%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP486-1 : 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 : n016.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 12:39:55 PM UTC 2026
% Result : Unsatisfiable 0.37s 0.49s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 7 RR)
% Number of literals : 45 ( 44 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c_0_3,axiom,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
single_axiom ).
cnf(c_0_4,plain,
double_divide(double_divide(double_divide(double_divide(X1,identity),X2),X3),double_divide(X2,identity)) = double_divide(double_divide(X1,X3),double_divide(identity,identity)),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
double_divide(double_divide(double_divide(X1,identity),double_divide(double_divide(X1,X2),double_divide(identity,identity))),double_divide(identity,identity)) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
multiply ).
cnf(c_0_7,plain,
double_divide(X1,multiply(double_divide(identity,identity),double_divide(X2,X1))) = double_divide(double_divide(X2,double_divide(identity,identity)),double_divide(identity,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_5]),c_0_6]) ).
cnf(c_0_8,plain,
double_divide(double_divide(double_divide(X1,X2),double_divide(double_divide(multiply(X2,X1),X3),double_divide(identity,identity))),double_divide(identity,identity)) = X3,
inference(spm,[status(thm)],[c_0_3,c_0_6]) ).
cnf(c_0_9,plain,
multiply(double_divide(identity,identity),double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity)))) = double_divide(X3,identity),
inference(spm,[status(thm)],[c_0_6,c_0_3]) ).
cnf(c_0_10,plain,
double_divide(double_divide(X1,double_divide(multiply(X2,X1),double_divide(X2,identity))),double_divide(identity,identity)) = identity,
inference(spm,[status(thm)],[c_0_3,c_0_6]) ).
cnf(c_0_11,plain,
double_divide(double_divide(identity,identity),multiply(double_divide(identity,identity),X1)) = double_divide(X1,double_divide(identity,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_12,plain,
multiply(double_divide(identity,identity),double_divide(X1,double_divide(identity,multiply(double_divide(X2,identity),multiply(X2,X1))))) = multiply(identity,identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_6]),c_0_6]) ).
cnf(c_0_13,plain,
double_divide(double_divide(X1,double_divide(identity,multiply(double_divide(X2,identity),multiply(X2,X1)))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_10]),c_0_6]) ).
cnf(c_0_14,plain,
multiply(double_divide(identity,identity),double_divide(double_divide(X1,identity),double_divide(double_divide(X1,X2),double_divide(identity,identity)))) = double_divide(X2,identity),
inference(spm,[status(thm)],[c_0_9,c_0_4]) ).
cnf(c_0_15,plain,
double_divide(double_divide(identity,identity),multiply(identity,identity)) = double_divide(identity,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_16,plain,
double_divide(double_divide(identity,identity),double_divide(X1,identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_14]),c_0_5]) ).
cnf(c_0_17,plain,
double_divide(double_divide(multiply(identity,X1),X2),double_divide(identity,identity)) = double_divide(double_divide(X1,X2),double_divide(identity,identity)),
inference(spm,[status(thm)],[c_0_4,c_0_6]) ).
cnf(c_0_18,plain,
multiply(identity,identity) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_15]),c_0_6]),c_0_16]),c_0_17]),c_0_16]) ).
cnf(c_0_19,plain,
double_divide(identity,identity) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_18]),c_0_6]),c_0_18]) ).
cnf(c_0_20,plain,
double_divide(identity,double_divide(X1,identity)) = X1,
inference(rw,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_21,plain,
double_divide(multiply(identity,X1),double_divide(identity,identity)) = double_divide(multiply(X2,X1),double_divide(X2,identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_10]),c_0_6]) ).
cnf(c_0_22,plain,
double_divide(identity,multiply(X1,X2)) = double_divide(X2,X1),
inference(spm,[status(thm)],[c_0_20,c_0_6]) ).
cnf(c_0_23,plain,
multiply(X1,multiply(identity,X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_19]),c_0_6]),c_0_19]),c_0_6]) ).
cnf(c_0_24,plain,
multiply(double_divide(identity,identity),multiply(identity,X1)) = multiply(double_divide(X2,identity),multiply(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_21]),c_0_6]) ).
cnf(c_0_25,plain,
double_divide(multiply(identity,X1),X2) = double_divide(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_22]) ).
cnf(c_0_26,plain,
multiply(double_divide(X1,identity),multiply(X1,X2)) = multiply(double_divide(X3,identity),multiply(X3,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_24]) ).
cnf(c_0_27,plain,
multiply(identity,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_20]) ).
cnf(c_0_28,plain,
multiply(double_divide(X1,identity),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19]),c_0_27]) ).
cnf(c_0_29,plain,
double_divide(identity,X1) = double_divide(X1,identity),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_30,plain,
multiply(multiply(X1,X2),double_divide(X2,identity)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_19]),c_0_6]),c_0_19]),c_0_6]) ).
cnf(c_0_31,plain,
multiply(double_divide(identity,X1),multiply(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
multiply(multiply(X1,X2),double_divide(identity,X2)) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_33,plain,
double_divide(double_divide(X1,identity),multiply(X2,X1)) = double_divide(identity,X2),
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_34,plain,
multiply(double_divide(X1,X2),X2) = double_divide(identity,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_22]) ).
cnf(c_0_35,plain,
double_divide(identity,double_divide(X1,X2)) = multiply(X2,X1),
inference(rw,[status(thm)],[c_0_6,c_0_29]) ).
cnf(c_0_36,plain,
multiply(X1,double_divide(X1,X2)) = double_divide(X2,identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_28]),c_0_22]) ).
cnf(c_0_37,plain,
double_divide(double_divide(double_divide(double_divide(X1,identity),X2),X3),double_divide(X2,identity)) = multiply(X3,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4,c_0_19]),c_0_6]) ).
cnf(c_0_38,plain,
double_divide(double_divide(X1,identity),double_divide(identity,X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_39,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_36]),c_0_20]) ).
cnf(c_0_40,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(fof_simplification,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_0_41,plain,
double_divide(double_divide(multiply(X1,X2),X3),X2) = multiply(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_42,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
c_0_40 ).
cnf(c_0_43,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_41]),c_0_35]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP486-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 20:19:08 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.37/0.49 % Version: 3.5.1
% 0.37/0.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.37/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.37/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.37/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.37/0.49 % Starting sh5l with 300s (1) cores
% 0.37/0.49 % new_bool_3 with pid 708337 completed with status 0
% 0.37/0.49 % Result found by new_bool_3
% 0.37/0.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.37/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.37/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.37/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.37/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.37/0.49 % Search class: FUUPS-FFSF22-MFFFFFNN
% 0.37/0.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.49 % Starting SubtermCWHack with 31s (1) cores
% 0.37/0.49 % SubtermCWHack with pid 708342 completed with status 0
% 0.37/0.49 % Result found by SubtermCWHack
% 0.37/0.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.37/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.37/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.37/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.37/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.37/0.49 % Search class: FUUPS-FFSF22-MFFFFFNN
% 0.37/0.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.49 % Starting SubtermCWHack with 31s (1) cores
% 0.37/0.49 % Preprocessing time : 0.001 s
% 0.37/0.49
% 0.37/0.49 % Proof found!
% 0.37/0.49 % SZS status Unsatisfiable
% 0.37/0.49 % SZS output start CNFRefutation
% See solution above
% 0.37/0.49 % Parsed axioms : 5
% 0.37/0.49 % Removed by relevancy pruning/SinE : 2
% 0.37/0.49 % Initial clauses : 3
% 0.37/0.49 % Removed in clause preprocessing : 0
% 0.37/0.49 % Initial clauses in saturation : 3
% 0.37/0.49 % Processed clauses : 610
% 0.37/0.49 % ...of these trivial : 201
% 0.37/0.49 % ...subsumed : 252
% 0.37/0.49 % ...remaining for further processing : 157
% 0.37/0.49 % Other redundant clauses eliminated : 0
% 0.37/0.49 % Clauses deleted for lack of memory : 0
% 0.37/0.49 % Backward-subsumed : 2
% 0.37/0.49 % Backward-rewritten : 114
% 0.37/0.49 % Generated clauses : 5850
% 0.37/0.49 % ...of the previous two non-redundant : 3370
% 0.37/0.49 % ...aggressively subsumed : 0
% 0.37/0.49 % Contextual simplify-reflections : 0
% 0.37/0.49 % Paramodulations : 5850
% 0.37/0.49 % Factorizations : 0
% 0.37/0.49 % NegExts : 0
% 0.37/0.49 % Equation resolutions : 0
% 0.37/0.49 % Disequality decompositions : 0
% 0.37/0.49 % Total rewrite steps : 9442
% 0.37/0.49 % ...of those cached : 8072
% 0.37/0.49 % Propositional unsat checks : 0
% 0.37/0.49 % Propositional check models : 0
% 0.37/0.49 % Propositional check unsatisfiable : 0
% 0.37/0.49 % Propositional clauses : 0
% 0.37/0.49 % Propositional clauses after purity: 0
% 0.37/0.49 % Propositional unsat core size : 0
% 0.37/0.49 % Propositional preprocessing time : 0.000
% 0.37/0.49 % Propositional encoding time : 0.000
% 0.37/0.49 % Propositional solver time : 0.000
% 0.37/0.49 % Success case prop preproc time : 0.000
% 0.37/0.49 % Success case prop encoding time : 0.000
% 0.37/0.49 % Success case prop solver time : 0.000
% 0.37/0.49 % Current number of processed clauses : 41
% 0.37/0.49 % Positive orientable unit clauses : 40
% 0.37/0.49 % Positive unorientable unit clauses: 1
% 0.37/0.49 % Negative unit clauses : 0
% 0.37/0.49 % Non-unit-clauses : 0
% 0.37/0.49 % Current number of unprocessed clauses: 1215
% 0.37/0.49 % ...number of literals in the above : 1215
% 0.37/0.49 % Current number of archived formulas : 0
% 0.37/0.49 % Current number of archived clauses : 116
% 0.37/0.49 % Clause-clause subsumption calls (NU) : 0
% 0.37/0.49 % Rec. Clause-clause subsumption calls : 0
% 0.37/0.49 % Non-unit clause-clause subsumptions : 0
% 0.37/0.49 % Unit Clause-clause subsumption calls : 19
% 0.37/0.49 % Rewrite failures with RHS unbound : 156
% 0.37/0.49 % BW rewrite match attempts : 220
% 0.37/0.49 % BW rewrite match successes : 107
% 0.37/0.49 % Condensation attempts : 0
% 0.37/0.49 % Condensation successes : 0
% 0.37/0.49 % Termbank termtop insertions : 72760
% 0.37/0.49 % Search garbage collected termcells : 7
% 0.37/0.49
% 0.37/0.49 % -------------------------------------------------
% 0.37/0.49 % User time : 0.056 s
% 0.37/0.49 % System time : 0.004 s
% 0.37/0.49 % Total time : 0.060 s
% 0.37/0.49 % Maximum resident set size: 3376 pages
% 0.37/0.49
% 0.37/0.49 % -------------------------------------------------
% 0.37/0.49 % User time : 0.057 s
% 0.37/0.49 % System time : 0.009 s
% 0.37/0.49 % Total time : 0.066 s
% 0.37/0.49 % Maximum resident set size: 4608 pages
% 0.37/0.49 % E exiting
%------------------------------------------------------------------------------