%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP102-1 : 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 : n013.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 12:37:53 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.80s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of clauses : 38 ( 28 unt; 0 nHn; 14 RR)
% Number of literals : 61 ( 60 equ; 35 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 : 36 ( 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(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(identity,axiom,
identity = double_divide(X1,inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
cnf(c_0_4,plain,
double_divide(double_divide(X1,identity),double_divide(identity,identity)) = double_divide(double_divide(identity,X1),identity) ).
cnf(c_0_5,plain,
double_divide(identity,identity) = identity ).
cnf(c_0_6,plain,
double_divide(double_divide(X1,double_divide(identity,double_divide(X2,identity))),double_divide(identity,identity)) = double_divide(double_divide(X2,X1),identity) ).
cnf(c_0_7,plain,
double_divide(X1,identity) = double_divide(identity,X1) ).
cnf(c_0_8,plain,
double_divide(identity,double_divide(X1,double_divide(identity,X2))) = double_divide(X2,double_divide(identity,X1)) ).
cnf(c_0_9,plain,
double_divide(double_divide(X1,X2),double_divide(X3,X4)) = double_divide(double_divide(X1,X3),double_divide(X2,X4)) ).
cnf(c_0_10,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_11,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_10 ).
cnf(c_0_12,axiom,
inverse(X1) = double_divide(X1,identity),
inverse ).
cnf(c_0_13,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
multiply ).
cnf(c_0_14,axiom,
identity = double_divide(X1,inverse(X1)),
identity ).
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_11,c_0_12]),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,
identity = double_divide(X1,double_divide(X1,identity)),
inference(rw,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_17,plain,
double_divide(double_divide(X1,identity),identity) = double_divide(double_divide(identity,X1),identity),
inference(rw,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_18,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_16]) ).
cnf(c_0_19,plain,
double_divide(double_divide(identity,double_divide(identity,X1)),identity) = double_divide(double_divide(identity,double_divide(X1,identity)),identity),
inference(rw,[status(thm)],[c_0_17]) ).
cnf(c_0_20,plain,
double_divide(double_divide(X1,double_divide(identity,double_divide(X2,identity))),identity) = double_divide(double_divide(X2,X1),identity),
inference(rw,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_21,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_18,c_0_5])]) ).
cnf(c_0_22,plain,
double_divide(double_divide(X1,identity),identity) = double_divide(identity,double_divide(X1,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( double_divide(double_divide(identity,a2),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_21,c_0_17]) ).
cnf(c_0_24,plain,
double_divide(double_divide(identity,X1),identity) = double_divide(identity,double_divide(X1,identity)),
inference(rw,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_25,plain,
double_divide(double_divide(X1,double_divide(identity,double_divide(identity,X2))),identity) = double_divide(double_divide(X1,X2),identity),
inference(rw,[status(thm)],[c_0_6]) ).
cnf(c_0_26,plain,
double_divide(double_divide(double_divide(X1,identity),X2),double_divide(X1,identity)) = double_divide(double_divide(identity,X2),identity),
inference(rw,[status(thm)],[c_0_5]) ).
cnf(c_0_27,negated_conjecture,
( double_divide(identity,double_divide(a2,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_23,c_0_24]) ).
cnf(c_0_28,plain,
double_divide(identity,double_divide(X1,identity)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25]),c_0_26]),c_0_24]),c_0_20]),c_0_22]) ).
cnf(c_0_29,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_27,c_0_28])]) ).
cnf(c_0_30,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X1,identity)))) = double_divide(identity,double_divide(X1,identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17]),c_0_20]),c_0_22]),c_0_24]),c_0_22]) ).
cnf(c_0_31,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_29,c_0_7]),c_0_7]),c_0_7]),c_0_7]),c_0_7]),c_0_7]) ).
cnf(c_0_32,plain,
double_divide(identity,double_divide(X1,X2)) = double_divide(identity,double_divide(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28]),c_0_7]) ).
cnf(c_0_33,plain,
double_divide(identity,double_divide(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_28]),c_0_28]) ).
cnf(c_0_34,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_31,c_0_32]),c_0_32])]) ).
cnf(c_0_35,plain,
double_divide(X1,X2) = double_divide(X2,X1),
inference(rw,[status(thm)],[c_0_33]) ).
cnf(c_0_36,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)],[c_0_34,c_0_8]),c_0_35]),c_0_8]),c_0_35]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_9]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP102-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.57 % Computer : n013.cluster.edu
% 0.12/0.57 % Model : x86_64 x86_64
% 0.12/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.57 % Memory : 8046.5625MB
% 0.12/0.57 % OS : Linux 6.8.0-71-generic
% 0.12/0.57 % CPULimit : 300
% 0.12/0.57 % WCLimit : 300
% 0.12/0.57 % DateTime : Sun Sep 20 19:56:51 UTC 2026
% 0.12/0.57 % CPUTime :
% 0.12/0.57 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.62 Running first-order theorem proving
% 0.15/0.62 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
% 0.15/0.80 % Version: 3.5.1
% 0.15/0.80 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.15/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.80 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.15/0.80 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.80 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.80 % Starting sh5l with 300s (1) cores
% 0.15/0.80 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 3277964 completed with status 0
% 0.15/0.80 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.15/0.80 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.15/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.80 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.15/0.80 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.80 % No SInE strategy applied
% 0.15/0.80 % Search class: FUHPS-FFSF22-MFFFFFNN
% 0.15/0.80 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 0.15/0.80 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.80 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.80 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.15/0.80 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 0.15/0.80 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.80 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.80 % G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with pid 3277972 completed with status 0
% 0.15/0.80 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni
% 0.15/0.80 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.15/0.80 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.80 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.15/0.80 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.80 % No SInE strategy applied
% 0.15/0.80 % Search class: FUHPS-FFSF22-MFFFFFNN
% 0.15/0.80 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 0.15/0.80 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.80 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.80 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.15/0.80 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 0.15/0.80 % Preprocessing time : 0.001 s
% 0.15/0.80 % Presaturation interreduction done
% 0.15/0.80
% 0.15/0.80 % Proof found!
% 0.15/0.80 % SZS status Unsatisfiable
% 0.15/0.80 % SZS output start CNFRefutation
% See solution above
% 0.15/0.80 % Parsed axioms : 5
% 0.15/0.80 % Removed by relevancy pruning/SinE : 0
% 0.15/0.80 % Initial clauses : 5
% 0.15/0.80 % Removed in clause preprocessing : 2
% 0.15/0.80 % Initial clauses in saturation : 3
% 0.15/0.80 % Processed clauses : 2651
% 0.15/0.80 % ...of these trivial : 1407
% 0.15/0.80 % ...subsumed : 1115
% 0.15/0.80 % ...remaining for further processing : 129
% 0.15/0.80 % Other redundant clauses eliminated : 0
% 0.15/0.80 % Clauses deleted for lack of memory : 0
% 0.15/0.80 % Backward-subsumed : 6
% 0.15/0.80 % Backward-rewritten : 83
% 0.15/0.80 % Generated clauses : 12282
% 0.15/0.80 % ...of the previous two non-redundant : 10017
% 0.15/0.80 % ...aggressively subsumed : 0
% 0.15/0.80 % Contextual simplify-reflections : 0
% 0.15/0.80 % Paramodulations : 12282
% 0.15/0.80 % Factorizations : 0
% 0.15/0.80 % NegExts : 0
% 0.15/0.80 % Equation resolutions : 0
% 0.15/0.80 % Disequality decompositions : 0
% 0.15/0.80 % Total rewrite steps : 22681
% 0.15/0.80 % ...of those cached : 17029
% 0.15/0.80 % Propositional unsat checks : 0
% 0.15/0.80 % Propositional check models : 0
% 0.15/0.80 % Propositional check unsatisfiable : 0
% 0.15/0.80 % Propositional clauses : 0
% 0.15/0.80 % Propositional clauses after purity: 0
% 0.15/0.80 % Propositional unsat core size : 0
% 0.15/0.80 % Propositional preprocessing time : 0.000
% 0.15/0.80 % Propositional encoding time : 0.000
% 0.15/0.80 % Propositional solver time : 0.000
% 0.15/0.80 % Success case prop preproc time : 0.000
% 0.15/0.80 % Success case prop encoding time : 0.000
% 0.15/0.80 % Success case prop solver time : 0.000
% 0.15/0.80 % Current number of processed clauses : 37
% 0.15/0.80 % Positive orientable unit clauses : 17
% 0.15/0.80 % Positive unorientable unit clauses: 20
% 0.15/0.80 % Negative unit clauses : 0
% 0.15/0.80 % Non-unit-clauses : 0
% 0.15/0.80 % Current number of unprocessed clauses: 7372
% 0.15/0.80 % ...number of literals in the above : 7372
% 0.15/0.80 % Current number of archived formulas : 0
% 0.15/0.80 % Current number of archived clauses : 94
% 0.15/0.80 % Clause-clause subsumption calls (NU) : 0
% 0.15/0.80 % Rec. Clause-clause subsumption calls : 0
% 0.15/0.80 % Non-unit clause-clause subsumptions : 0
% 0.15/0.80 % Unit Clause-clause subsumption calls : 271
% 0.15/0.80 % Rewrite failures with RHS unbound : 0
% 0.15/0.80 % BW rewrite match attempts : 9194
% 0.15/0.80 % BW rewrite match successes : 537
% 0.15/0.80 % Condensation attempts : 0
% 0.15/0.80 % Condensation successes : 0
% 0.15/0.80 % Termbank termtop insertions : 154355
% 0.15/0.80 % Search garbage collected termcells : 11
% 0.15/0.80
% 0.15/0.80 % -------------------------------------------------
% 0.15/0.80 % User time : 0.144 s
% 0.15/0.80 % System time : 0.014 s
% 0.15/0.80 % Total time : 0.158 s
% 0.15/0.80 % Maximum resident set size: 3636 pages
% 0.15/0.80
% 0.15/0.80 % -------------------------------------------------
% 0.15/0.80 % User time : 0.740 s
% 0.15/0.80 % System time : 0.061 s
% 0.15/0.80 % Total time : 0.801 s
% 0.15/0.80 % Maximum resident set size: 4608 pages
% 0.15/0.80 % E exiting
%------------------------------------------------------------------------------