X26))),complement(X26)) = complement(X26),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_19,plain,
! [X4,X5] : join(X4,X5) = join(X5,X4),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_20,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14]) ).
fof(c_0_21,plain,
! [X28] : zero = meet(X28,complement(X28)),
inference(variable_rename,[status(thm)],[def_zero]) ).
fof(c_0_22,plain,
! [X11,X12] : meet(X11,X12) = complement(join(complement(X11),complement(X12))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_23,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_26,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_28,plain,
! [X27] : top = join(X27,complement(X27)),
inference(variable_rename,[status(thm)],[def_top]) ).
cnf(c_0_29,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_31,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_33,plain,
! [X9,X10] : X9 = join(complement(join(complement(X9),complement(X10))),complement(join(complement(X9),X10))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_34,negated_conjecture,
~ ! [X1,X2,X3] :
( join(join(X1,X2),X3) = X3
=> ( join(X2,X3) = X3
& join(X1,X3) = X3 ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_35,plain,
! [X6,X7,X8] : join(X6,join(X7,X8)) = join(join(X6,X7),X8),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_0_36,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_25]),c_0_30]) ).
cnf(c_0_37,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_39,negated_conjecture,
( ( join(esk2_0,esk3_0) != esk3_0
| join(esk1_0,esk3_0) != esk3_0 )
& join(join(esk1_0,esk2_0),esk3_0) = esk3_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])]) ).
cnf(c_0_40,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_38,c_0_24]) ).
cnf(c_0_43,negated_conjecture,
join(join(esk1_0,esk2_0),esk3_0) = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_36]),c_0_32]),c_0_37]),c_0_24]) ).
cnf(c_0_46,negated_conjecture,
join(esk3_0,join(esk1_0,esk2_0)) = esk3_0,
inference(rw,[status(thm)],[c_0_43,c_0_24]) ).
cnf(c_0_47,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
join(esk3_0,join(esk1_0,join(esk2_0,X1))) = join(esk3_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_46]),c_0_40]) ).
cnf(c_0_49,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_45,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
join(esk3_0,join(esk1_0,join(X1,esk2_0))) = join(esk3_0,X1),
inference(spm,[status(thm)],[c_0_48,c_0_24]) ).
cnf(c_0_51,negated_conjecture,
( join(esk2_0,esk3_0) != esk3_0
| join(esk1_0,esk3_0) != esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_52,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
join(esk3_0,join(esk1_0,join(X1,join(esk2_0,X2)))) = join(esk3_0,join(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_50]),c_0_40]),c_0_40]),c_0_40]) ).
cnf(c_0_54,negated_conjecture,
( join(esk3_0,esk2_0) != esk3_0
| join(esk3_0,esk1_0) != esk3_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_24]),c_0_24]) ).
cnf(c_0_55,negated_conjecture,
join(esk3_0,esk2_0) = esk3_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_52]),c_0_46]) ).
cnf(c_0_56,negated_conjecture,
join(esk3_0,join(X1,esk2_0)) = join(esk3_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_52]),c_0_50]) ).
cnf(c_0_57,negated_conjecture,
join(esk3_0,esk1_0) != esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_56]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:09:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.44 % Version: 3.5.1
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.44 % Starting sh5l with 300s (1) cores
% 0.11/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1968560 completed with status 0
% 0.11/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.44 % No SInE strategy applied
% 0.11/0.44 % Search class: FUHPM-FFSF21-MFFFFFNN
% 0.11/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.44 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 0.11/0.44 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 136s (1) cores
% 0.11/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1968566 completed with status 0
% 0.11/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.11/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.11/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.11/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.44 % No SInE strategy applied
% 0.11/0.44 % Search class: FUHPM-FFSF21-MFFFFFNN
% 0.11/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.11/0.44 % Preprocessing time : 0.001 s
% 0.11/0.44 % Presaturation interreduction done
% 0.11/0.44
% 0.11/0.44 % Proof found!
% 0.11/0.44 % SZS status Theorem
% 0.11/0.44 % SZS output start CNFRefutation
% See solution above
% 0.11/0.44 % Parsed axioms : 14
% 0.11/0.44 % Removed by relevancy pruning/SinE : 0
% 0.11/0.44 % Initial clauses : 15
% 0.11/0.44 % Removed in clause preprocessing : 1
% 0.11/0.44 % Initial clauses in saturation : 14
% 0.11/0.44 % Processed clauses : 93
% 0.11/0.44 % ...of these trivial : 23
% 0.11/0.44 % ...subsumed : 4
% 0.11/0.44 % ...remaining for further processing : 66
% 0.11/0.44 % Other redundant clauses eliminated : 0
% 0.11/0.44 % Clauses deleted for lack of memory : 0
% 0.11/0.44 % Backward-subsumed : 0
% 0.11/0.44 % Backward-rewritten : 15
% 0.11/0.44 % Generated clauses : 293
% 0.11/0.44 % ...of the previous two non-redundant : 207
% 0.11/0.44 % ...aggressively subsumed : 0
% 0.11/0.44 % Contextual simplify-reflections : 0
% 0.11/0.44 % Paramodulations : 293
% 0.11/0.44 % Factorizations : 0
% 0.11/0.44 % NegExts : 0
% 0.11/0.44 % Equation resolutions : 0
% 0.11/0.44 % Disequality decompositions : 0
% 0.11/0.44 % Total rewrite steps : 309
% 0.11/0.44 % ...of those cached : 149
% 0.11/0.44 % Propositional unsat checks : 0
% 0.11/0.44 % Propositional check models : 0
% 0.11/0.44 % Propositional check unsatisfiable : 0
% 0.11/0.44 % Propositional clauses : 0
% 0.11/0.44 % Propositional clauses after purity: 0
% 0.11/0.44 % Propositional unsat core size : 0
% 0.11/0.44 % Propositional preprocessing time : 0.000
% 0.11/0.44 % Propositional encoding time : 0.000
% 0.11/0.44 % Propositional solver time : 0.000
% 0.11/0.44 % Success case prop preproc time : 0.000
% 0.11/0.44 % Success case prop encoding time : 0.000
% 0.11/0.44 % Success case prop solver time : 0.000
% 0.11/0.44 % Current number of processed clauses : 37
% 0.11/0.44 % Positive orientable unit clauses : 35
% 0.11/0.44 % Positive unorientable unit clauses: 1
% 0.11/0.44 % Negative unit clauses : 1
% 0.11/0.44 % Non-unit-clauses : 0
% 0.11/0.44 % Current number of unprocessed clauses: 141
% 0.11/0.44 % ...number of literals in the above : 141
% 0.11/0.44 % Current number of archived formulas : 0
% 0.11/0.44 % Current number of archived clauses : 30
% 0.11/0.44 % Clause-clause subsumption calls (NU) : 0
% 0.11/0.44 % Rec. Clause-clause subsumption calls : 0
% 0.11/0.44 % Non-unit clause-clause subsumptions : 0
% 0.11/0.44 % Unit Clause-clause subsumption calls : 0
% 0.11/0.44 % Rewrite failures with RHS unbound : 0
% 0.11/0.44 % BW rewrite match attempts : 93
% 0.11/0.44 % BW rewrite match successes : 25
% 0.11/0.44 % Condensation attempts : 0
% 0.11/0.44 % Condensation successes : 0
% 0.11/0.44 % Termbank termtop insertions : 3744
% 0.11/0.44 % Search garbage collected termcells : 42
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.008 s
% 0.11/0.44 % System time : 0.004 s
% 0.11/0.44 % Total time : 0.012 s
% 0.11/0.44 % Maximum resident set size: 3648 pages
% 0.11/0.44
% 0.11/0.44 % -------------------------------------------------
% 0.11/0.44 % User time : 0.043 s
% 0.11/0.44 % System time : 0.011 s
% 0.11/0.44 % Total time : 0.054 s
% 0.11/0.44 % Maximum resident set size: 4608 pages
% 0.11/0.44 % E exiting
%------------------------------------------------------------------------------