%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP503-1 : 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 : n007.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 7.47s 1.65s
% Output : CNFRefutation 7.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 9 RR)
% Number of literals : 44 ( 43 equ; 8 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 2 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 : 130 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X1,inverse(double_divide(X2,X3))),double_divide(inverse(X2),inverse(double_divide(X4,double_divide(X1,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(double_divide(X1,inverse(double_divide(X2,X3))),double_divide(inverse(X2),inverse(double_divide(X4,double_divide(X1,X4))))) = X3,
single_axiom ).
cnf(c_0_4,plain,
double_divide(double_divide(X1,inverse(X2)),double_divide(inverse(double_divide(X3,inverse(double_divide(X4,X2)))),inverse(double_divide(X5,double_divide(X1,X5))))) = double_divide(inverse(X4),inverse(double_divide(X6,double_divide(X3,X6)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
double_divide(inverse(X1),inverse(double_divide(X2,double_divide(X3,X2)))) = double_divide(inverse(X1),inverse(double_divide(X4,double_divide(X3,X4)))),
inference(spm,[status(thm)],[c_0_4,c_0_4]) ).
cnf(c_0_6,plain,
inverse(double_divide(X1,double_divide(X2,X1))) = inverse(double_divide(X3,double_divide(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_5]),c_0_3]) ).
cnf(c_0_7,plain,
double_divide(double_divide(X1,inverse(double_divide(X2,double_divide(X3,X2)))),double_divide(inverse(X4),inverse(double_divide(X5,double_divide(X1,X5))))) = double_divide(X3,X4),
inference(spm,[status(thm)],[c_0_3,c_0_6]) ).
cnf(c_0_8,plain,
double_divide(X1,double_divide(X2,double_divide(X3,X2))) = double_divide(X1,double_divide(X4,double_divide(X3,X4))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_6]),c_0_7]) ).
cnf(c_0_9,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(X3,double_divide(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_8]),c_0_3]) ).
cnf(c_0_10,plain,
double_divide(double_divide(X1,inverse(double_divide(X2,X3))),double_divide(double_divide(X4,inverse(X5)),double_divide(inverse(double_divide(X1,inverse(double_divide(X2,X5)))),inverse(double_divide(X6,double_divide(X4,X6)))))) = X3,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_11,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(double_divide(X3,X2),double_divide(X4,double_divide(X3,X4))),
inference(spm,[status(thm)],[c_0_9,c_0_9]) ).
cnf(c_0_12,plain,
double_divide(double_divide(X1,inverse(double_divide(double_divide(X2,X3),X4))),double_divide(X2,double_divide(X1,inverse(double_divide(X5,double_divide(X3,X5)))))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_7]) ).
cnf(c_0_13,plain,
double_divide(X1,double_divide(inverse(double_divide(double_divide(inverse(double_divide(X2,double_divide(X3,X2))),X3),X4)),X1)) = X4,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
double_divide(X1,double_divide(inverse(double_divide(X2,double_divide(X3,X2))),X1)) = double_divide(X3,double_divide(inverse(double_divide(X4,double_divide(X5,X4))),X5)),
inference(spm,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_15,plain,
double_divide(double_divide(inverse(X1),inverse(double_divide(double_divide(double_divide(X2,inverse(double_divide(X1,X3))),X2),X4))),X3) = X4,
inference(spm,[status(thm)],[c_0_12,c_0_3]) ).
cnf(c_0_16,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(double_divide(X3,X2),double_divide(double_divide(X4,X3),double_divide(X5,double_divide(X4,X5)))),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_17,plain,
double_divide(double_divide(X1,inverse(double_divide(double_divide(X2,inverse(X3)),double_divide(inverse(double_divide(X4,inverse(double_divide(X5,X3)))),inverse(double_divide(X6,double_divide(X2,X6))))))),double_divide(inverse(inverse(X5)),inverse(double_divide(X7,double_divide(X1,X7))))) = inverse(double_divide(X8,double_divide(X4,X8))),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_18,plain,
double_divide(double_divide(inverse(double_divide(X1,double_divide(X2,X1))),X2),double_divide(X3,double_divide(inverse(X4),X3))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_13]) ).
cnf(c_0_19,plain,
double_divide(double_divide(inverse(double_divide(double_divide(X1,inverse(double_divide(X2,inverse(X2)))),X1)),inverse(double_divide(X3,X4))),X3) = X4,
inference(spm,[status(thm)],[c_0_15,c_0_15]) ).
cnf(c_0_20,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(double_divide(inverse(double_divide(double_divide(inverse(double_divide(X3,double_divide(X4,X3))),X4),X5)),X2),X5),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_21,plain,
double_divide(X1,inverse(double_divide(inverse(double_divide(X2,double_divide(X3,X2))),X3))) = inverse(double_divide(X4,double_divide(X1,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_7]),c_0_7]) ).
cnf(c_0_22,plain,
double_divide(X1,double_divide(inverse(double_divide(inverse(double_divide(X2,double_divide(inverse(double_divide(X3,inverse(X3))),X2))),X4)),X1)) = X4,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
double_divide(inverse(double_divide(inverse(double_divide(X1,double_divide(X2,X1))),X2)),inverse(X3)) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_21]),c_0_13]) ).
cnf(c_0_24,plain,
double_divide(inverse(X1),X1) = inverse(double_divide(X2,inverse(X2))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(fof_simplification,[status(thm)],[prove_these_axioms_2]) ).
cnf(c_0_26,plain,
inverse(double_divide(X1,inverse(X1))) = inverse(double_divide(X2,inverse(X2))),
inference(spm,[status(thm)],[c_0_24,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
c_0_25 ).
cnf(c_0_28,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_29,plain,
double_divide(X1,inverse(X1)) = double_divide(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_26]),c_0_18]) ).
cnf(c_0_30,negated_conjecture,
inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).
cnf(c_0_31,plain,
double_divide(inverse(X1),X1) = double_divide(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_24,c_0_24]) ).
cnf(c_0_32,plain,
double_divide(X1,double_divide(X2,X1)) = double_divide(inverse(X2),double_divide(X3,inverse(X3))),
inference(spm,[status(thm)],[c_0_9,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
inverse(double_divide(a2,double_divide(inverse(X1),X1))) != a2,
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_34,plain,
double_divide(inverse(double_divide(X1,double_divide(X2,X1))),X2) = inverse(double_divide(inverse(X3),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_23]),c_0_23]) ).
cnf(c_0_35,plain,
double_divide(X1,double_divide(double_divide(X2,inverse(X2)),X1)) = double_divide(inverse(X3),X3),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
inverse(double_divide(X1,double_divide(inverse(a2),X1))) != a2,
inference(spm,[status(thm)],[c_0_33,c_0_9]) ).
cnf(c_0_37,plain,
double_divide(inverse(inverse(double_divide(inverse(X1),X1))),inverse(X2)) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_38,plain,
double_divide(double_divide(X1,inverse(X1)),inverse(X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_35]),c_0_7]) ).
cnf(c_0_39,negated_conjecture,
inverse(double_divide(double_divide(X1,inverse(a2)),double_divide(X2,double_divide(X1,X2)))) != a2,
inference(spm,[status(thm)],[c_0_36,c_0_9]) ).
cnf(c_0_40,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_37]),c_0_38]),c_0_37]) ).
cnf(c_0_41,negated_conjecture,
inverse(inverse(a2)) != a2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_40]) ).
cnf(c_0_42,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_38,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP503-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.42 % Computer : n007.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sun Sep 20 20:13:06 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.48 Running first-order theorem proving
% 0.18/0.48 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
% 7.47/1.65 % Version: 3.5.1
% 7.47/1.65 % Preprocessing class: FSSSSMSSSSSNFFN.
% 7.47/1.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.47/1.65 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 7.47/1.65 % Starting new_bool_3 with 300s (1) cores
% 7.47/1.65 % Starting new_bool_1 with 300s (1) cores
% 7.47/1.65 % Starting sh5l with 300s (1) cores
% 7.47/1.65 % new_bool_1 with pid 3493112 completed with status 0
% 7.47/1.65 % Result found by new_bool_1
% 7.47/1.65 % Preprocessing class: FSSSSMSSSSSNFFN.
% 7.47/1.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.47/1.65 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 7.47/1.65 % Starting new_bool_3 with 300s (1) cores
% 7.47/1.65 % Starting new_bool_1 with 300s (1) cores
% 7.47/1.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 7.47/1.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 7.47/1.65 % Search class: FUUPS-FFSF21-MFFFFFNN
% 7.47/1.65 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 7.47/1.65 % Starting SubtermCWHack with 28s (1) cores
% 7.47/1.65 % SubtermCWHack with pid 3493119 completed with status 0
% 7.47/1.65 % Result found by SubtermCWHack
% 7.47/1.65 % Preprocessing class: FSSSSMSSSSSNFFN.
% 7.47/1.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.47/1.65 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 7.47/1.65 % Starting new_bool_3 with 300s (1) cores
% 7.47/1.65 % Starting new_bool_1 with 300s (1) cores
% 7.47/1.65 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 7.47/1.65 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 7.47/1.65 % Search class: FUUPS-FFSF21-MFFFFFNN
% 7.47/1.65 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 7.47/1.65 % Starting SubtermCWHack with 28s (1) cores
% 7.47/1.65 % Preprocessing time : 0.001 s
% 7.47/1.65
% 7.47/1.65 % Proof found!
% 7.47/1.65 % SZS status Unsatisfiable
% 7.47/1.65 % SZS output start CNFRefutation
% See solution above
% 7.47/1.66 % Parsed axioms : 3
% 7.47/1.66 % Removed by relevancy pruning/SinE : 0
% 7.47/1.66 % Initial clauses : 3
% 7.47/1.66 % Removed in clause preprocessing : 0
% 7.47/1.66 % Initial clauses in saturation : 3
% 7.47/1.66 % Processed clauses : 474
% 7.47/1.66 % ...of these trivial : 20
% 7.47/1.66 % ...subsumed : 366
% 7.47/1.66 % ...remaining for further processing : 88
% 7.47/1.66 % Other redundant clauses eliminated : 0
% 7.47/1.66 % Clauses deleted for lack of memory : 0
% 7.47/1.66 % Backward-subsumed : 5
% 7.47/1.66 % Backward-rewritten : 4
% 7.47/1.66 % Generated clauses : 37279
% 7.47/1.66 % ...of the previous two non-redundant : 36478
% 7.47/1.66 % ...aggressively subsumed : 0
% 7.47/1.66 % Contextual simplify-reflections : 0
% 7.47/1.66 % Paramodulations : 37279
% 7.47/1.66 % Factorizations : 0
% 7.47/1.66 % NegExts : 0
% 7.47/1.66 % Equation resolutions : 0
% 7.47/1.66 % Disequality decompositions : 0
% 7.47/1.66 % Total rewrite steps : 1663
% 7.47/1.66 % ...of those cached : 644
% 7.47/1.66 % Propositional unsat checks : 0
% 7.47/1.66 % Propositional check models : 0
% 7.47/1.66 % Propositional check unsatisfiable : 0
% 7.47/1.66 % Propositional clauses : 0
% 7.47/1.66 % Propositional clauses after purity: 0
% 7.47/1.66 % Propositional unsat core size : 0
% 7.47/1.66 % Propositional preprocessing time : 0.000
% 7.47/1.66 % Propositional encoding time : 0.000
% 7.47/1.66 % Propositional solver time : 0.000
% 7.47/1.66 % Success case prop preproc time : 0.000
% 7.47/1.66 % Success case prop encoding time : 0.000
% 7.47/1.66 % Success case prop solver time : 0.000
% 7.47/1.66 % Current number of processed clauses : 79
% 7.47/1.66 % Positive orientable unit clauses : 36
% 7.47/1.66 % Positive unorientable unit clauses: 36
% 7.47/1.66 % Negative unit clauses : 7
% 7.47/1.66 % Non-unit-clauses : 0
% 7.47/1.66 % Current number of unprocessed clauses: 35905
% 7.47/1.66 % ...number of literals in the above : 35905
% 7.47/1.66 % Current number of archived formulas : 0
% 7.47/1.66 % Current number of archived clauses : 9
% 7.47/1.66 % Clause-clause subsumption calls (NU) : 0
% 7.47/1.66 % Rec. Clause-clause subsumption calls : 0
% 7.47/1.66 % Non-unit clause-clause subsumptions : 0
% 7.47/1.66 % Unit Clause-clause subsumption calls : 652
% 7.47/1.66 % Rewrite failures with RHS unbound : 3119
% 7.47/1.66 % BW rewrite match attempts : 1828
% 7.47/1.66 % BW rewrite match successes : 279
% 7.47/1.66 % Condensation attempts : 0
% 7.47/1.66 % Condensation successes : 0
% 7.47/1.66 % Termbank termtop insertions : 1301813
% 7.47/1.66 % Search garbage collected termcells : 2
% 7.47/1.66
% 7.47/1.66 % -------------------------------------------------
% 7.47/1.66 % User time : 0.979 s
% 7.47/1.66 % System time : 0.042 s
% 7.47/1.66 % Total time : 1.022 s
% 7.47/1.66 % Maximum resident set size: 3632 pages
% 7.47/1.66
% 7.47/1.66 % -------------------------------------------------
% 7.47/1.66 % User time : 0.979 s
% 7.47/1.66 % System time : 0.048 s
% 7.47/1.66 % Total time : 1.027 s
% 7.47/1.66 % Maximum resident set size: 4864 pages
% 7.47/1.66 % E exiting
%------------------------------------------------------------------------------