%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL031+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 02:04:04 PM UTC 2026
% Result : Theorem 2.96s 1.00s
% Output : CNFRefutation 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 40 unt; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 10 ( 4 ~; 0 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(goals,conjecture,
! [X1,X2] :
( ( join(composition(converse(X2),X2),one) = one
& join(composition(converse(X1),X1),one) = one )
=> join(composition(converse(composition(X1,X2)),composition(X1,X2)),one) = one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(composition_distributivity,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(converse_additivity,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(c_0_9,plain,
! [X23,X24] : converse(composition(X23,X24)) = composition(converse(X24),converse(X23)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_10,plain,
! [X20] : converse(converse(X20)) = X20,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X2] :
( ( join(composition(converse(X2),X2),one) = one
& join(composition(converse(X1),X1),one) = one )
=> join(composition(converse(composition(X1,X2)),composition(X1,X2)),one) = one ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_12,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X16] : composition(X16,one) = X16,
inference(variable_rename,[status(thm)],[composition_identity]) ).
fof(c_0_15,negated_conjecture,
( join(composition(converse(composition(esk1_0,esk2_0)),composition(esk1_0,esk2_0)),one) != one
& join(composition(converse(esk2_0),esk2_0),one) = one
& join(composition(converse(esk1_0),esk1_0),one) = one ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_16,plain,
! [X4,X5] : join(X4,X5) = join(X5,X4),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_17,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,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_20,negated_conjecture,
join(composition(converse(esk2_0),esk2_0),one) = one,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_13]) ).
cnf(c_0_23,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
join(one,composition(converse(esk2_0),esk2_0)) = one,
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_25,plain,
! [X17,X18,X19] : composition(join(X17,X18),X19) = join(composition(X17,X19),composition(X18,X19)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_26,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
join(one,join(composition(converse(esk2_0),esk2_0),X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_29,plain,
! [X21,X22] : converse(join(X21,X22)) = join(converse(X21),converse(X22)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_30,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_22,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
join(composition(converse(esk1_0),esk1_0),one) = one,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_32,plain,
! [X13,X14,X15] : composition(X13,composition(X14,X15)) = composition(composition(X13,X14),X15),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_33,negated_conjecture,
join(one,composition(join(converse(esk2_0),X1),esk2_0)) = join(one,composition(X1,esk2_0)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_28,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
join(one,composition(converse(esk1_0),esk1_0)) = one,
inference(rw,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_37,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,negated_conjecture,
join(composition(converse(composition(esk1_0,esk2_0)),composition(esk1_0,esk2_0)),one) != one,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_39,negated_conjecture,
join(one,composition(converse(join(esk2_0,X1)),esk2_0)) = join(one,composition(converse(X1),esk2_0)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
join(X1,composition(converse(esk1_0),composition(esk1_0,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_30]) ).
cnf(c_0_41,negated_conjecture,
join(one,composition(converse(composition(esk1_0,esk2_0)),composition(esk1_0,esk2_0))) != one,
inference(rw,[status(thm)],[c_0_38,c_0_21]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_24]),c_0_17]),c_0_37]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL031+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 % Computer : n006.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Mon Sep 21 04:03:57 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.50 Running first-order theorem proving
% 0.20/0.50 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 2.96/1.00 % Version: 3.5.1
% 2.96/1.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.96/1.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.96/1.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.96/1.00 % Starting new_bool_3 with 300s (1) cores
% 2.96/1.00 % Starting new_bool_1 with 300s (1) cores
% 2.96/1.00 % Starting sh5l with 300s (1) cores
% 2.96/1.00 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1973482 completed with status 0
% 2.96/1.00 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.96/1.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.96/1.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.96/1.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.96/1.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.96/1.00 % No SInE strategy applied
% 2.96/1.00 % Search class: FUUPM-FFMF21-DFFFFFNN
% 2.96/1.00 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.96/1.00 % Starting SubtermCWHack with 136s (1) cores
% 2.96/1.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.96/1.00 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 2.96/1.00 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 136s (1) cores
% 2.96/1.00 % Starting new_bool_3 with 136s (1) cores
% 2.96/1.00 % new_bool_3 with pid 1973490 completed with status 0
% 2.96/1.00 % Result found by new_bool_3
% 2.96/1.00 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.96/1.00 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.96/1.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.96/1.00 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.96/1.00 % No SInE strategy applied
% 2.96/1.00 % Search class: FUUPM-FFMF21-DFFFFFNN
% 2.96/1.00 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.96/1.00 % Starting SubtermCWHack with 136s (1) cores
% 2.96/1.00 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.96/1.00 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 2.96/1.00 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 136s (1) cores
% 2.96/1.00 % Starting new_bool_3 with 136s (1) cores
% 2.96/1.00 % Preprocessing time : 0.002 s
% 2.96/1.00 % Presaturation interreduction done
% 2.96/1.00
% 2.96/1.00 % Proof found!
% 2.96/1.00 % SZS status Theorem
% 2.96/1.00 % SZS output start CNFRefutation
% See solution above
% 2.96/1.00 % Parsed axioms : 17
% 2.96/1.00 % Removed by relevancy pruning/SinE : 0
% 2.96/1.00 % Initial clauses : 19
% 2.96/1.00 % Removed in clause preprocessing : 1
% 2.96/1.00 % Initial clauses in saturation : 18
% 2.96/1.00 % Processed clauses : 1002
% 2.96/1.00 % ...of these trivial : 484
% 2.96/1.00 % ...subsumed : 172
% 2.96/1.00 % ...remaining for further processing : 346
% 2.96/1.00 % Other redundant clauses eliminated : 0
% 2.96/1.00 % Clauses deleted for lack of memory : 0
% 2.96/1.00 % Backward-subsumed : 0
% 2.96/1.00 % Backward-rewritten : 74
% 2.96/1.00 % Generated clauses : 16223
% 2.96/1.00 % ...of the previous two non-redundant : 9851
% 2.96/1.00 % ...aggressively subsumed : 0
% 2.96/1.00 % Contextual simplify-reflections : 0
% 2.96/1.00 % Paramodulations : 16223
% 2.96/1.00 % Factorizations : 0
% 2.96/1.00 % NegExts : 0
% 2.96/1.00 % Equation resolutions : 0
% 2.96/1.00 % Disequality decompositions : 0
% 2.96/1.00 % Total rewrite steps : 34363
% 2.96/1.00 % ...of those cached : 29295
% 2.96/1.00 % Propositional unsat checks : 0
% 2.96/1.00 % Propositional check models : 0
% 2.96/1.00 % Propositional check unsatisfiable : 0
% 2.96/1.00 % Propositional clauses : 0
% 2.96/1.00 % Propositional clauses after purity: 0
% 2.96/1.00 % Propositional unsat core size : 0
% 2.96/1.00 % Propositional preprocessing time : 0.000
% 2.96/1.00 % Propositional encoding time : 0.000
% 2.96/1.00 % Propositional solver time : 0.000
% 2.96/1.00 % Success case prop preproc time : 0.000
% 2.96/1.00 % Success case prop encoding time : 0.000
% 2.96/1.00 % Success case prop solver time : 0.000
% 2.96/1.00 % Current number of processed clauses : 254
% 2.96/1.00 % Positive orientable unit clauses : 248
% 2.96/1.00 % Positive unorientable unit clauses: 5
% 2.96/1.00 % Negative unit clauses : 1
% 2.96/1.00 % Non-unit-clauses : 0
% 2.96/1.00 % Current number of unprocessed clauses: 8807
% 2.96/1.00 % ...number of literals in the above : 8807
% 2.96/1.00 % Current number of archived formulas : 0
% 2.96/1.00 % Current number of archived clauses : 93
% 2.96/1.00 % Clause-clause subsumption calls (NU) : 0
% 2.96/1.00 % Rec. Clause-clause subsumption calls : 0
% 2.96/1.00 % Non-unit clause-clause subsumptions : 0
% 2.96/1.00 % Unit Clause-clause subsumption calls : 85
% 2.96/1.00 % Rewrite failures with RHS unbound : 0
% 2.96/1.00 % BW rewrite match attempts : 1425
% 2.96/1.00 % BW rewrite match successes : 250
% 2.96/1.00 % Condensation attempts : 0
% 2.96/1.00 % Condensation successes : 0
% 2.96/1.00 % Termbank termtop insertions : 349622
% 2.96/1.00 % Search garbage collected termcells : 44
% 2.96/1.00
% 2.96/1.00 % -------------------------------------------------
% 2.96/1.00 % User time : 0.387 s
% 2.96/1.00 % System time : 0.030 s
% 2.96/1.00 % Total time : 0.417 s
% 2.96/1.00 % Maximum resident set size: 3396 pages
% 2.96/1.00
% 2.96/1.00 % -------------------------------------------------
% 2.96/1.00 % User time : 1.973 s
% 2.96/1.00 % System time : 0.126 s
% 2.96/1.00 % Total time : 2.099 s
% 2.96/1.00 % Maximum resident set size: 4608 pages
% 2.96/1.00 % E exiting
%------------------------------------------------------------------------------