%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL002+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 : n019.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 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 3 sgn 26 !; 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(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(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(goals,conjecture,
! [X1] : join(X1,top) = top,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_8,plain,
! [X23,X24] : converse(composition(X23,X24)) = composition(converse(X24),converse(X23)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_9,plain,
! [X20] : converse(converse(X20)) = X20,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_10,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X16] : composition(X16,one) = X16,
inference(variable_rename,[status(thm)],[composition_identity]) ).
cnf(c_0_13,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_15,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_16,plain,
! [X4,X5] : join(X4,X5) = join(X5,X4),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_17,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_11]) ).
fof(c_0_18,plain,
! [X6,X7,X8] : join(X6,join(X7,X8)) = join(join(X6,X7),X8),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
fof(c_0_19,plain,
! [X27] : top = join(X27,complement(X27)),
inference(variable_rename,[status(thm)],[def_top]) ).
cnf(c_0_20,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
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,
converse(one) = one,
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_23,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_17,c_0_22]) ).
fof(c_0_27,negated_conjecture,
~ ! [X1] : join(X1,top) = top,
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_28,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_30,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_22]),c_0_26]) ).
fof(c_0_31,negated_conjecture,
join(esk1_0,top) != top,
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
cnf(c_0_32,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_28,c_0_24]) ).
cnf(c_0_33,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_24]),c_0_21]) ).
cnf(c_0_34,negated_conjecture,
join(esk1_0,top) != top,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_35,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
join(top,esk1_0) != top,
inference(rw,[status(thm)],[c_0_34,c_0_21]) ).
cnf(c_0_37,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL002+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 03:57:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.44 % Version: 3.5.1
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1638170 completed with status 0
% 0.14/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.44 % No SInE strategy applied
% 0.14/0.44 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.14/0.44 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.44 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 0.14/0.44 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 0.14/0.44 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 0.14/0.44 % SubtermCWHack with pid 1638174 completed with status 0
% 0.14/0.44 % Result found by SubtermCWHack
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.44 % No SInE strategy applied
% 0.14/0.44 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.14/0.44 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.44 % Preprocessing time : 0.001 s
% 0.14/0.44
% 0.14/0.44 % Proof found!
% 0.14/0.44 % SZS status Theorem
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44 % Parsed axioms : 14
% 0.14/0.44 % Removed by relevancy pruning/SinE : 0
% 0.14/0.44 % Initial clauses : 14
% 0.14/0.44 % Removed in clause preprocessing : 1
% 0.14/0.44 % Initial clauses in saturation : 13
% 0.14/0.44 % Processed clauses : 64
% 0.14/0.44 % ...of these trivial : 18
% 0.14/0.44 % ...subsumed : 8
% 0.14/0.44 % ...remaining for further processing : 38
% 0.14/0.44 % Other redundant clauses eliminated : 0
% 0.14/0.44 % Clauses deleted for lack of memory : 0
% 0.14/0.44 % Backward-subsumed : 0
% 0.14/0.44 % Backward-rewritten : 10
% 0.14/0.44 % Generated clauses : 282
% 0.14/0.44 % ...of the previous two non-redundant : 206
% 0.14/0.44 % ...aggressively subsumed : 0
% 0.14/0.44 % Contextual simplify-reflections : 0
% 0.14/0.44 % Paramodulations : 282
% 0.14/0.44 % Factorizations : 0
% 0.14/0.44 % NegExts : 0
% 0.14/0.44 % Equation resolutions : 0
% 0.14/0.44 % Disequality decompositions : 0
% 0.14/0.44 % Total rewrite steps : 270
% 0.14/0.44 % ...of those cached : 134
% 0.14/0.44 % Propositional unsat checks : 0
% 0.14/0.44 % Propositional check models : 0
% 0.14/0.44 % Propositional check unsatisfiable : 0
% 0.14/0.44 % Propositional clauses : 0
% 0.14/0.44 % Propositional clauses after purity: 0
% 0.14/0.44 % Propositional unsat core size : 0
% 0.14/0.44 % Propositional preprocessing time : 0.000
% 0.14/0.44 % Propositional encoding time : 0.000
% 0.14/0.44 % Propositional solver time : 0.000
% 0.14/0.44 % Success case prop preproc time : 0.000
% 0.14/0.44 % Success case prop encoding time : 0.000
% 0.14/0.44 % Success case prop solver time : 0.000
% 0.14/0.44 % Current number of processed clauses : 28
% 0.14/0.44 % Positive orientable unit clauses : 27
% 0.14/0.44 % Positive unorientable unit clauses: 1
% 0.14/0.44 % Negative unit clauses : 0
% 0.14/0.44 % Non-unit-clauses : 0
% 0.14/0.44 % Current number of unprocessed clauses: 154
% 0.14/0.44 % ...number of literals in the above : 154
% 0.14/0.44 % Current number of archived formulas : 0
% 0.14/0.44 % Current number of archived clauses : 11
% 0.14/0.44 % Clause-clause subsumption calls (NU) : 0
% 0.14/0.44 % Rec. Clause-clause subsumption calls : 0
% 0.14/0.44 % Non-unit clause-clause subsumptions : 0
% 0.14/0.44 % Unit Clause-clause subsumption calls : 0
% 0.14/0.44 % Rewrite failures with RHS unbound : 0
% 0.14/0.44 % BW rewrite match attempts : 16
% 0.14/0.44 % BW rewrite match successes : 14
% 0.14/0.44 % Condensation attempts : 0
% 0.14/0.44 % Condensation successes : 0
% 0.14/0.44 % Termbank termtop insertions : 3166
% 0.14/0.44 % Search garbage collected termcells : 9
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.005 s
% 0.14/0.44 % System time : 0.003 s
% 0.14/0.44 % Total time : 0.008 s
% 0.14/0.44 % Maximum resident set size: 3648 pages
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.015 s
% 0.14/0.44 % System time : 0.015 s
% 0.14/0.44 % Total time : 0.030 s
% 0.14/0.44 % Maximum resident set size: 4864 pages
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------