%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP443-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:39:49 PM UTC 2026
% Result : Unsatisfiable 0.32s 0.83s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 6 RR)
% Number of literals : 51 ( 50 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 139 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(X1,X2))))))) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(c_0_2,axiom,
inverse(multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(X1,X2))))))) = X4,
single_axiom ).
cnf(c_0_3,plain,
inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X4,X1)))),multiply(multiply(X5,inverse(X5)),X3)))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
inverse(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,X4)))),multiply(multiply(multiply(X5,inverse(X5)),X2),multiply(multiply(X6,inverse(X6)),X3)))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
inverse(multiply(multiply(multiply(X1,inverse(X1)),X2),multiply(multiply(multiply(X3,inverse(X3)),X4),multiply(multiply(X5,inverse(X5)),X6)))) = multiply(multiply(X7,inverse(X7)),inverse(multiply(X2,multiply(X4,X6)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_6,plain,
multiply(multiply(b2,inverse(b2)),inverse(multiply(inverse(multiply(X1,multiply(X2,X3))),multiply(X1,X2)))) = X3,
inference(rw,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
multiply(multiply(b2,inverse(b2)),X1) = multiply(multiply(X2,inverse(X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_3]),c_0_2]) ).
cnf(c_0_8,plain,
multiply(b2,inverse(b2)) = multiply(X1,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_7]),c_0_2]) ).
cnf(c_0_9,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_10,plain,
inverse(multiply(X1,multiply(inverse(X1),multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,multiply(X4,inverse(X4)))))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_9]) ).
cnf(c_0_11,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(X3,X4))),multiply(X2,X3)))) = X4,
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
cnf(c_0_12,plain,
multiply(multiply(b2,inverse(b2)),inverse(multiply(inverse(multiply(X1,multiply(X2,inverse(X2)))),multiply(X1,X3)))) = inverse(X3),
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
cnf(c_0_13,plain,
inverse(multiply(X1,multiply(inverse(X1),X2))) = inverse(multiply(X3,multiply(inverse(X3),X2))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(X3,inverse(X3)))),multiply(X2,X4)))) = inverse(X4),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_15,plain,
inverse(multiply(inverse(X1),multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,multiply(inverse(X4),X2))))))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_13]) ).
cnf(c_0_16,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(X2,multiply(inverse(X2),X3))),multiply(X4,inverse(X4))))) = X3,
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_17,plain,
inverse(multiply(X1,multiply(inverse(X1),inverse(inverse(X2))))) = inverse(multiply(X2,multiply(X3,inverse(X3)))),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_18,plain,
multiply(X1,inverse(X1)) = multiply(multiply(X2,multiply(inverse(X2),X3)),inverse(multiply(X4,multiply(inverse(X4),X3)))),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_19,plain,
inverse(multiply(inverse(X1),multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),X3))) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
multiply(X1,multiply(inverse(X1),inverse(inverse(X2)))) = multiply(X2,multiply(X3,inverse(X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_17]),c_0_15]) ).
cnf(c_0_21,plain,
multiply(multiply(inverse(X1),multiply(inverse(inverse(inverse(multiply(X2,multiply(inverse(X2),X3))))),X3)),X1) = multiply(b2,inverse(b2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_18]) ).
cnf(c_0_22,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(X3,multiply(inverse(X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_15]) ).
cnf(c_0_23,plain,
multiply(X1,multiply(inverse(X1),inverse(multiply(X2,inverse(X2))))) = multiply(b2,inverse(b2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]) ).
cnf(c_0_24,plain,
multiply(X1,multiply(X2,multiply(inverse(X2),X3))) = multiply(X4,multiply(inverse(X4),multiply(inverse(inverse(X1)),X3))),
inference(spm,[status(thm)],[c_0_22,c_0_22]) ).
cnf(c_0_25,plain,
multiply(inverse(X1),inverse(multiply(X2,inverse(X2)))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_23]),c_0_14]) ).
cnf(c_0_26,plain,
multiply(X1,multiply(inverse(X1),multiply(inverse(multiply(X2,multiply(inverse(X2),X3))),X3))) = multiply(b2,inverse(b2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_24]),c_0_19]) ).
cnf(c_0_27,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_28,plain,
multiply(inverse(X1),multiply(inverse(multiply(X2,multiply(inverse(X2),X3))),X3)) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_26]),c_0_14]) ).
cnf(c_0_29,plain,
inverse(multiply(X1,multiply(X2,multiply(multiply(multiply(X3,multiply(X4,multiply(multiply(X5,inverse(X5)),inverse(multiply(X6,multiply(X3,X4)))))),X6),inverse(multiply(X7,multiply(X1,X2))))))) = X7,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_30,plain,
inverse(multiply(inverse(X1),multiply(inverse(multiply(X2,inverse(X2))),multiply(X3,inverse(X3))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_27]),c_0_27]) ).
cnf(c_0_31,plain,
multiply(X1,multiply(inverse(multiply(X2,multiply(inverse(X2),X3))),X3)) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_15]) ).
cnf(c_0_32,plain,
multiply(X1,multiply(X2,multiply(multiply(X3,inverse(X3)),inverse(multiply(inverse(X4),multiply(X1,X2)))))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_27]) ).
cnf(c_0_33,plain,
multiply(multiply(X1,inverse(X1)),multiply(inverse(multiply(X2,inverse(X2))),multiply(multiply(X3,inverse(X3)),X4))) = X4,
inference(spm,[status(thm)],[c_0_11,c_0_30]) ).
cnf(c_0_34,plain,
multiply(X1,multiply(inverse(multiply(X2,multiply(X3,inverse(X3)))),inverse(inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_9]) ).
cnf(c_0_35,plain,
inverse(multiply(inverse(X1),multiply(X2,inverse(X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_27]) ).
cnf(c_0_36,plain,
inverse(inverse(multiply(X1,multiply(X2,inverse(X2))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_33]),c_0_27]) ).
cnf(c_0_37,plain,
multiply(X1,multiply(X2,inverse(inverse(inverse(X2))))) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
multiply(multiply(inverse(X1),multiply(inverse(multiply(X2,inverse(X2))),multiply(X3,inverse(X3)))),X1) = multiply(b2,inverse(b2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_30]),c_0_18]) ).
cnf(c_0_39,plain,
multiply(inverse(multiply(X1,multiply(X2,inverse(X2)))),X1) = multiply(b2,inverse(b2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_36]),c_0_18]) ).
cnf(c_0_40,plain,
multiply(multiply(X1,inverse(X1)),X2) = inverse(inverse(inverse(inverse(X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_37]),c_0_36]) ).
cnf(c_0_41,plain,
inverse(multiply(X1,inverse(X1))) = multiply(b2,inverse(b2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_36]),c_0_35]) ).
cnf(c_0_42,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(fof_simplification,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_0_43,plain,
multiply(X1,multiply(b2,inverse(b2))) = X1,
inference(rw,[status(thm)],[c_0_27,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
c_0_42 ).
cnf(c_0_45,plain,
multiply(inverse(X1),X1) = multiply(b2,inverse(b2)),
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_21,c_0_43]),c_0_43]),c_0_41]),c_0_41]),c_0_41]),c_0_43]) ).
cnf(c_0_46,negated_conjecture,
multiply(multiply(b2,inverse(b2)),a2) != a2,
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_47,plain,
inverse(inverse(X1)) = X1,
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_19,c_0_43]),c_0_43]),c_0_41]),c_0_41]),c_0_41]),c_0_43]) ).
cnf(c_0_48,negated_conjecture,
multiply(multiply(X1,inverse(X1)),a2) != a2,
inference(spm,[status(thm)],[c_0_46,c_0_9]) ).
cnf(c_0_49,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_47]),c_0_47]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP443-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.47 % Computer : n026.cluster.edu
% 0.23/0.47 % Model : x86_64 x86_64
% 0.23/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.47 % Memory : 8046.5625MB
% 0.23/0.47 % OS : Linux 6.8.0-71-generic
% 0.23/0.47 % CPULimit : 300
% 0.23/0.47 % WCLimit : 300
% 0.23/0.47 % DateTime : Sun Sep 20 20:16:23 UTC 2026
% 0.23/0.48 % CPUTime :
% 0.23/0.48 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.57 Running first-order theorem proving
% 0.26/0.57 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
% 0.32/0.83 % Version: 3.5.1
% 0.32/0.83 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.32/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.32/0.83 % Starting new_bool_3 with 300s (1) cores
% 0.32/0.83 % Starting new_bool_1 with 300s (1) cores
% 0.32/0.83 % Starting sh5l with 300s (1) cores
% 0.32/0.83 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 506277 completed with status 0
% 0.32/0.83 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.32/0.83 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.32/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.32/0.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.32/0.83 % No SInE strategy applied
% 0.32/0.83 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.32/0.83 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.32/0.83 % Starting SubtermCWHack with 136s (1) cores
% 0.32/0.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.32/0.83 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.32/0.83 % Starting new_bool_3 with 136s (1) cores
% 0.32/0.83 % Starting new_bool_1 with 136s (1) cores
% 0.32/0.83 % U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 506281 completed with status 0
% 0.32/0.83 % Result found by U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.32/0.83 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.32/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.32/0.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.32/0.83 % No SInE strategy applied
% 0.32/0.83 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.32/0.83 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.32/0.83 % Starting SubtermCWHack with 136s (1) cores
% 0.32/0.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.32/0.83 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.32/0.83 % Preprocessing time : 0.001 s
% 0.32/0.83 % Presaturation interreduction done
% 0.32/0.83
% 0.32/0.83 % Proof found!
% 0.32/0.83 % SZS status Unsatisfiable
% 0.32/0.83 % SZS output start CNFRefutation
% See solution above
% 0.32/0.84 % Parsed axioms : 2
% 0.32/0.84 % Removed by relevancy pruning/SinE : 0
% 0.32/0.84 % Initial clauses : 2
% 0.32/0.84 % Removed in clause preprocessing : 0
% 0.32/0.84 % Initial clauses in saturation : 2
% 0.32/0.84 % Processed clauses : 427
% 0.32/0.84 % ...of these trivial : 76
% 0.32/0.84 % ...subsumed : 271
% 0.32/0.84 % ...remaining for further processing : 80
% 0.32/0.84 % Other redundant clauses eliminated : 0
% 0.32/0.84 % Clauses deleted for lack of memory : 0
% 0.32/0.84 % Backward-subsumed : 4
% 0.32/0.84 % Backward-rewritten : 30
% 0.32/0.84 % Generated clauses : 10556
% 0.32/0.84 % ...of the previous two non-redundant : 9309
% 0.32/0.84 % ...aggressively subsumed : 0
% 0.32/0.84 % Contextual simplify-reflections : 0
% 0.32/0.84 % Paramodulations : 10556
% 0.32/0.84 % Factorizations : 0
% 0.32/0.84 % NegExts : 0
% 0.32/0.84 % Equation resolutions : 0
% 0.32/0.84 % Disequality decompositions : 0
% 0.32/0.84 % Total rewrite steps : 7555
% 0.32/0.84 % ...of those cached : 6351
% 0.32/0.84 % Propositional unsat checks : 0
% 0.32/0.84 % Propositional check models : 0
% 0.32/0.84 % Propositional check unsatisfiable : 0
% 0.32/0.84 % Propositional clauses : 0
% 0.32/0.84 % Propositional clauses after purity: 0
% 0.32/0.84 % Propositional unsat core size : 0
% 0.32/0.84 % Propositional preprocessing time : 0.000
% 0.32/0.84 % Propositional encoding time : 0.000
% 0.32/0.84 % Propositional solver time : 0.000
% 0.32/0.84 % Success case prop preproc time : 0.000
% 0.32/0.84 % Success case prop encoding time : 0.000
% 0.32/0.84 % Success case prop solver time : 0.000
% 0.32/0.84 % Current number of processed clauses : 44
% 0.32/0.84 % Positive orientable unit clauses : 38
% 0.32/0.84 % Positive unorientable unit clauses: 4
% 0.32/0.84 % Negative unit clauses : 2
% 0.32/0.84 % Non-unit-clauses : 0
% 0.32/0.84 % Current number of unprocessed clauses: 8749
% 0.32/0.84 % ...number of literals in the above : 8749
% 0.32/0.84 % Current number of archived formulas : 0
% 0.32/0.84 % Current number of archived clauses : 36
% 0.32/0.84 % Clause-clause subsumption calls (NU) : 0
% 0.32/0.84 % Rec. Clause-clause subsumption calls : 0
% 0.32/0.84 % Non-unit clause-clause subsumptions : 0
% 0.32/0.84 % Unit Clause-clause subsumption calls : 80
% 0.32/0.84 % Rewrite failures with RHS unbound : 0
% 0.32/0.84 % BW rewrite match attempts : 530
% 0.32/0.84 % BW rewrite match successes : 65
% 0.32/0.84 % Condensation attempts : 0
% 0.32/0.84 % Condensation successes : 0
% 0.32/0.84 % Termbank termtop insertions : 273100
% 0.32/0.84 % Search garbage collected termcells : 2
% 0.32/0.84
% 0.32/0.84 % -------------------------------------------------
% 0.32/0.84 % User time : 0.202 s
% 0.32/0.84 % System time : 0.020 s
% 0.32/0.84 % Total time : 0.222 s
% 0.32/0.84 % Maximum resident set size: 3632 pages
% 0.32/0.84
% 0.32/0.84 % -------------------------------------------------
% 0.32/0.84 % User time : 1.009 s
% 0.32/0.84 % System time : 0.082 s
% 0.32/0.84 % Total time : 1.091 s
% 0.32/0.84 % Maximum resident set size: 4864 pages
% 0.32/0.84 % E exiting
%------------------------------------------------------------------------------