%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP099-1 : 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 : n008.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 12:41:47 PM UTC 2026
% Result : Unsatisfiable 2.06s 0.83s
% Output : CNFRefutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 28 ( 20 unt; 0 nHn; 13 RR)
% Number of literals : 47 ( 46 equ; 30 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_these_axioms,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(identity,axiom,
identity = double_divide(X1,inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(inverse,axiom,
inverse(X1) = double_divide(X1,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_4,plain,
double_divide(identity,X1) = double_divide(X1,identity) ).
cnf(c_0_5,plain,
double_divide(X1,X2) = double_divide(X2,X1) ).
cnf(c_0_6,plain,
double_divide(identity,double_divide(X1,double_divide(identity,X2))) = double_divide(X2,double_divide(X1,identity)) ).
cnf(c_0_7,plain,
double_divide(double_divide(X1,X2),double_divide(X3,X4)) = double_divide(double_divide(X1,X4),double_divide(X3,X2)) ).
cnf(c_0_8,plain,
double_divide(X1,double_divide(X2,double_divide(double_divide(X1,X3),X4))) = double_divide(X4,double_divide(X2,X3)) ).
cnf(c_0_9,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(fof_simplification,[status(thm)],[prove_these_axioms]) ).
cnf(c_0_10,axiom,
identity = double_divide(X1,inverse(X1)),
identity ).
cnf(c_0_11,axiom,
inverse(X1) = double_divide(X1,identity),
inverse ).
cnf(c_0_12,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
c_0_9 ).
cnf(c_0_13,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
multiply ).
cnf(c_0_14,plain,
identity = double_divide(X1,double_divide(X1,identity)),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity)
| double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| double_divide(double_divide(a1,double_divide(a1,identity)),identity) != identity
| double_divide(double_divide(a2,identity),identity) != a2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_11]),c_0_13]),c_0_13]),c_0_13]),c_0_13]),c_0_13]),c_0_13]),c_0_13]),c_0_13]) ).
cnf(c_0_16,plain,
double_divide(double_divide(X1,identity),double_divide(identity,identity)) = X1,
inference(rw,[status(thm)],[c_0_14]) ).
cnf(c_0_17,negated_conjecture,
( double_divide(identity,identity) != identity
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(double_divide(a4,b4),identity) != double_divide(double_divide(b4,a4),identity)
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(rw,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_18,plain,
double_divide(identity,identity) = identity,
inference(rw,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( double_divide(double_divide(a2,identity),identity) != a2
| double_divide(double_divide(a4,b4),identity) != double_divide(double_divide(b4,a4),identity)
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_20,plain,
double_divide(double_divide(X1,identity),identity) = X1,
inference(rw,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( double_divide(double_divide(a4,b4),identity) != double_divide(double_divide(b4,a4),identity)
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).
cnf(c_0_22,negated_conjecture,
( double_divide(identity,double_divide(a4,b4)) != double_divide(identity,double_divide(b4,a4))
| double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_4]),c_0_4]),c_0_4]),c_0_4]),c_0_4]),c_0_4]) ).
cnf(c_0_23,negated_conjecture,
double_divide(identity,double_divide(a3,double_divide(identity,double_divide(c3,b3)))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_5]),c_0_5])]) ).
cnf(c_0_24,negated_conjecture,
double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(double_divide(identity,c3),double_divide(b3,a3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_6]),c_0_5]),c_0_5]),c_0_6]),c_0_5]),c_0_5]) ).
cnf(c_0_25,negated_conjecture,
double_divide(double_divide(identity,b3),double_divide(c3,a3)) != double_divide(double_divide(identity,c3),double_divide(b3,a3)),
inference(rw,[status(thm)],[c_0_24,c_0_7]) ).
cnf(c_0_26,plain,
double_divide(double_divide(X1,X2),double_divide(X3,X4)) = double_divide(double_divide(X1,X3),double_divide(X2,X4)),
inference(rw,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP099-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.45 % Computer : n008.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 20 19:58:24 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 2.06/0.83 % Version: 3.5.1
% 2.06/0.83 % Preprocessing class: FSSSSMSMSSSNFFN.
% 2.06/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.06/0.83 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 2.06/0.83 % Starting new_bool_3 with 300s (1) cores
% 2.06/0.83 % Starting new_bool_1 with 300s (1) cores
% 2.06/0.83 % Starting sh5l with 300s (1) cores
% 2.06/0.83 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 3479655 completed with status 0
% 2.06/0.83 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 2.06/0.83 % Preprocessing class: FSSSSMSMSSSNFFN.
% 2.06/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.06/0.83 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 2.06/0.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.06/0.83 % No SInE strategy applied
% 2.06/0.83 % Search class: FUHPS-FFSF22-MFFFFFNN
% 2.06/0.83 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 2.06/0.83 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.06/0.83 % Starting SubtermCWHack with 136s (1) cores
% 2.06/0.83 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 2.06/0.83 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 2.06/0.83 % Starting new_bool_3 with 136s (1) cores
% 2.06/0.83 % Starting new_bool_1 with 136s (1) cores
% 2.06/0.83 % G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with pid 3479661 completed with status 0
% 2.06/0.83 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni
% 2.06/0.83 % Preprocessing class: FSSSSMSMSSSNFFN.
% 2.06/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.06/0.83 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 2.06/0.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.06/0.83 % No SInE strategy applied
% 2.06/0.83 % Search class: FUHPS-FFSF22-MFFFFFNN
% 2.06/0.83 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 2.06/0.83 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.06/0.83 % Starting SubtermCWHack with 136s (1) cores
% 2.06/0.83 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 2.06/0.83 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 2.06/0.83 % Preprocessing time : 0.002 s
% 2.06/0.83 % Presaturation interreduction done
% 2.06/0.83
% 2.06/0.83 % Proof found!
% 2.06/0.83 % SZS status Unsatisfiable
% 2.06/0.83 % SZS output start CNFRefutation
% See solution above
% 2.06/0.83 % Parsed axioms : 5
% 2.06/0.83 % Removed by relevancy pruning/SinE : 0
% 2.06/0.83 % Initial clauses : 5
% 2.06/0.83 % Removed in clause preprocessing : 2
% 2.06/0.83 % Initial clauses in saturation : 3
% 2.06/0.83 % Processed clauses : 2694
% 2.06/0.83 % ...of these trivial : 1427
% 2.06/0.83 % ...subsumed : 1150
% 2.06/0.83 % ...remaining for further processing : 117
% 2.06/0.83 % Other redundant clauses eliminated : 0
% 2.06/0.83 % Clauses deleted for lack of memory : 0
% 2.06/0.83 % Backward-subsumed : 6
% 2.06/0.83 % Backward-rewritten : 69
% 2.06/0.83 % Generated clauses : 13660
% 2.06/0.83 % ...of the previous two non-redundant : 10969
% 2.06/0.83 % ...aggressively subsumed : 0
% 2.06/0.83 % Contextual simplify-reflections : 0
% 2.06/0.83 % Paramodulations : 13660
% 2.06/0.83 % Factorizations : 0
% 2.06/0.83 % NegExts : 0
% 2.06/0.83 % Equation resolutions : 0
% 2.06/0.83 % Disequality decompositions : 0
% 2.06/0.83 % Total rewrite steps : 27013
% 2.06/0.83 % ...of those cached : 20014
% 2.06/0.83 % Propositional unsat checks : 0
% 2.06/0.83 % Propositional check models : 0
% 2.06/0.83 % Propositional check unsatisfiable : 0
% 2.06/0.83 % Propositional clauses : 0
% 2.06/0.83 % Propositional clauses after purity: 0
% 2.06/0.83 % Propositional unsat core size : 0
% 2.06/0.83 % Propositional preprocessing time : 0.000
% 2.06/0.83 % Propositional encoding time : 0.000
% 2.06/0.83 % Propositional solver time : 0.000
% 2.06/0.83 % Success case prop preproc time : 0.000
% 2.06/0.83 % Success case prop encoding time : 0.000
% 2.06/0.83 % Success case prop solver time : 0.000
% 2.06/0.83 % Current number of processed clauses : 39
% 2.06/0.83 % Positive orientable unit clauses : 20
% 2.06/0.83 % Positive unorientable unit clauses: 19
% 2.06/0.83 % Negative unit clauses : 0
% 2.06/0.83 % Non-unit-clauses : 0
% 2.06/0.83 % Current number of unprocessed clauses: 8281
% 2.06/0.83 % ...number of literals in the above : 8281
% 2.06/0.83 % Current number of archived formulas : 0
% 2.06/0.83 % Current number of archived clauses : 80
% 2.06/0.83 % Clause-clause subsumption calls (NU) : 0
% 2.06/0.83 % Rec. Clause-clause subsumption calls : 0
% 2.06/0.83 % Non-unit clause-clause subsumptions : 0
% 2.06/0.83 % Unit Clause-clause subsumption calls : 323
% 2.06/0.83 % Rewrite failures with RHS unbound : 0
% 2.06/0.83 % BW rewrite match attempts : 9637
% 2.06/0.83 % BW rewrite match successes : 623
% 2.06/0.83 % Condensation attempts : 0
% 2.06/0.83 % Condensation successes : 0
% 2.06/0.83 % Termbank termtop insertions : 183873
% 2.06/0.83 % Search garbage collected termcells : 11
% 2.06/0.83
% 2.06/0.83 % -------------------------------------------------
% 2.06/0.83 % User time : 0.261 s
% 2.06/0.83 % System time : 0.018 s
% 2.06/0.83 % Total time : 0.279 s
% 2.06/0.83 % Maximum resident set size: 3636 pages
% 2.06/0.83
% 2.06/0.83 % -------------------------------------------------
% 2.06/0.83 % User time : 1.278 s
% 2.06/0.83 % System time : 0.072 s
% 2.06/0.83 % Total time : 1.350 s
% 2.06/0.83 % Maximum resident set size: 4864 pages
% 2.06/0.83 % E exiting
%------------------------------------------------------------------------------