%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL001+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 : n010.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 02:03:47 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 47 ( 47 unt; 0 def)
% Number of atoms : 47 ( 46 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 36 !; 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(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(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).
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(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(goals,conjecture,
! [X1] : join(zero,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_11,plain,
! [X27,X28] : converse(composition(X27,X28)) = composition(converse(X28),converse(X27)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_12,plain,
! [X29] : converse(converse(X29)) = X29,
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,
! [X26] : composition(X26,one) = X26,
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,
! [X19,X20] : join(composition(converse(X19),complement(composition(X19,X20))),complement(X20)) = complement(X20),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_19,plain,
! [X5,X6] : join(X5,X6) = join(X6,X5),
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]) ).
cnf(c_0_21,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
fof(c_0_24,plain,
! [X12,X13] : meet(X12,X13) = complement(join(complement(X12),complement(X13))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
fof(c_0_25,plain,
! [X22] : top = join(X22,complement(X22)),
inference(variable_rename,[status(thm)],[def_top]) ).
fof(c_0_26,plain,
! [X21] : zero = meet(X21,complement(X21)),
inference(variable_rename,[status(thm)],[def_zero]) ).
cnf(c_0_27,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_29,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_32,plain,
! [X10,X11] : X10 = join(complement(join(complement(X10),complement(X11))),complement(join(complement(X10),X11))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_33,plain,
! [X7,X8,X9] : join(X7,join(X8,X9)) = join(join(X7,X8),X9),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_0_34,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_23]),c_0_28]) ).
cnf(c_0_35,plain,
complement(top) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_36,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_37,negated_conjecture,
~ ! [X1] : join(zero,X1) = X1,
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_38,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
join(complement(join(complement(X1),X2)),meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_29]),c_0_22]) ).
fof(c_0_41,negated_conjecture,
join(zero,esk1_0) != esk1_0,
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])])]) ).
cnf(c_0_42,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_31]),c_0_34]),c_0_22]) ).
cnf(c_0_44,negated_conjecture,
join(zero,esk1_0) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL001+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.34 % Computer : n010.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 03:57:40 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.41 % Version: 3.5.1
% 0.12/0.41 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.41 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.41 % Starting sh5l with 300s (1) cores
% 0.12/0.41 % sh5l with pid 4174952 completed with status 0
% 0.12/0.41 % Result found by sh5l
% 0.12/0.41 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.41 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.41 % Starting sh5l with 300s (1) cores
% 0.12/0.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.12/0.41 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.41 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.12/0.41 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.41 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.41 % SubtermCWHack with pid 4174953 completed with status 0
% 0.12/0.41 % Result found by SubtermCWHack
% 0.12/0.41 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.41 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.41 % Starting sh5l with 300s (1) cores
% 0.12/0.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.12/0.41 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.41 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.12/0.41 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.41 % Starting SubtermCWHack with 28s (1) cores
% 0.12/0.41 % Preprocessing time : 0.001 s
% 0.12/0.41
% 0.12/0.41 % Proof found!
% 0.12/0.41 % SZS status Theorem
% 0.12/0.41 % SZS output start CNFRefutation
% See solution above
% 0.12/0.41 % Parsed axioms : 14
% 0.12/0.41 % Removed by relevancy pruning/SinE : 0
% 0.12/0.41 % Initial clauses : 14
% 0.12/0.41 % Removed in clause preprocessing : 0
% 0.12/0.41 % Initial clauses in saturation : 14
% 0.12/0.41 % Processed clauses : 81
% 0.12/0.41 % ...of these trivial : 20
% 0.12/0.41 % ...subsumed : 7
% 0.12/0.41 % ...remaining for further processing : 54
% 0.12/0.41 % Other redundant clauses eliminated : 0
% 0.12/0.41 % Clauses deleted for lack of memory : 0
% 0.12/0.41 % Backward-subsumed : 0
% 0.12/0.41 % Backward-rewritten : 21
% 0.12/0.41 % Generated clauses : 364
% 0.12/0.41 % ...of the previous two non-redundant : 248
% 0.12/0.41 % ...aggressively subsumed : 0
% 0.12/0.41 % Contextual simplify-reflections : 0
% 0.12/0.41 % Paramodulations : 364
% 0.12/0.41 % Factorizations : 0
% 0.12/0.41 % NegExts : 0
% 0.12/0.41 % Equation resolutions : 0
% 0.12/0.41 % Disequality decompositions : 0
% 0.12/0.41 % Total rewrite steps : 409
% 0.12/0.41 % ...of those cached : 250
% 0.12/0.41 % Propositional unsat checks : 0
% 0.12/0.41 % Propositional check models : 0
% 0.12/0.41 % Propositional check unsatisfiable : 0
% 0.12/0.41 % Propositional clauses : 0
% 0.12/0.41 % Propositional clauses after purity: 0
% 0.12/0.41 % Propositional unsat core size : 0
% 0.12/0.41 % Propositional preprocessing time : 0.000
% 0.12/0.41 % Propositional encoding time : 0.000
% 0.12/0.41 % Propositional solver time : 0.000
% 0.12/0.41 % Success case prop preproc time : 0.000
% 0.12/0.41 % Success case prop encoding time : 0.000
% 0.12/0.41 % Success case prop solver time : 0.000
% 0.12/0.41 % Current number of processed clauses : 33
% 0.12/0.42 % Positive orientable unit clauses : 31
% 0.12/0.42 % Positive unorientable unit clauses: 2
% 0.12/0.42 % Negative unit clauses : 0
% 0.12/0.42 % Non-unit-clauses : 0
% 0.12/0.42 % Current number of unprocessed clauses: 174
% 0.12/0.42 % ...number of literals in the above : 174
% 0.12/0.42 % Current number of archived formulas : 0
% 0.12/0.42 % Current number of archived clauses : 21
% 0.12/0.42 % Clause-clause subsumption calls (NU) : 0
% 0.12/0.42 % Rec. Clause-clause subsumption calls : 0
% 0.12/0.42 % Non-unit clause-clause subsumptions : 0
% 0.12/0.42 % Unit Clause-clause subsumption calls : 0
% 0.12/0.42 % Rewrite failures with RHS unbound : 0
% 0.12/0.42 % BW rewrite match attempts : 34
% 0.12/0.42 % BW rewrite match successes : 27
% 0.12/0.42 % Condensation attempts : 0
% 0.12/0.42 % Condensation successes : 0
% 0.12/0.42 % Termbank termtop insertions : 3760
% 0.12/0.42 % Search garbage collected termcells : 9
% 0.12/0.42
% 0.12/0.42 % -------------------------------------------------
% 0.12/0.42 % User time : 0.008 s
% 0.12/0.42 % System time : 0.001 s
% 0.12/0.42 % Total time : 0.009 s
% 0.12/0.42 % Maximum resident set size: 3648 pages
% 0.12/0.42
% 0.12/0.42 % -------------------------------------------------
% 0.12/0.42 % User time : 0.012 s
% 0.12/0.42 % System time : 0.003 s
% 0.12/0.42 % Total time : 0.015 s
% 0.12/0.42 % Maximum resident set size: 4608 pages
% 0.12/0.42 % E exiting
%------------------------------------------------------------------------------