%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP615-1 : 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 : n019.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 12:44:21 PM UTC 2026
% Result : Unsatisfiable 0.60s 0.51s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of clauses : 41 ( 41 unt; 0 nHn; 5 RR)
% Number of literals : 41 ( 40 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(inverse(double_divide(inverse(double_divide(X1,inverse(X2))),X3)),double_divide(X1,X3)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
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(inverse(double_divide(inverse(double_divide(X1,inverse(X2))),X3)),double_divide(X1,X3)) = X2,
single_axiom ).
cnf(c_0_4,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_5,plain,
double_divide(multiply(X1,multiply(inverse(X2),X3)),double_divide(X3,X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_3,c_0_4]),c_0_4]) ).
cnf(c_0_6,plain,
multiply(double_divide(X1,X2),multiply(X2,multiply(inverse(X3),X1))) = inverse(X3),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
multiply(X1,multiply(double_divide(X2,X3),multiply(inverse(X4),multiply(X3,multiply(inverse(X1),X2))))) = inverse(X4),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_8,plain,
multiply(X1,multiply(inverse(X2),inverse(X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_7]),c_0_5]) ).
cnf(c_0_9,plain,
double_divide(multiply(double_divide(X1,X2),multiply(inverse(X3),multiply(X2,multiply(inverse(X4),X1)))),X4) = X3,
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_10,plain,
double_divide(inverse(X1),double_divide(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_11,plain,
double_divide(multiply(inverse(X1),inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_7]),c_0_5]) ).
cnf(c_0_12,plain,
double_divide(multiply(X1,X2),double_divide(inverse(X3),X3)) = double_divide(X2,X1),
inference(spm,[status(thm)],[c_0_10,c_0_4]) ).
cnf(c_0_13,plain,
double_divide(multiply(X1,inverse(X1)),inverse(X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_4]) ).
cnf(c_0_14,plain,
double_divide(multiply(inverse(X1),multiply(X2,X3)),double_divide(X3,X2)) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_4]) ).
cnf(c_0_15,plain,
double_divide(inverse(X1),double_divide(multiply(inverse(X1),X2),double_divide(X2,inverse(X3)))) = X3,
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_16,plain,
multiply(inverse(X1),multiply(X2,inverse(X2))) = inverse(X1),
inference(spm,[status(thm)],[c_0_4,c_0_13]) ).
cnf(c_0_17,plain,
double_divide(inverse(X1),double_divide(inverse(inverse(X2)),inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_8]) ).
cnf(c_0_18,plain,
double_divide(inverse(X1),double_divide(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_13]) ).
cnf(c_0_19,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_19]) ).
cnf(c_0_22,plain,
multiply(X1,multiply(X2,inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_19]) ).
cnf(c_0_23,plain,
double_divide(X1,X2) = double_divide(X2,X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
multiply(inverse(X1),multiply(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_25,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_23]),c_0_4]) ).
cnf(c_0_26,plain,
inverse(multiply(X1,X2)) = double_divide(X2,X1),
inference(spm,[status(thm)],[c_0_19,c_0_4]) ).
cnf(c_0_27,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
double_divide(multiply(X1,X2),inverse(X2)) = inverse(X1),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_29,plain,
multiply(X1,double_divide(X1,X2)) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_20]),c_0_25]) ).
cnf(c_0_30,plain,
double_divide(multiply(X1,X2),inverse(X1)) = inverse(X2),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
multiply(double_divide(X1,X2),multiply(X2,multiply(X3,X1))) = X3,
inference(spm,[status(thm)],[c_0_6,c_0_19]) ).
cnf(c_0_32,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(fof_simplification,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_0_33,plain,
double_divide(inverse(X1),multiply(X1,X2)) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_4]) ).
cnf(c_0_34,plain,
double_divide(multiply(X1,X2),X3) = double_divide(X1,multiply(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_4]),c_0_26]) ).
cnf(c_0_35,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
c_0_32 ).
cnf(c_0_36,plain,
double_divide(X1,multiply(X2,X3)) = double_divide(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_31]),c_0_4]),c_0_26]),c_0_34]),c_0_34]) ).
cnf(c_0_37,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_34]),c_0_4]) ).
cnf(c_0_38,negated_conjecture,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[c_0_35,c_0_25]) ).
cnf(c_0_39,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_36]),c_0_4]),c_0_37]),c_0_37]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP615-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:18:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.60/0.50 % Version: 3.5.1
% 0.60/0.50 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.60/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.60/0.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.60/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.60/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.60/0.50 % Starting sh5l with 300s (1) cores
% 0.60/0.50 % new_bool_3 with pid 844260 completed with status 0
% 0.60/0.50 % Result found by new_bool_3
% 0.60/0.50 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.60/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.60/0.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.60/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.60/0.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.60/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.60/0.50 % Search class: FUUPS-FFSF21-DFFFFFNN
% 0.60/0.50 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.60/0.50 % Starting SubtermCWHack with 31s (1) cores
% 0.60/0.50 % SubtermCWHack with pid 844268 completed with status 0
% 0.60/0.50 % Result found by SubtermCWHack
% 0.60/0.50 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.60/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.60/0.51 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.60/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.60/0.51 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.60/0.51 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.60/0.51 % Search class: FUUPS-FFSF21-DFFFFFNN
% 0.60/0.51 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.60/0.51 % Starting SubtermCWHack with 31s (1) cores
% 0.60/0.51 % Preprocessing time : 0.001 s
% 0.60/0.51
% 0.60/0.51 % Proof found!
% 0.60/0.51 % SZS status Unsatisfiable
% 0.60/0.51 % SZS output start CNFRefutation
% See solution above
% 0.60/0.51 % Parsed axioms : 3
% 0.60/0.51 % Removed by relevancy pruning/SinE : 0
% 0.60/0.51 % Initial clauses : 3
% 0.60/0.51 % Removed in clause preprocessing : 0
% 0.60/0.51 % Initial clauses in saturation : 3
% 0.60/0.51 % Processed clauses : 327
% 0.60/0.51 % ...of these trivial : 110
% 0.60/0.51 % ...subsumed : 113
% 0.60/0.51 % ...remaining for further processing : 104
% 0.60/0.51 % Other redundant clauses eliminated : 0
% 0.60/0.51 % Clauses deleted for lack of memory : 0
% 0.60/0.51 % Backward-subsumed : 0
% 0.60/0.51 % Backward-rewritten : 61
% 0.60/0.51 % Generated clauses : 5624
% 0.60/0.51 % ...of the previous two non-redundant : 4589
% 0.60/0.51 % ...aggressively subsumed : 0
% 0.60/0.51 % Contextual simplify-reflections : 0
% 0.60/0.51 % Paramodulations : 5624
% 0.60/0.51 % Factorizations : 0
% 0.60/0.51 % NegExts : 0
% 0.60/0.51 % Equation resolutions : 0
% 0.60/0.51 % Disequality decompositions : 0
% 0.60/0.51 % Total rewrite steps : 7802
% 0.60/0.51 % ...of those cached : 5329
% 0.60/0.51 % Propositional unsat checks : 0
% 0.60/0.51 % Propositional check models : 0
% 0.60/0.51 % Propositional check unsatisfiable : 0
% 0.60/0.51 % Propositional clauses : 0
% 0.60/0.51 % Propositional clauses after purity: 0
% 0.60/0.51 % Propositional unsat core size : 0
% 0.60/0.51 % Propositional preprocessing time : 0.000
% 0.60/0.51 % Propositional encoding time : 0.000
% 0.60/0.51 % Propositional solver time : 0.000
% 0.60/0.51 % Success case prop preproc time : 0.000
% 0.60/0.51 % Success case prop encoding time : 0.000
% 0.60/0.51 % Success case prop solver time : 0.000
% 0.60/0.51 % Current number of processed clauses : 43
% 0.60/0.51 % Positive orientable unit clauses : 37
% 0.60/0.51 % Positive unorientable unit clauses: 6
% 0.60/0.51 % Negative unit clauses : 0
% 0.60/0.51 % Non-unit-clauses : 0
% 0.60/0.51 % Current number of unprocessed clauses: 3913
% 0.60/0.51 % ...number of literals in the above : 3913
% 0.60/0.51 % Current number of archived formulas : 0
% 0.60/0.51 % Current number of archived clauses : 61
% 0.60/0.51 % Clause-clause subsumption calls (NU) : 0
% 0.60/0.51 % Rec. Clause-clause subsumption calls : 0
% 0.60/0.51 % Non-unit clause-clause subsumptions : 0
% 0.60/0.51 % Unit Clause-clause subsumption calls : 80
% 0.60/0.51 % Rewrite failures with RHS unbound : 24
% 0.60/0.51 % BW rewrite match attempts : 375
% 0.60/0.51 % BW rewrite match successes : 240
% 0.60/0.51 % Condensation attempts : 0
% 0.60/0.51 % Condensation successes : 0
% 0.60/0.51 % Termbank termtop insertions : 69671
% 0.60/0.51 % Search garbage collected termcells : 2
% 0.60/0.51
% 0.60/0.51 % -------------------------------------------------
% 0.60/0.51 % User time : 0.066 s
% 0.60/0.51 % System time : 0.008 s
% 0.60/0.51 % Total time : 0.074 s
% 0.60/0.51 % Maximum resident set size: 3632 pages
% 0.60/0.51
% 0.60/0.51 % -------------------------------------------------
% 0.60/0.51 % User time : 0.066 s
% 0.60/0.51 % System time : 0.014 s
% 0.60/0.51 % Total time : 0.080 s
% 0.60/0.51 % Maximum resident set size: 4608 pages
% 0.60/0.51 % E exiting
%------------------------------------------------------------------------------