%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP500-1 : 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 : 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 12:39:57 PM UTC 2026
% Result : Unsatisfiable 0.22s 5.74s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 6 RR)
% Number of literals : 39 ( 38 equ; 4 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 116 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X1,double_divide(X2,X3))),double_divide(X4,double_divide(X2,X4))))) = X3,
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(multiply,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_3,axiom,
double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X1,double_divide(X2,X3))),double_divide(X4,double_divide(X2,X4))))) = X3,
single_axiom ).
cnf(c_0_4,plain,
double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X1,X2)),double_divide(X3,double_divide(inverse(X4),X3))))) = inverse(double_divide(inverse(double_divide(X4,double_divide(X5,X2))),double_divide(X6,double_divide(X5,X6)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
inverse(double_divide(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),X3)))),double_divide(X4,double_divide(X2,X4)))) = X3,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,plain,
double_divide(inverse(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),X3))))),inverse(double_divide(X3,double_divide(X4,double_divide(X5,X4))))) = double_divide(X2,X5),
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_7,plain,
double_divide(inverse(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),inverse(double_divide(X3,double_divide(X4,double_divide(inverse(X3),X5))))))))),X5) = double_divide(X2,X4),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_8,plain,
double_divide(inverse(inverse(double_divide(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),X3)))),double_divide(X4,double_divide(X2,inverse(X3)))))),X5) = double_divide(X4,X5),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
double_divide(X1,inverse(inverse(double_divide(inverse(double_divide(X2,double_divide(X3,double_divide(inverse(X2),X4)))),double_divide(X5,double_divide(X3,inverse(X4))))))) = double_divide(X1,X5),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_7]) ).
cnf(c_0_10,plain,
inverse(inverse(double_divide(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),X3)))),double_divide(X4,double_divide(X2,inverse(X3)))))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_5]) ).
cnf(c_0_11,plain,
double_divide(inverse(inverse(double_divide(X1,double_divide(X2,inverse(double_divide(inverse(double_divide(inverse(double_divide(X1,X3)),double_divide(X4,X3))),double_divide(X5,double_divide(X4,X5)))))))),X6) = double_divide(X2,X6),
inference(spm,[status(thm)],[c_0_7,c_0_4]) ).
cnf(c_0_12,plain,
inverse(inverse(double_divide(X1,double_divide(X2,inverse(double_divide(inverse(double_divide(inverse(double_divide(X1,X3)),double_divide(X4,X3))),double_divide(X5,double_divide(X4,X5)))))))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_10]) ).
cnf(c_0_13,plain,
inverse(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X3,X4)),double_divide(X5,X4)))))))) = inverse(inverse(double_divide(X3,double_divide(X2,X5)))),
inference(spm,[status(thm)],[c_0_12,c_0_6]) ).
cnf(c_0_14,plain,
double_divide(inverse(inverse(double_divide(X1,double_divide(X2,X3)))),inverse(double_divide(inverse(double_divide(inverse(double_divide(X1,X4)),double_divide(X3,X4))),double_divide(X5,double_divide(X6,X5))))) = double_divide(X2,X6),
inference(spm,[status(thm)],[c_0_6,c_0_13]) ).
cnf(c_0_15,plain,
inverse(double_divide(inverse(double_divide(X1,double_divide(X2,double_divide(X3,double_divide(X4,X3))))),double_divide(X5,double_divide(X2,X5)))) = double_divide(X4,inverse(X1)),
inference(spm,[status(thm)],[c_0_4,c_0_14]) ).
cnf(c_0_16,plain,
double_divide(inverse(X1),double_divide(X2,inverse(X1))) = double_divide(X3,double_divide(X2,X3)),
inference(spm,[status(thm)],[c_0_3,c_0_15]) ).
cnf(c_0_17,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(X3,double_divide(X2,X3)),
inference(spm,[status(thm)],[c_0_16,c_0_16]) ).
cnf(c_0_18,plain,
double_divide(inverse(X1),inverse(double_divide(inverse(double_divide(X2,double_divide(X3,X2))),double_divide(X4,double_divide(X3,X4))))) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_17]) ).
cnf(c_0_19,plain,
inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),inverse(double_divide(X3,double_divide(X4,X3))))))) = double_divide(X2,X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_18]),c_0_18]) ).
cnf(c_0_20,plain,
double_divide(inverse(X1),double_divide(X2,inverse(double_divide(X3,double_divide(X2,X3))))) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_21,plain,
double_divide(inverse(X1),inverse(X2)) = inverse(double_divide(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
inverse(double_divide(double_divide(inverse(double_divide(double_divide(X1,X2),X1)),X2),X3)) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_21]),c_0_21]),c_0_21]) ).
cnf(c_0_23,plain,
inverse(double_divide(double_divide(X1,inverse(X1)),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_20]),c_0_20]) ).
cnf(c_0_24,plain,
inverse(double_divide(inverse(double_divide(inverse(X1),X1)),X2)) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_25,plain,
inverse(inverse(double_divide(X1,double_divide(inverse(X2),X2)))) = inverse(X1),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_26,plain,
inverse(double_divide(X1,double_divide(inverse(X2),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_20]) ).
cnf(c_0_27,plain,
inverse(double_divide(inverse(double_divide(X1,double_divide(X2,double_divide(inverse(X1),X2)))),double_divide(X3,double_divide(X4,X3)))) = X4,
inference(spm,[status(thm)],[c_0_5,c_0_17]) ).
cnf(c_0_28,plain,
double_divide(inverse(X1),double_divide(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(fof_simplification,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_0_30,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24]) ).
cnf(c_0_31,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
c_0_29 ).
cnf(c_0_32,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_33,plain,
double_divide(X1,inverse(X1)) = double_divide(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_23,c_0_26]) ).
cnf(c_0_34,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_32]) ).
cnf(c_0_36,plain,
inverse(double_divide(b2,inverse(b2))) = double_divide(b2,inverse(b2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_33]),c_0_33]),c_0_33]) ).
cnf(c_0_37,plain,
double_divide(X1,double_divide(X2,inverse(X2))) = inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_34]),c_0_30]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP500-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/5.45 % Computer : n017.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Sun Sep 20 20:10:32 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/5.53 Running first-order theorem proving
% 0.22/5.53 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
% 0.22/5.74 % Version: 3.5.1
% 0.22/5.74 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.22/5.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.74 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.22/5.74 % Starting new_bool_3 with 300s (1) cores
% 0.22/5.74 % Starting new_bool_1 with 300s (1) cores
% 0.22/5.74 % Starting sh5l with 300s (1) cores
% 0.22/5.74 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 533540 completed with status 0
% 0.22/5.74 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.22/5.74 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.22/5.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.74 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.22/5.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/5.74 % No SInE strategy applied
% 0.22/5.74 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.22/5.74 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/5.74 % Starting SubtermCWHack with 136s (1) cores
% 0.22/5.74 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.22/5.74 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.22/5.74 % Starting new_bool_3 with 136s (1) cores
% 0.22/5.74 % Starting new_bool_1 with 136s (1) cores
% 0.22/5.74 % U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 533546 completed with status 0
% 0.22/5.74 % Result found by U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.22/5.74 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.22/5.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.74 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.22/5.74 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/5.74 % No SInE strategy applied
% 0.22/5.74 % Search class: FUUPF-FFSF21-DFFFFFNN
% 0.22/5.74 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/5.74 % Starting SubtermCWHack with 136s (1) cores
% 0.22/5.74 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.22/5.74 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.22/5.74 % Preprocessing time : 0.002 s
% 0.22/5.74 % Presaturation interreduction done
% 0.22/5.74
% 0.22/5.74 % Proof found!
% 0.22/5.74 % SZS status Unsatisfiable
% 0.22/5.74 % SZS output start CNFRefutation
% See solution above
% 0.22/5.74 % Parsed axioms : 3
% 0.22/5.74 % Removed by relevancy pruning/SinE : 0
% 0.22/5.74 % Initial clauses : 3
% 0.22/5.74 % Removed in clause preprocessing : 1
% 0.22/5.74 % Initial clauses in saturation : 2
% 0.22/5.74 % Processed clauses : 110
% 0.22/5.74 % ...of these trivial : 16
% 0.22/5.74 % ...subsumed : 43
% 0.22/5.74 % ...remaining for further processing : 51
% 0.22/5.74 % Other redundant clauses eliminated : 0
% 0.22/5.74 % Clauses deleted for lack of memory : 0
% 0.22/5.74 % Backward-subsumed : 0
% 0.22/5.74 % Backward-rewritten : 28
% 0.22/5.74 % Generated clauses : 3152
% 0.22/5.74 % ...of the previous two non-redundant : 2815
% 0.22/5.74 % ...aggressively subsumed : 0
% 0.22/5.74 % Contextual simplify-reflections : 0
% 0.22/5.74 % Paramodulations : 3152
% 0.22/5.74 % Factorizations : 0
% 0.22/5.74 % NegExts : 0
% 0.22/5.74 % Equation resolutions : 0
% 0.22/5.74 % Disequality decompositions : 0
% 0.22/5.74 % Total rewrite steps : 1487
% 0.22/5.74 % ...of those cached : 872
% 0.22/5.74 % Propositional unsat checks : 0
% 0.22/5.74 % Propositional check models : 0
% 0.22/5.74 % Propositional check unsatisfiable : 0
% 0.22/5.74 % Propositional clauses : 0
% 0.22/5.74 % Propositional clauses after purity: 0
% 0.22/5.74 % Propositional unsat core size : 0
% 0.22/5.74 % Propositional preprocessing time : 0.000
% 0.22/5.74 % Propositional encoding time : 0.000
% 0.22/5.74 % Propositional solver time : 0.000
% 0.22/5.74 % Success case prop preproc time : 0.000
% 0.22/5.74 % Success case prop encoding time : 0.000
% 0.22/5.74 % Success case prop solver time : 0.000
% 0.22/5.74 % Current number of processed clauses : 21
% 0.22/5.74 % Positive orientable unit clauses : 19
% 0.22/5.74 % Positive unorientable unit clauses: 1
% 0.22/5.74 % Negative unit clauses : 1
% 0.22/5.74 % Non-unit-clauses : 0
% 0.22/5.74 % Current number of unprocessed clauses: 2653
% 0.22/5.74 % ...number of literals in the above : 2653
% 0.22/5.74 % Current number of archived formulas : 0
% 0.22/5.74 % Current number of archived clauses : 31
% 0.22/5.74 % Clause-clause subsumption calls (NU) : 0
% 0.22/5.74 % Rec. Clause-clause subsumption calls : 0
% 0.22/5.74 % Non-unit clause-clause subsumptions : 0
% 0.22/5.74 % Unit Clause-clause subsumption calls : 74
% 0.22/5.74 % Rewrite failures with RHS unbound : 0
% 0.22/5.74 % BW rewrite match attempts : 235
% 0.22/5.74 % BW rewrite match successes : 41
% 0.22/5.74 % Condensation attempts : 0
% 0.22/5.74 % Condensation successes : 0
% 0.22/5.74 % Termbank termtop insertions : 53947
% 0.22/5.74 % Search garbage collected termcells : 2
% 0.22/5.74
% 0.22/5.74 % -------------------------------------------------
% 0.22/5.75 % User time : 0.071 s
% 0.22/5.75 % System time : 0.009 s
% 0.22/5.75 % Total time : 0.080 s
% 0.22/5.75 % Maximum resident set size: 3376 pages
% 0.22/5.75
% 0.22/5.75 % -------------------------------------------------
% 0.22/5.75 % User time : 0.363 s
% 0.22/5.75 % System time : 0.039 s
% 0.22/5.75 % Total time : 0.402 s
% 0.22/5.75 % Maximum resident set size: 4864 pages
% 0.22/5.75 % E exiting
%------------------------------------------------------------------------------