%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL045-2 : 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 : n017.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 02:04:09 PM UTC 2026
% Result : Unsatisfiable 5.11s 1.31s
% Output : CNFRefutation 5.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of clauses : 64 ( 64 unt; 0 nHn; 9 RR)
% Number of literals : 64 ( 63 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 93 ( 7 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(converse_additivity_9,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_additivity_9) ).
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(dedekind_law_14,axiom,
join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-1.ax',dedekind_law_14) ).
cnf(goals_17,negated_conjecture,
join(sk1,composition(composition(sk1,converse(sk1)),sk1)) != composition(composition(sk1,converse(sk1)),sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
cnf(composition_associativity_5,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_associativity_5) ).
cnf(c_0_15,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_16,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_17,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_19,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_21,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_22,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_23,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_24,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
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_19,c_0_22]) ).
cnf(c_0_27,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
cnf(c_0_29,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]) ).
cnf(c_0_30,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
maddux3_a_kind_of_de_Morgan_3 ).
cnf(c_0_32,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_33,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_35,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,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_34,c_0_29]),c_0_28]),c_0_30]),c_0_21]) ).
cnf(c_0_37,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_40,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_39]) ).
cnf(c_0_41,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_42,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_43,plain,
join(X1,top) = top,
inference(spm,[status(thm)],[c_0_40,c_0_28]) ).
cnf(c_0_44,plain,
join(converse(X1),converse(complement(X1))) = converse(top),
inference(spm,[status(thm)],[c_0_41,c_0_28]) ).
cnf(c_0_45,axiom,
join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
dedekind_law_14 ).
cnf(c_0_46,plain,
join(composition(X1,X2),composition(top,X2)) = composition(top,X2),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
join(converse(X1),converse(top)) = converse(top),
inference(spm,[status(thm)],[c_0_40,c_0_44]) ).
cnf(c_0_48,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_34]),c_0_21]) ).
cnf(c_0_49,negated_conjecture,
join(sk1,composition(composition(sk1,converse(sk1)),sk1)) != composition(composition(sk1,converse(sk1)),sk1),
inference(fof_simplification,[status(thm)],[goals_17]) ).
cnf(c_0_50,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),complement(join(complement(X2),complement(composition(converse(X1),X3)))))) = composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),complement(join(complement(X2),complement(composition(converse(X1),X3))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]) ).
cnf(c_0_51,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_46,c_0_26]) ).
cnf(c_0_52,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_21,c_0_43]) ).
cnf(c_0_53,plain,
join(X1,converse(top)) = converse(top),
inference(spm,[status(thm)],[c_0_47,c_0_18]) ).
cnf(c_0_54,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(spm,[status(thm)],[c_0_48,c_0_38]) ).
cnf(c_0_55,negated_conjecture,
join(sk1,composition(composition(sk1,converse(sk1)),sk1)) != composition(composition(sk1,converse(sk1)),sk1),
c_0_49 ).
cnf(c_0_56,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
composition_associativity_5 ).
cnf(c_0_57,plain,
join(complement(join(complement(composition(converse(X1),X2)),complement(X3))),composition(complement(join(complement(converse(X1)),complement(composition(X3,converse(X2))))),complement(join(complement(X2),complement(composition(X1,X3)))))) = composition(complement(join(complement(converse(X1)),complement(composition(X3,converse(X2))))),complement(join(complement(X2),complement(composition(X1,X3))))),
inference(spm,[status(thm)],[c_0_50,c_0_18]) ).
cnf(c_0_58,plain,
join(X1,complement(composition(top,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_51]) ).
cnf(c_0_59,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,plain,
join(complement(X1),complement(composition(top,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_54,c_0_51]) ).
cnf(c_0_61,negated_conjecture,
join(sk1,composition(sk1,composition(converse(sk1),sk1))) != composition(sk1,composition(converse(sk1),sk1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_56]) ).
cnf(c_0_62,plain,
join(X1,composition(X1,composition(converse(X1),X1))) = composition(X1,composition(converse(X1),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_38]),c_0_21]),c_0_60]),c_0_38]),c_0_59]),c_0_30]),c_0_38]),c_0_37]),c_0_38]),c_0_38]),c_0_56]),c_0_59]),c_0_30]),c_0_38]),c_0_37]),c_0_38]),c_0_38]),c_0_56]) ).
cnf(c_0_63,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL045-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.51 % Computer : n017.cluster.edu
% 0.10/0.51 % Model : x86_64 x86_64
% 0.10/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.51 % Memory : 8046.5625MB
% 0.10/0.51 % OS : Linux 6.8.0-71-generic
% 0.10/0.51 % CPULimit : 300
% 0.10/0.51 % WCLimit : 300
% 0.10/0.51 % DateTime : Mon Sep 21 04:03:43 UTC 2026
% 0.10/0.52 % CPUTime :
% 0.10/0.52 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.56 Running first-order theorem proving
% 0.10/0.56 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
% 5.11/1.31 % Version: 3.5.1
% 5.11/1.31 % Preprocessing class: FSMSSMSSSSSNFFN.
% 5.11/1.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.11/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.11/1.31 % Starting new_bool_3 with 300s (1) cores
% 5.11/1.31 % Starting new_bool_1 with 300s (1) cores
% 5.11/1.31 % Starting sh5l with 300s (1) cores
% 5.11/1.31 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1387986 completed with status 0
% 5.11/1.31 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 5.11/1.31 % Preprocessing class: FSMSSMSSSSSNFFN.
% 5.11/1.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.11/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.11/1.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.11/1.31 % No SInE strategy applied
% 5.11/1.31 % Search class: FUUPM-FFMF21-DFFFFFNN
% 5.11/1.31 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.11/1.31 % Starting SubtermCWHack with 136s (1) cores
% 5.11/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 5.11/1.31 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 5.11/1.31 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 136s (1) cores
% 5.11/1.31 % Starting new_bool_3 with 136s (1) cores
% 5.11/1.31 % H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with pid 1387994 completed with status 0
% 5.11/1.31 % Result found by H----_047_B31_F1_PI_AE_R4_CS_SP_S2S
% 5.11/1.31 % Preprocessing class: FSMSSMSSSSSNFFN.
% 5.11/1.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 5.11/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 5.11/1.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 5.11/1.31 % No SInE strategy applied
% 5.11/1.31 % Search class: FUUPM-FFMF21-DFFFFFNN
% 5.11/1.31 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 5.11/1.31 % Starting SubtermCWHack with 136s (1) cores
% 5.11/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 5.11/1.31 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 5.11/1.31 % Preprocessing time : 0.001 s
% 5.11/1.31
% 5.11/1.31 % Proof found!
% 5.11/1.31 % SZS status Unsatisfiable
% 5.11/1.31 % SZS output start CNFRefutation
% See solution above
% 5.11/1.31 % Parsed axioms : 17
% 5.11/1.31 % Removed by relevancy pruning/SinE : 0
% 5.11/1.31 % Initial clauses : 17
% 5.11/1.31 % Removed in clause preprocessing : 1
% 5.11/1.31 % Initial clauses in saturation : 16
% 5.11/1.31 % Processed clauses : 2196
% 5.11/1.31 % ...of these trivial : 1354
% 5.11/1.31 % ...subsumed : 428
% 5.11/1.31 % ...remaining for further processing : 414
% 5.11/1.31 % Other redundant clauses eliminated : 0
% 5.11/1.31 % Clauses deleted for lack of memory : 0
% 5.11/1.31 % Backward-subsumed : 0
% 5.11/1.31 % Backward-rewritten : 83
% 5.11/1.31 % Generated clauses : 50914
% 5.11/1.31 % ...of the previous two non-redundant : 26146
% 5.11/1.31 % ...aggressively subsumed : 0
% 5.11/1.31 % Contextual simplify-reflections : 0
% 5.11/1.31 % Paramodulations : 50914
% 5.11/1.31 % Factorizations : 0
% 5.11/1.31 % NegExts : 0
% 5.11/1.31 % Equation resolutions : 0
% 5.11/1.31 % Disequality decompositions : 0
% 5.11/1.31 % Total rewrite steps : 161989
% 5.11/1.31 % ...of those cached : 143328
% 5.11/1.31 % Propositional unsat checks : 0
% 5.11/1.31 % Propositional check models : 0
% 5.11/1.31 % Propositional check unsatisfiable : 0
% 5.11/1.31 % Propositional clauses : 0
% 5.11/1.31 % Propositional clauses after purity: 0
% 5.11/1.31 % Propositional unsat core size : 0
% 5.11/1.31 % Propositional preprocessing time : 0.000
% 5.11/1.31 % Propositional encoding time : 0.000
% 5.11/1.31 % Propositional solver time : 0.000
% 5.11/1.31 % Success case prop preproc time : 0.000
% 5.11/1.31 % Success case prop encoding time : 0.000
% 5.11/1.31 % Success case prop solver time : 0.000
% 5.11/1.31 % Current number of processed clauses : 331
% 5.11/1.31 % Positive orientable unit clauses : 327
% 5.11/1.31 % Positive unorientable unit clauses: 4
% 5.11/1.31 % Negative unit clauses : 0
% 5.11/1.31 % Non-unit-clauses : 0
% 5.11/1.31 % Current number of unprocessed clauses: 23680
% 5.11/1.31 % ...number of literals in the above : 23680
% 5.11/1.31 % Current number of archived formulas : 0
% 5.11/1.31 % Current number of archived clauses : 84
% 5.11/1.31 % Clause-clause subsumption calls (NU) : 0
% 5.11/1.31 % Rec. Clause-clause subsumption calls : 0
% 5.11/1.31 % Non-unit clause-clause subsumptions : 0
% 5.11/1.31 % Unit Clause-clause subsumption calls : 21
% 5.11/1.31 % Rewrite failures with RHS unbound : 0
% 5.11/1.31 % BW rewrite match attempts : 2001
% 5.11/1.31 % BW rewrite match successes : 206
% 5.11/1.31 % Condensation attempts : 0
% 5.11/1.31 % Condensation successes : 0
% 5.11/1.31 % Termbank termtop insertions : 1063964
% 5.11/1.31 % Search garbage collected termcells : 2
% 5.11/1.31
% 5.11/1.31 % -------------------------------------------------
% 5.11/1.31 % User time : 0.658 s
% 5.11/1.31 % System time : 0.044 s
% 5.11/1.31 % Total time : 0.702 s
% 5.11/1.31 % Maximum resident set size: 3596 pages
% 5.11/1.31
% 5.11/1.31 % -------------------------------------------------
% 5.11/1.31 % User time : 3.329 s
% 5.11/1.31 % System time : 0.185 s
% 5.11/1.31 % Total time : 3.514 s
% 5.11/1.31 % Maximum resident set size: 4608 pages
% 5.11/1.31 % E exiting
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