%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP594-1 : 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 : n012.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 12:40:19 PM UTC 2026
% Result : Unsatisfiable 0.03s 0.34s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 6 RR)
% Number of literals : 35 ( 34 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 72 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(double_divide(X3,X2)))))) = 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,
inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(double_divide(X3,X2)))))) = X3,
single_axiom ).
cnf(c_0_4,plain,
inverse(double_divide(double_divide(double_divide(X1,X2),inverse(double_divide(X3,X2))),X3)) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,X3)))) = double_divide(double_divide(X3,X4),inverse(double_divide(X2,X4))),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,plain,
inverse(double_divide(double_divide(X1,inverse(double_divide(X2,inverse(double_divide(X3,X4))))),inverse(double_divide(X1,X3)))) = double_divide(X2,X4),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_7,plain,
double_divide(double_divide(inverse(double_divide(X1,X2)),X3),inverse(double_divide(X2,X3))) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_8,plain,
double_divide(inverse(double_divide(double_divide(X1,inverse(double_divide(X2,X3))),X2)),X3) = X1,
inference(spm,[status(thm)],[c_0_4,c_0_6]) ).
cnf(c_0_9,plain,
inverse(double_divide(double_divide(double_divide(inverse(double_divide(X1,X2)),X3),X3),inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_7]) ).
cnf(c_0_10,plain,
double_divide(inverse(double_divide(X1,X2)),inverse(double_divide(inverse(X1),X3))) = double_divide(X2,X3),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
inverse(double_divide(inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,X3)))),X2)) = X3,
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_12,plain,
double_divide(inverse(double_divide(double_divide(X1,X2),inverse(X3))),X2) = inverse(double_divide(X3,X1)),
inference(spm,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_13,plain,
inverse(inverse(double_divide(double_divide(X1,X2),X1))) = X2,
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_7]) ).
cnf(c_0_15,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_15]) ).
cnf(c_0_17,plain,
double_divide(double_divide(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_15]),c_0_14]) ).
cnf(c_0_18,plain,
double_divide(X1,X2) = double_divide(X2,X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
inverse(double_divide(inverse(X1),inverse(double_divide(X1,X2)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_18]),c_0_18]),c_0_16]) ).
cnf(c_0_20,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_21,plain,
double_divide(inverse(X1),inverse(double_divide(X1,X2))) = inverse(X2),
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_22,plain,
double_divide(inverse(X1),inverse(X2)) = inverse(double_divide(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
inverse(double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),X3)),X2)))) = X3,
inference(spm,[status(thm)],[c_0_11,c_0_4]) ).
cnf(c_0_24,plain,
inverse(double_divide(X1,inverse(X2))) = double_divide(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_22,c_0_14]) ).
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,
double_divide(inverse(X1),double_divide(X2,inverse(double_divide(double_divide(X1,X2),X3)))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_18]) ).
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,
inverse(double_divide(double_divide(X1,inverse(X1)),X2)) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
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(double_divide(X1,inverse(X1)),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_14,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
double_divide(inverse(a2),double_divide(b2,inverse(b2))) != a2,
inference(rw,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_33,plain,
double_divide(X1,double_divide(X2,inverse(X2))) = inverse(X1),
inference(spm,[status(thm)],[c_0_18,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP594-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sun Sep 20 20:17:37 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 Running first-order theorem proving
% 0.03/0.31 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
% 0.03/0.34 % Version: 3.5.1
% 0.03/0.34 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.03/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.03/0.34 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.03/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.03/0.34 % Starting new_bool_1 with 300s (1) cores
% 0.03/0.34 % Starting sh5l with 300s (1) cores
% 0.03/0.34 % new_bool_1 with pid 784467 completed with status 0
% 0.03/0.34 % Result found by new_bool_1
% 0.03/0.34 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.03/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.03/0.34 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.03/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.03/0.34 % Starting new_bool_1 with 300s (1) cores
% 0.03/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.03/0.34 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.03/0.34 % Search class: FUUPS-FFSF21-DFFFFFNN
% 0.03/0.34 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.03/0.34 % Starting SubtermCWHack with 31s (1) cores
% 0.03/0.34 % SubtermCWHack with pid 784474 completed with status 0
% 0.03/0.34 % Result found by SubtermCWHack
% 0.03/0.34 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.03/0.34 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.03/0.34 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.03/0.34 % Starting new_bool_3 with 300s (1) cores
% 0.03/0.34 % Starting new_bool_1 with 300s (1) cores
% 0.03/0.34 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.03/0.34 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.03/0.34 % Search class: FUUPS-FFSF21-DFFFFFNN
% 0.03/0.34 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.03/0.34 % Starting SubtermCWHack with 31s (1) cores
% 0.03/0.34 % Preprocessing time : 0.001 s
% 0.03/0.34
% 0.03/0.34 % Proof found!
% 0.03/0.34 % SZS status Unsatisfiable
% 0.03/0.34 % SZS output start CNFRefutation
% See solution above
% 0.03/0.34 % Parsed axioms : 3
% 0.03/0.34 % Removed by relevancy pruning/SinE : 0
% 0.03/0.34 % Initial clauses : 3
% 0.03/0.34 % Removed in clause preprocessing : 0
% 0.03/0.34 % Initial clauses in saturation : 3
% 0.03/0.34 % Processed clauses : 58
% 0.03/0.34 % ...of these trivial : 5
% 0.03/0.34 % ...subsumed : 11
% 0.03/0.34 % ...remaining for further processing : 42
% 0.03/0.34 % Other redundant clauses eliminated : 0
% 0.03/0.34 % Clauses deleted for lack of memory : 0
% 0.03/0.34 % Backward-subsumed : 0
% 0.03/0.34 % Backward-rewritten : 23
% 0.03/0.34 % Generated clauses : 1366
% 0.03/0.34 % ...of the previous two non-redundant : 1238
% 0.03/0.34 % ...aggressively subsumed : 0
% 0.03/0.34 % Contextual simplify-reflections : 0
% 0.03/0.34 % Paramodulations : 1366
% 0.03/0.34 % Factorizations : 0
% 0.03/0.34 % NegExts : 0
% 0.03/0.34 % Equation resolutions : 0
% 0.03/0.34 % Disequality decompositions : 0
% 0.03/0.34 % Total rewrite steps : 497
% 0.03/0.34 % ...of those cached : 258
% 0.03/0.34 % Propositional unsat checks : 0
% 0.03/0.34 % Propositional check models : 0
% 0.03/0.34 % Propositional check unsatisfiable : 0
% 0.03/0.34 % Propositional clauses : 0
% 0.03/0.34 % Propositional clauses after purity: 0
% 0.03/0.34 % Propositional unsat core size : 0
% 0.03/0.34 % Propositional preprocessing time : 0.000
% 0.03/0.34 % Propositional encoding time : 0.000
% 0.03/0.34 % Propositional solver time : 0.000
% 0.03/0.34 % Success case prop preproc time : 0.000
% 0.03/0.34 % Success case prop encoding time : 0.000
% 0.03/0.34 % Success case prop solver time : 0.000
% 0.03/0.34 % Current number of processed clauses : 19
% 0.03/0.34 % Positive orientable unit clauses : 17
% 0.03/0.34 % Positive unorientable unit clauses: 2
% 0.03/0.34 % Negative unit clauses : 0
% 0.03/0.34 % Non-unit-clauses : 0
% 0.03/0.34 % Current number of unprocessed clauses: 591
% 0.03/0.34 % ...number of literals in the above : 591
% 0.03/0.34 % Current number of archived formulas : 0
% 0.03/0.34 % Current number of archived clauses : 23
% 0.03/0.34 % Clause-clause subsumption calls (NU) : 0
% 0.03/0.34 % Rec. Clause-clause subsumption calls : 0
% 0.03/0.34 % Non-unit clause-clause subsumptions : 0
% 0.03/0.34 % Unit Clause-clause subsumption calls : 19
% 0.03/0.34 % Rewrite failures with RHS unbound : 19
% 0.03/0.34 % BW rewrite match attempts : 145
% 0.03/0.34 % BW rewrite match successes : 70
% 0.03/0.34 % Condensation attempts : 0
% 0.03/0.34 % Condensation successes : 0
% 0.03/0.34 % Termbank termtop insertions : 14198
% 0.03/0.34 % Search garbage collected termcells : 2
% 0.03/0.34
% 0.03/0.34 % -------------------------------------------------
% 0.03/0.34 % User time : 0.008 s
% 0.03/0.34 % System time : 0.003 s
% 0.03/0.34 % Total time : 0.010 s
% 0.03/0.34 % Maximum resident set size: 3632 pages
% 0.03/0.34
% 0.03/0.34 % -------------------------------------------------
% 0.03/0.34 % User time : 0.009 s
% 0.03/0.34 % System time : 0.005 s
% 0.03/0.34 % Total time : 0.014 s
% 0.03/0.34 % Maximum resident set size: 4608 pages
% 0.03/0.34 % E exiting
%------------------------------------------------------------------------------