%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL015-1 : 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 : n011.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 02:03:54 PM UTC 2026
% Result : Unsatisfiable 0.25s 0.55s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 7 RR)
% Number of literals : 45 ( 44 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(converse_multiplicativity_10,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_multiplicativity_10) ).
cnf(composition_identity_6,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_identity_6) ).
cnf(converse_idempotence_8,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_idempotence_8) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_cancellativity_11) ).
cnf(maddux1_join_commutativity_1,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux1_join_commutativity_1) ).
cnf(def_zero_13,axiom,
zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_zero_13) ).
cnf(maddux4_definiton_of_meet_4,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(def_top_12,axiom,
top = join(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_top_12) ).
cnf(maddux3_a_kind_of_de_Morgan_3,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux3_a_kind_of_de_Morgan_3) ).
cnf(maddux2_join_associativity_2,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux2_join_associativity_2) ).
cnf(composition_distributivity_7,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_distributivity_7) ).
cnf(goals_14,negated_conjecture,
composition(top,top) != top,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
cnf(c_0_12,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_13,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_14,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_16,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_18,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_19,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_20,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_21,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
cnf(c_0_22,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_24,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
cnf(c_0_26,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_19]),c_0_23]) ).
cnf(c_0_27,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
maddux3_a_kind_of_de_Morgan_3 ).
cnf(c_0_29,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_30,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_28,c_0_18]) ).
cnf(c_0_32,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,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_31,c_0_26]),c_0_25]),c_0_27]),c_0_18]) ).
cnf(c_0_34,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_35,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_26]),c_0_25]) ).
cnf(c_0_37,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_33,c_0_35]) ).
cnf(c_0_38,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_39,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,plain,
join(composition(top,X1),composition(X2,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,negated_conjecture,
composition(top,top) != top,
inference(fof_simplification,[status(thm)],[goals_14]) ).
cnf(c_0_42,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_23]),c_0_18]) ).
cnf(c_0_43,negated_conjecture,
composition(top,top) != top,
c_0_41 ).
cnf(c_0_44,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_42]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL015-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 % Computer : n011.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Mon Sep 21 03:59:12 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.48 Running first-order theorem proving
% 0.15/0.48 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
% 0.25/0.55 % Version: 3.5.1
% 0.25/0.55 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.55 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.55 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.55 % Starting sh5l with 300s (1) cores
% 0.25/0.55 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 928249 completed with status 0
% 0.25/0.55 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.25/0.55 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.55 % No SInE strategy applied
% 0.25/0.55 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.25/0.55 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.25/0.55 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 0.25/0.55 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 0.25/0.55 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 0.25/0.55 % H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with pid 928255 completed with status 0
% 0.25/0.55 % Result found by H----_047_B31_F1_PI_AE_R4_CS_SP_S2S
% 0.25/0.55 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.55 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.55 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.55 % No SInE strategy applied
% 0.25/0.55 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.25/0.55 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.55 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.55 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.25/0.55 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 0.25/0.55 % Preprocessing time : 0.002 s
% 0.25/0.55
% 0.25/0.55 % Proof found!
% 0.25/0.55 % SZS status Unsatisfiable
% 0.25/0.55 % SZS output start CNFRefutation
% See solution above
% 0.25/0.55 % Parsed axioms : 14
% 0.25/0.55 % Removed by relevancy pruning/SinE : 0
% 0.25/0.55 % Initial clauses : 14
% 0.25/0.55 % Removed in clause preprocessing : 1
% 0.25/0.55 % Initial clauses in saturation : 13
% 0.25/0.55 % Processed clauses : 126
% 0.25/0.55 % ...of these trivial : 44
% 0.25/0.55 % ...subsumed : 6
% 0.25/0.55 % ...remaining for further processing : 76
% 0.25/0.55 % Other redundant clauses eliminated : 0
% 0.25/0.55 % Clauses deleted for lack of memory : 0
% 0.25/0.55 % Backward-subsumed : 0
% 0.25/0.55 % Backward-rewritten : 20
% 0.25/0.55 % Generated clauses : 1320
% 0.25/0.55 % ...of the previous two non-redundant : 433
% 0.25/0.55 % ...aggressively subsumed : 0
% 0.25/0.55 % Contextual simplify-reflections : 0
% 0.25/0.55 % Paramodulations : 1320
% 0.25/0.55 % Factorizations : 0
% 0.25/0.55 % NegExts : 0
% 0.25/0.55 % Equation resolutions : 0
% 0.25/0.55 % Disequality decompositions : 0
% 0.25/0.55 % Total rewrite steps : 1898
% 0.25/0.55 % ...of those cached : 1453
% 0.25/0.55 % Propositional unsat checks : 0
% 0.25/0.55 % Propositional check models : 0
% 0.25/0.55 % Propositional check unsatisfiable : 0
% 0.25/0.55 % Propositional clauses : 0
% 0.25/0.55 % Propositional clauses after purity: 0
% 0.25/0.55 % Propositional unsat core size : 0
% 0.25/0.55 % Propositional preprocessing time : 0.000
% 0.25/0.55 % Propositional encoding time : 0.000
% 0.25/0.55 % Propositional solver time : 0.000
% 0.25/0.55 % Success case prop preproc time : 0.000
% 0.25/0.55 % Success case prop encoding time : 0.000
% 0.25/0.55 % Success case prop solver time : 0.000
% 0.25/0.55 % Current number of processed clauses : 56
% 0.25/0.55 % Positive orientable unit clauses : 54
% 0.25/0.55 % Positive unorientable unit clauses: 1
% 0.25/0.55 % Negative unit clauses : 1
% 0.25/0.55 % Non-unit-clauses : 0
% 0.25/0.55 % Current number of unprocessed clauses: 283
% 0.25/0.55 % ...number of literals in the above : 283
% 0.25/0.55 % Current number of archived formulas : 0
% 0.25/0.55 % Current number of archived clauses : 21
% 0.25/0.55 % Clause-clause subsumption calls (NU) : 0
% 0.25/0.55 % Rec. Clause-clause subsumption calls : 0
% 0.25/0.55 % Non-unit clause-clause subsumptions : 0
% 0.25/0.55 % Unit Clause-clause subsumption calls : 0
% 0.25/0.55 % Rewrite failures with RHS unbound : 0
% 0.25/0.55 % BW rewrite match attempts : 60
% 0.25/0.55 % BW rewrite match successes : 20
% 0.25/0.55 % Condensation attempts : 0
% 0.25/0.55 % Condensation successes : 0
% 0.25/0.55 % Termbank termtop insertions : 9479
% 0.25/0.55 % Search garbage collected termcells : 2
% 0.25/0.55
% 0.25/0.55 % -------------------------------------------------
% 0.25/0.55 % User time : 0.013 s
% 0.25/0.55 % System time : 0.005 s
% 0.25/0.55 % Total time : 0.018 s
% 0.25/0.55 % Maximum resident set size: 3388 pages
% 0.25/0.55
% 0.25/0.55 % -------------------------------------------------
% 0.25/0.55 % User time : 0.068 s
% 0.25/0.55 % System time : 0.026 s
% 0.25/0.55 % Total time : 0.094 s
% 0.25/0.55 % Maximum resident set size: 4608 pages
% 0.25/0.55 % E exiting
%------------------------------------------------------------------------------