%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP502-1 : 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 : n018.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 0.15s 5.74s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 5 RR)
% Number of literals : 30 ( 29 equ; 4 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 : 104 ( 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/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(multiply,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
file('/export/starexec/sandbox/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,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(fof_simplification,[status(thm)],[prove_these_axioms_1]) ).
cnf(c_0_20,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_21,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_22,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_23,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
c_0_19 ).
cnf(c_0_24,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_25,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_20,c_0_21]) ).
cnf(c_0_26,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_22]),c_0_13]) ).
cnf(c_0_27,negated_conjecture,
inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24]) ).
cnf(c_0_28,plain,
double_divide(inverse(X1),X1) = inverse(double_divide(X2,inverse(X2))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP502-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.53 % Computer : n018.cluster.edu
% 0.11/5.53 % Model : x86_64 x86_64
% 0.11/5.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.53 % Memory : 8046.5625MB
% 0.11/5.53 % OS : Linux 6.8.0-71-generic
% 0.11/5.53 % CPULimit : 300
% 0.11/5.53 % WCLimit : 300
% 0.11/5.53 % DateTime : Sun Sep 20 20:17:18 UTC 2026
% 0.11/5.53 % CPUTime :
% 0.11/5.53 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.57 Running first-order theorem proving
% 0.11/5.57 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
% 0.15/5.74 % Version: 3.5.1
% 0.15/5.74 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.74 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.74 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.74 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.74 % Starting sh5l with 300s (1) cores
% 0.15/5.74 % new_bool_1 with pid 99105 completed with status 0
% 0.15/5.74 % Result found by new_bool_1
% 0.15/5.74 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.74 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.74 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.74 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.74 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.74 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.74 % Search class: FUUPS-FFSF21-MFFFFFNN
% 0.15/5.74 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.74 % Starting SubtermCWHack with 28s (1) cores
% 0.15/5.74 % SubtermCWHack with pid 99111 completed with status 0
% 0.15/5.74 % Result found by SubtermCWHack
% 0.15/5.74 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.74 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.74 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.74 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.74 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.74 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.74 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.74 % Search class: FUUPS-FFSF21-MFFFFFNN
% 0.15/5.74 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.74 % Starting SubtermCWHack with 28s (1) cores
% 0.15/5.74 % Preprocessing time : 0.001 s
% 0.15/5.74
% 0.15/5.74 % Proof found!
% 0.15/5.74 % SZS status Unsatisfiable
% 0.15/5.74 % SZS output start CNFRefutation
% See solution above
% 0.15/5.75 % Parsed axioms : 3
% 0.15/5.75 % Removed by relevancy pruning/SinE : 0
% 0.15/5.75 % Initial clauses : 3
% 0.15/5.75 % Removed in clause preprocessing : 0
% 0.15/5.75 % Initial clauses in saturation : 3
% 0.15/5.75 % Processed clauses : 247
% 0.15/5.75 % ...of these trivial : 15
% 0.15/5.75 % ...subsumed : 182
% 0.15/5.75 % ...remaining for further processing : 50
% 0.15/5.75 % Other redundant clauses eliminated : 0
% 0.15/5.75 % Clauses deleted for lack of memory : 0
% 0.15/5.75 % Backward-subsumed : 3
% 0.15/5.75 % Backward-rewritten : 1
% 0.15/5.75 % Generated clauses : 14014
% 0.15/5.75 % ...of the previous two non-redundant : 13398
% 0.15/5.75 % ...aggressively subsumed : 0
% 0.15/5.75 % Contextual simplify-reflections : 0
% 0.15/5.75 % Paramodulations : 14014
% 0.15/5.75 % Factorizations : 0
% 0.15/5.75 % NegExts : 0
% 0.15/5.75 % Equation resolutions : 0
% 0.15/5.75 % Disequality decompositions : 0
% 0.15/5.75 % Total rewrite steps : 613
% 0.15/5.75 % ...of those cached : 225
% 0.15/5.75 % Propositional unsat checks : 0
% 0.15/5.75 % Propositional check models : 0
% 0.15/5.75 % Propositional check unsatisfiable : 0
% 0.15/5.75 % Propositional clauses : 0
% 0.15/5.75 % Propositional clauses after purity: 0
% 0.15/5.75 % Propositional unsat core size : 0
% 0.15/5.75 % Propositional preprocessing time : 0.000
% 0.15/5.75 % Propositional encoding time : 0.000
% 0.15/5.75 % Propositional solver time : 0.000
% 0.15/5.75 % Success case prop preproc time : 0.000
% 0.15/5.75 % Success case prop encoding time : 0.000
% 0.15/5.75 % Success case prop solver time : 0.000
% 0.15/5.75 % Current number of processed clauses : 46
% 0.15/5.75 % Positive orientable unit clauses : 21
% 0.15/5.75 % Positive unorientable unit clauses: 24
% 0.15/5.75 % Negative unit clauses : 1
% 0.15/5.75 % Non-unit-clauses : 0
% 0.15/5.75 % Current number of unprocessed clauses: 13015
% 0.15/5.75 % ...number of literals in the above : 13015
% 0.15/5.75 % Current number of archived formulas : 0
% 0.15/5.75 % Current number of archived clauses : 4
% 0.15/5.75 % Clause-clause subsumption calls (NU) : 0
% 0.15/5.75 % Rec. Clause-clause subsumption calls : 0
% 0.15/5.75 % Non-unit clause-clause subsumptions : 0
% 0.15/5.75 % Unit Clause-clause subsumption calls : 232
% 0.15/5.75 % Rewrite failures with RHS unbound : 1657
% 0.15/5.75 % BW rewrite match attempts : 743
% 0.15/5.75 % BW rewrite match successes : 156
% 0.15/5.75 % Condensation attempts : 0
% 0.15/5.75 % Condensation successes : 0
% 0.15/5.75 % Termbank termtop insertions : 446139
% 0.15/5.75 % Search garbage collected termcells : 2
% 0.15/5.75
% 0.15/5.75 % -------------------------------------------------
% 0.15/5.75 % User time : 0.135 s
% 0.15/5.75 % System time : 0.016 s
% 0.15/5.75 % Total time : 0.151 s
% 0.15/5.75 % Maximum resident set size: 3632 pages
% 0.15/5.75
% 0.15/5.75 % -------------------------------------------------
% 0.15/5.75 % User time : 0.136 s
% 0.15/5.75 % System time : 0.019 s
% 0.15/5.75 % Total time : 0.154 s
% 0.15/5.75 % Maximum resident set size: 4608 pages
% 0.15/5.75 % E exiting
%------------------------------------------------------------------------------