%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP104-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 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 12:41:48 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of clauses : 47 ( 43 unt; 0 nHn; 6 RR)
% Number of literals : 57 ( 56 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),inverse(X3))),X2))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(multiply,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(c_0_3,axiom,
double_divide(X1,inverse(double_divide(inverse(double_divide(double_divide(X1,X2),inverse(X3))),X2))) = X3,
single_axiom ).
cnf(c_0_4,axiom,
multiply(X1,X2) = inverse(double_divide(X2,X1)),
multiply ).
cnf(c_0_5,plain,
double_divide(X1,multiply(X2,multiply(inverse(X3),double_divide(X1,X2)))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_3,c_0_4]),c_0_4]) ).
cnf(c_0_6,plain,
double_divide(X1,multiply(multiply(X2,multiply(inverse(X3),double_divide(X1,X2))),multiply(inverse(X4),X3))) = X4,
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_7,plain,
multiply(multiply(X1,multiply(inverse(X2),double_divide(X3,X1))),X3) = inverse(X2),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_8,plain,
double_divide(multiply(inverse(X1),X2),inverse(X2)) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
multiply(inverse(X1),multiply(inverse(X2),X1)) = inverse(X2),
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_10,plain,
double_divide(inverse(X1),inverse(multiply(inverse(X1),X2))) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
double_divide(inverse(X1),inverse(inverse(X2))) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_12,plain,
double_divide(inverse(X1),inverse(multiply(X2,X3))) = multiply(multiply(X2,X3),X1),
inference(spm,[status(thm)],[c_0_11,c_0_4]) ).
cnf(c_0_13,plain,
multiply(multiply(inverse(X1),X2),X1) = X2,
inference(rw,[status(thm)],[c_0_10,c_0_12]) ).
cnf(c_0_14,plain,
double_divide(multiply(X1,X2),inverse(multiply(multiply(X1,X2),X3))) = X3,
inference(spm,[status(thm)],[c_0_10,c_0_4]) ).
cnf(c_0_15,plain,
double_divide(multiply(multiply(X1,X2),X3),inverse(X3)) = double_divide(X2,X1),
inference(spm,[status(thm)],[c_0_8,c_0_4]) ).
cnf(c_0_16,plain,
multiply(inverse(X1),double_divide(X2,inverse(X2))) = inverse(X1),
inference(spm,[status(thm)],[c_0_7,c_0_13]) ).
cnf(c_0_17,plain,
double_divide(X1,inverse(multiply(X1,X2))) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_18,plain,
double_divide(double_divide(X1,inverse(X1)),inverse(X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_8]) ).
cnf(c_0_19,plain,
multiply(double_divide(X1,inverse(X1)),X2) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,plain,
double_divide(inverse(X1),inverse(X2)) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_21,plain,
multiply(inverse(multiply(inverse(X1),X2)),inverse(X1)) = inverse(X2),
inference(spm,[status(thm)],[c_0_9,c_0_9]) ).
cnf(c_0_22,plain,
double_divide(inverse(X1),multiply(inverse(X2),X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_16]),c_0_4]) ).
cnf(c_0_23,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
multiply(inverse(multiply(multiply(X1,X2),X3)),multiply(X1,X2)) = inverse(X3),
inference(spm,[status(thm)],[c_0_21,c_0_4]) ).
cnf(c_0_25,plain,
double_divide(X1,multiply(inverse(X1),inverse(X2))) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_16]) ).
cnf(c_0_26,plain,
double_divide(inverse(X1),multiply(inverse(X2),X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_22]),c_0_23]) ).
cnf(c_0_27,plain,
multiply(inverse(X1),multiply(multiply(X2,X3),X1)) = multiply(X2,X3),
inference(spm,[status(thm)],[c_0_9,c_0_4]) ).
cnf(c_0_28,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(spm,[status(thm)],[c_0_24,c_0_13]) ).
cnf(c_0_29,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
multiply(inverse(X1),multiply(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_27,c_0_13]) ).
cnf(c_0_31,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_28]),c_0_20]) ).
cnf(c_0_32,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(fof_simplification,[status(thm)],[prove_these_axioms]) ).
cnf(c_0_33,plain,
multiply(multiply(X1,multiply(multiply(X2,X3),double_divide(X4,X1))),X4) = multiply(X2,X3),
inference(spm,[status(thm)],[c_0_7,c_0_4]) ).
cnf(c_0_34,plain,
double_divide(X1,X2) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_4]) ).
cnf(c_0_35,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
c_0_32 ).
cnf(c_0_37,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_38,plain,
multiply(X1,multiply(X2,multiply(multiply(X3,X4),inverse(multiply(X2,X1))))) = multiply(X3,X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_31]),c_0_34]) ).
cnf(c_0_39,plain,
multiply(multiply(X1,X2),inverse(X1)) = X2,
inference(spm,[status(thm)],[c_0_35,c_0_31]) ).
cnf(c_0_40,negated_conjecture,
( multiply(a1,inverse(a1)) != multiply(b1,inverse(b1))
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_23])]),c_0_31]),c_0_31]),c_0_31]),c_0_31])]) ).
cnf(c_0_41,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_31]),c_0_31]) ).
cnf(c_0_42,plain,
multiply(multiply(X1,X2),X3) = multiply(X2,multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(sr,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,plain,
multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_42]) ).
cnf(c_0_45,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_31]),c_0_42]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP104-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 % Computer : n018.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 20 19:59:27 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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
% 0.20/0.52 % Version: 3.5.1
% 0.20/0.52 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.20/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.20/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.52 % Starting sh5l with 300s (1) cores
% 0.20/0.52 % new_bool_3 with pid 54143 completed with status 0
% 0.20/0.52 % Result found by new_bool_3
% 0.20/0.52 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.20/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.20/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.52 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.52 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.52 % Search class: FUHPS-FFSF21-DFFFFFNN
% 0.20/0.52 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.52 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.52 % SubtermCWHack with pid 54150 completed with status 0
% 0.20/0.52 % Result found by SubtermCWHack
% 0.20/0.52 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.20/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.52 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.20/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.52 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.20/0.52 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.52 % Search class: FUHPS-FFSF21-DFFFFFNN
% 0.20/0.52 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.52 % Starting SubtermCWHack with 31s (1) cores
% 0.20/0.52 % Preprocessing time : 0.001 s
% 0.20/0.52
% 0.20/0.52 % Proof found!
% 0.20/0.52 % SZS status Unsatisfiable
% 0.20/0.52 % SZS output start CNFRefutation
% See solution above
% 0.20/0.52 % Parsed axioms : 3
% 0.20/0.52 % Removed by relevancy pruning/SinE : 0
% 0.20/0.52 % Initial clauses : 3
% 0.20/0.52 % Removed in clause preprocessing : 0
% 0.20/0.52 % Initial clauses in saturation : 3
% 0.20/0.52 % Processed clauses : 314
% 0.20/0.52 % ...of these trivial : 99
% 0.20/0.52 % ...subsumed : 132
% 0.20/0.52 % ...remaining for further processing : 82
% 0.20/0.52 % Other redundant clauses eliminated : 0
% 0.20/0.52 % Clauses deleted for lack of memory : 0
% 0.20/0.52 % Backward-subsumed : 0
% 0.20/0.52 % Backward-rewritten : 62
% 0.20/0.52 % Generated clauses : 2858
% 0.20/0.52 % ...of the previous two non-redundant : 2044
% 0.20/0.52 % ...aggressively subsumed : 0
% 0.20/0.52 % Contextual simplify-reflections : 0
% 0.20/0.52 % Paramodulations : 2857
% 0.20/0.52 % Factorizations : 0
% 0.20/0.52 % NegExts : 0
% 0.20/0.52 % Equation resolutions : 0
% 0.20/0.52 % Disequality decompositions : 0
% 0.20/0.52 % Total rewrite steps : 3221
% 0.20/0.52 % ...of those cached : 2062
% 0.20/0.52 % Propositional unsat checks : 0
% 0.20/0.52 % Propositional check models : 0
% 0.20/0.52 % Propositional check unsatisfiable : 0
% 0.20/0.52 % Propositional clauses : 0
% 0.20/0.52 % Propositional clauses after purity: 0
% 0.20/0.52 % Propositional unsat core size : 0
% 0.20/0.52 % Propositional preprocessing time : 0.000
% 0.20/0.52 % Propositional encoding time : 0.000
% 0.20/0.52 % Propositional solver time : 0.000
% 0.20/0.52 % Success case prop preproc time : 0.000
% 0.20/0.52 % Success case prop encoding time : 0.000
% 0.20/0.52 % Success case prop solver time : 0.000
% 0.20/0.52 % Current number of processed clauses : 19
% 0.20/0.52 % Positive orientable unit clauses : 15
% 0.20/0.52 % Positive unorientable unit clauses: 4
% 0.20/0.52 % Negative unit clauses : 0
% 0.20/0.52 % Non-unit-clauses : 0
% 0.20/0.52 % Current number of unprocessed clauses: 787
% 0.20/0.52 % ...number of literals in the above : 787
% 0.20/0.52 % Current number of archived formulas : 0
% 0.20/0.52 % Current number of archived clauses : 63
% 0.20/0.52 % Clause-clause subsumption calls (NU) : 0
% 0.20/0.52 % Rec. Clause-clause subsumption calls : 0
% 0.20/0.52 % Non-unit clause-clause subsumptions : 0
% 0.20/0.52 % Unit Clause-clause subsumption calls : 54
% 0.20/0.52 % Rewrite failures with RHS unbound : 116
% 0.20/0.52 % BW rewrite match attempts : 336
% 0.20/0.52 % BW rewrite match successes : 237
% 0.20/0.52 % Condensation attempts : 0
% 0.20/0.52 % Condensation successes : 0
% 0.20/0.52 % Termbank termtop insertions : 30787
% 0.20/0.52 % Search garbage collected termcells : 11
% 0.20/0.52
% 0.20/0.52 % -------------------------------------------------
% 0.20/0.52 % User time : 0.016 s
% 0.20/0.52 % System time : 0.004 s
% 0.20/0.52 % Total time : 0.020 s
% 0.20/0.52 % Maximum resident set size: 3596 pages
% 0.20/0.52
% 0.20/0.52 % -------------------------------------------------
% 0.20/0.52 % User time : 0.018 s
% 0.20/0.52 % System time : 0.008 s
% 0.20/0.52 % Total time : 0.026 s
% 0.20/0.52 % Maximum resident set size: 4608 pages
% 0.20/0.52 % E exiting
%------------------------------------------------------------------------------