%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP440-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:43:48 PM UTC 2026
% Result : Unsatisfiable 0.19s 6.06s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 5 RR)
% Number of literals : 39 ( 38 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 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 : 118 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X1,X3))))))) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(c_0_2,axiom,
inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(X4,multiply(X1,X3))))))) = X4,
single_axiom ).
cnf(c_0_3,plain,
inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),X3),inverse(multiply(X4,multiply(X5,X3))))),X4)))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),multiply(multiply(inverse(X3),X4),inverse(multiply(X5,multiply(X6,X4))))),X5)),X6)))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
inverse(multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(inverse(X1),multiply(multiply(X3,X4),inverse(multiply(X5,multiply(X6,X4))))),X5)),X6)))) = multiply(X7,multiply(X8,multiply(multiply(inverse(X8),X9),inverse(multiply(X3,multiply(X7,X9)))))),
inference(spm,[status(thm)],[c_0_4,c_0_2]) ).
cnf(c_0_6,plain,
multiply(X1,multiply(X2,multiply(multiply(inverse(X2),X3),inverse(multiply(inverse(X4),multiply(X1,X3)))))) = X4,
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
inverse(multiply(X1,multiply(X2,multiply(X3,inverse(multiply(X4,multiply(X1,multiply(X5,multiply(multiply(inverse(X5),X6),inverse(multiply(inverse(X3),multiply(inverse(X2),X6)))))))))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_6]) ).
cnf(c_0_8,plain,
inverse(multiply(inverse(X1),multiply(X1,multiply(X2,inverse(multiply(X3,X2)))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_5]),c_0_4]) ).
cnf(c_0_9,plain,
multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(X3,inverse(multiply(X4,X3)))),X4))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_8]),c_0_4]) ).
cnf(c_0_10,plain,
inverse(multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(X3,X1)))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_9]),c_0_9]) ).
cnf(c_0_11,plain,
multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X3),X1))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_9]),c_0_9]) ).
cnf(c_0_12,plain,
multiply(X1,multiply(X2,multiply(multiply(inverse(X2),multiply(multiply(X3,multiply(inverse(X3),inverse(multiply(X4,X5)))),X4)),X5))) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
multiply(multiply(X1,multiply(X2,inverse(multiply(X3,X2)))),multiply(X4,multiply(inverse(X4),X3))) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_8]) ).
cnf(c_0_14,plain,
multiply(X1,multiply(X2,multiply(inverse(X2),multiply(multiply(X3,multiply(inverse(X3),inverse(X4))),X4)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_12]),c_0_12]) ).
cnf(c_0_15,plain,
multiply(X1,multiply(X2,inverse(multiply(multiply(multiply(X3,multiply(inverse(X3),inverse(X4))),X4),X2)))) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
inverse(multiply(multiply(X1,multiply(inverse(X1),inverse(multiply(X2,X3)))),multiply(X4,multiply(inverse(X4),X2)))) = X3,
inference(spm,[status(thm)],[c_0_10,c_0_10]) ).
cnf(c_0_17,plain,
inverse(multiply(inverse(X1),X1)) = multiply(multiply(X2,multiply(inverse(X2),inverse(X3))),X3),
inference(spm,[status(thm)],[c_0_2,c_0_15]) ).
cnf(c_0_18,plain,
inverse(inverse(multiply(inverse(X1),X1))) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
cnf(c_0_20,plain,
inverse(multiply(X1,multiply(inverse(multiply(X2,X1)),multiply(inverse(X3),X3)))) = X2,
inference(spm,[status(thm)],[c_0_10,c_0_19]) ).
cnf(c_0_21,plain,
inverse(multiply(X1,multiply(inverse(X2),X2))) = inverse(X1),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_22,plain,
inverse(multiply(inverse(X1),multiply(X1,multiply(multiply(X2,multiply(X3,inverse(multiply(X4,X3)))),X4)))) = inverse(X2),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_23,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_21]),c_0_4]) ).
cnf(c_0_24,plain,
multiply(X1,multiply(X2,multiply(inverse(X2),inverse(multiply(inverse(X3),X3))))) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_25,plain,
multiply(inverse(X1),multiply(X1,multiply(multiply(X2,multiply(X3,inverse(multiply(X4,X3)))),X4))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_22]),c_0_4]) ).
cnf(c_0_26,plain,
multiply(X1,inverse(multiply(inverse(X2),X2))) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_23]) ).
cnf(c_0_27,plain,
multiply(X1,multiply(X2,inverse(multiply(inverse(multiply(inverse(X3),X3)),X2)))) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_28,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(fof_simplification,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_0_29,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_23]),c_0_24]) ).
cnf(c_0_30,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_31,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
c_0_28 ).
cnf(c_0_32,plain,
multiply(multiply(X1,multiply(X2,inverse(multiply(multiply(inverse(inverse(X3)),inverse(multiply(inverse(X4),X3))),X2)))),X4) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_33,plain,
multiply(X1,inverse(multiply(X2,inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_34,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_35,plain,
inverse(multiply(X1,inverse(multiply(X2,X1)))) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_36,negated_conjecture,
multiply(multiply(inverse(X1),X1),a2) != a2,
inference(spm,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_37,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP440-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.41 % Computer : n008.cluster.edu
% 0.15/5.41 % Model : x86_64 x86_64
% 0.15/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.41 % Memory : 8046.5625MB
% 0.15/5.41 % OS : Linux 6.8.0-71-generic
% 0.15/5.41 % CPULimit : 300
% 0.15/5.41 % WCLimit : 300
% 0.15/5.41 % DateTime : Sun Sep 20 20:14:14 UTC 2026
% 0.15/5.41 % CPUTime :
% 0.15/5.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.49 Running first-order theorem proving
% 0.15/5.49 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
% 0.19/6.06 % Version: 3.5.1
% 0.19/6.06 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.19/6.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/6.06 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.19/6.06 % Starting new_bool_3 with 300s (1) cores
% 0.19/6.06 % Starting new_bool_1 with 300s (1) cores
% 0.19/6.06 % Starting sh5l with 300s (1) cores
% 0.19/6.06 % new_bool_1 with pid 3512797 completed with status 0
% 0.19/6.06 % Result found by new_bool_1
% 0.19/6.06 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.19/6.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/6.06 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.19/6.06 % Starting new_bool_3 with 300s (1) cores
% 0.19/6.06 % Starting new_bool_1 with 300s (1) cores
% 0.19/6.06 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/6.06 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/6.06 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.19/6.06 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/6.06 % Starting SubtermCWHack with 31s (1) cores
% 0.19/6.06 % SubtermCWHack with pid 3512803 completed with status 0
% 0.19/6.06 % Result found by SubtermCWHack
% 0.19/6.06 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.19/6.06 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/6.06 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.19/6.06 % Starting new_bool_3 with 300s (1) cores
% 0.19/6.06 % Starting new_bool_1 with 300s (1) cores
% 0.19/6.06 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.19/6.06 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/6.06 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.19/6.06 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/6.06 % Starting SubtermCWHack with 31s (1) cores
% 0.19/6.06 % Preprocessing time : 0.002 s
% 0.19/6.06
% 0.19/6.06 % Proof found!
% 0.19/6.06 % SZS status Unsatisfiable
% 0.19/6.06 % SZS output start CNFRefutation
% See solution above
% 0.19/6.06 % Parsed axioms : 2
% 0.19/6.06 % Removed by relevancy pruning/SinE : 0
% 0.19/6.06 % Initial clauses : 2
% 0.19/6.06 % Removed in clause preprocessing : 0
% 0.19/6.06 % Initial clauses in saturation : 2
% 0.19/6.06 % Processed clauses : 142
% 0.19/6.06 % ...of these trivial : 35
% 0.19/6.06 % ...subsumed : 38
% 0.19/6.06 % ...remaining for further processing : 69
% 0.19/6.06 % Other redundant clauses eliminated : 0
% 0.19/6.06 % Clauses deleted for lack of memory : 0
% 0.19/6.06 % Backward-subsumed : 1
% 0.19/6.06 % Backward-rewritten : 16
% 0.19/6.06 % Generated clauses : 13944
% 0.19/6.06 % ...of the previous two non-redundant : 13624
% 0.19/6.06 % ...aggressively subsumed : 0
% 0.19/6.06 % Contextual simplify-reflections : 0
% 0.19/6.06 % Paramodulations : 13944
% 0.19/6.06 % Factorizations : 0
% 0.19/6.06 % NegExts : 0
% 0.19/6.06 % Equation resolutions : 0
% 0.19/6.06 % Disequality decompositions : 0
% 0.19/6.06 % Total rewrite steps : 2108
% 0.19/6.06 % ...of those cached : 1264
% 0.19/6.06 % Propositional unsat checks : 0
% 0.19/6.06 % Propositional check models : 0
% 0.19/6.06 % Propositional check unsatisfiable : 0
% 0.19/6.06 % Propositional clauses : 0
% 0.19/6.06 % Propositional clauses after purity: 0
% 0.19/6.06 % Propositional unsat core size : 0
% 0.19/6.06 % Propositional preprocessing time : 0.000
% 0.19/6.06 % Propositional encoding time : 0.000
% 0.19/6.06 % Propositional solver time : 0.000
% 0.19/6.06 % Success case prop preproc time : 0.000
% 0.19/6.06 % Success case prop encoding time : 0.000
% 0.19/6.06 % Success case prop solver time : 0.000
% 0.19/6.06 % Current number of processed clauses : 52
% 0.19/6.06 % Positive orientable unit clauses : 44
% 0.19/6.06 % Positive unorientable unit clauses: 4
% 0.19/6.06 % Negative unit clauses : 4
% 0.19/6.06 % Non-unit-clauses : 0
% 0.19/6.06 % Current number of unprocessed clauses: 13347
% 0.19/6.06 % ...number of literals in the above : 13347
% 0.19/6.06 % Current number of archived formulas : 0
% 0.19/6.06 % Current number of archived clauses : 17
% 0.19/6.06 % Clause-clause subsumption calls (NU) : 0
% 0.19/6.06 % Rec. Clause-clause subsumption calls : 0
% 0.19/6.06 % Non-unit clause-clause subsumptions : 0
% 0.19/6.06 % Unit Clause-clause subsumption calls : 121
% 0.19/6.06 % Rewrite failures with RHS unbound : 107
% 0.19/6.06 % BW rewrite match attempts : 750
% 0.19/6.06 % BW rewrite match successes : 37
% 0.19/6.06 % Condensation attempts : 0
% 0.19/6.06 % Condensation successes : 0
% 0.19/6.06 % Termbank termtop insertions : 393884
% 0.19/6.06 % Search garbage collected termcells : 2
% 0.19/6.06
% 0.19/6.06 % -------------------------------------------------
% 0.19/6.06 % User time : 0.484 s
% 0.19/6.06 % System time : 0.031 s
% 0.19/6.06 % Total time : 0.515 s
% 0.19/6.06 % Maximum resident set size: 3632 pages
% 0.19/6.06
% 0.19/6.06 % -------------------------------------------------
% 0.19/6.06 % User time : 0.489 s
% 0.19/6.06 % System time : 0.035 s
% 0.19/6.06 % Total time : 0.525 s
% 0.19/6.06 % Maximum resident set size: 4608 pages
% 0.19/6.06 % E exiting
%------------------------------------------------------------------------------