%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP076-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:37:48 PM UTC 2026
% Result : Unsatisfiable 0.12s 11.05s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of clauses : 50 ( 44 unt; 0 nHn; 12 RR)
% Number of literals : 61 ( 60 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(single_axiom,axiom,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( 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(multiply,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_5,axiom,
identity = double_divide(X1,inverse(X1)),
identity ).
cnf(c_0_6,axiom,
inverse(X1) = double_divide(X1,identity),
inverse ).
cnf(c_0_7,axiom,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
single_axiom ).
cnf(c_0_8,plain,
identity = double_divide(X1,double_divide(X1,identity)),
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,plain,
double_divide(double_divide(X1,double_divide(identity,double_divide(X2,identity))),double_divide(identity,identity)) = double_divide(double_divide(X1,X2),identity),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
double_divide(double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity))),double_divide(double_divide(X3,X4),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = X4,
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_11,plain,
double_divide(double_divide(X1,identity),double_divide(identity,identity)) = double_divide(double_divide(X1,identity),identity),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_12,plain,
double_divide(identity,identity) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_10]) ).
cnf(c_0_13,plain,
double_divide(double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity))),double_divide(double_divide(X3,X4),identity)),identity) = X4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_12]),c_0_12]),c_0_12]) ).
cnf(c_0_14,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity))),identity) = X3,
inference(rw,[status(thm)],[c_0_7,c_0_12]) ).
cnf(c_0_15,plain,
double_divide(double_divide(double_divide(X1,X2),X1),double_divide(X2,identity)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_8]),c_0_12]) ).
cnf(c_0_16,plain,
double_divide(double_divide(X1,double_divide(identity,double_divide(X2,identity))),identity) = double_divide(double_divide(X1,X2),identity),
inference(rw,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_17,plain,
double_divide(double_divide(X1,identity),identity) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
double_divide(identity,double_divide(X1,identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_16]),c_0_13]) ).
cnf(c_0_19,plain,
double_divide(double_divide(identity,X1),identity) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_17]),c_0_12]),c_0_8]),c_0_18]) ).
cnf(c_0_20,plain,
double_divide(identity,X1) = double_divide(X1,identity),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( 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_22,plain,
double_divide(identity,double_divide(identity,X1)) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
double_divide(identity,double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity)))) = X3,
inference(rw,[status(thm)],[c_0_14,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
c_0_21 ).
cnf(c_0_25,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
multiply ).
cnf(c_0_26,plain,
double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity))) = double_divide(identity,X3),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,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(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)],[c_0_24,c_0_6]),c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_25]) ).
cnf(c_0_28,plain,
double_divide(double_divide(double_divide(identity,X1),X2),double_divide(X1,identity)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_26]),c_0_22]) ).
cnf(c_0_29,plain,
double_divide(X1,double_divide(identity,double_divide(double_divide(X1,identity),X2))) = double_divide(identity,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_20]),c_0_12]),c_0_20]) ).
cnf(c_0_30,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_23]),c_0_20]),c_0_23]),c_0_22]) ).
cnf(c_0_31,negated_conjecture,
( double_divide(identity,identity) != identity
| double_divide(double_divide(a2,identity),identity) != a2
| 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_27,c_0_8]) ).
cnf(c_0_32,plain,
double_divide(double_divide(identity,X1),double_divide(X2,identity)) = double_divide(identity,double_divide(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_20]),c_0_22]) ).
cnf(c_0_33,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_30,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( double_divide(double_divide(a2,identity),identity) != a2
| 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_31,c_0_12])]) ).
cnf(c_0_35,plain,
double_divide(identity,double_divide(X1,double_divide(X2,identity))) = double_divide(X2,double_divide(X1,identity)),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
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_34,c_0_17])]) ).
cnf(c_0_37,plain,
double_divide(identity,double_divide(double_divide(identity,X1),X2)) = double_divide(double_divide(identity,X2),X1),
inference(spm,[status(thm)],[c_0_32,c_0_30]) ).
cnf(c_0_38,plain,
double_divide(identity,double_divide(double_divide(X1,identity),X2)) = double_divide(double_divide(identity,X2),X1),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_39,plain,
double_divide(X1,double_divide(identity,double_divide(double_divide(double_divide(X2,X3),X1),X4))) = double_divide(X2,double_divide(identity,double_divide(X3,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_26]),c_0_35]),c_0_20]),c_0_32]) ).
cnf(c_0_40,plain,
double_divide(double_divide(identity,X1),double_divide(identity,X2)) = double_divide(identity,double_divide(X2,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_41,negated_conjecture,
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)],[c_0_36,c_0_20]),c_0_20]),c_0_20]),c_0_20]) ).
cnf(c_0_42,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(X2,identity),X3)) = double_divide(identity,double_divide(double_divide(double_divide(identity,X3),X2),X1)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
double_divide(double_divide(double_divide(identity,X1),X2),X3) = double_divide(identity,double_divide(double_divide(X1,X3),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_37]),c_0_39]),c_0_40]),c_0_22]) ).
cnf(c_0_44,negated_conjecture,
double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))) != double_divide(double_divide(identity,a3),double_divide(c3,b3)),
inference(rw,[status(thm)],[c_0_41,c_0_37]) ).
cnf(c_0_45,plain,
double_divide(identity,double_divide(X1,double_divide(identity,X2))) = double_divide(X2,double_divide(X1,identity)),
inference(spm,[status(thm)],[c_0_32,c_0_22]) ).
cnf(c_0_46,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(X2,identity),X3)) = double_divide(double_divide(X3,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_22]) ).
cnf(c_0_47,negated_conjecture,
double_divide(double_divide(b3,a3),double_divide(identity,c3)) != double_divide(double_divide(identity,a3),double_divide(c3,b3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_45]),c_0_20]) ).
cnf(c_0_48,plain,
double_divide(double_divide(identity,X1),double_divide(X2,X3)) = double_divide(double_divide(X3,X1),double_divide(identity,X2)),
inference(spm,[status(thm)],[c_0_46,c_0_30]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP076-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/10.93 % Computer : n010.cluster.edu
% 0.12/10.93 % Model : x86_64 x86_64
% 0.12/10.93 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.93 % Memory : 8046.5625MB
% 0.12/10.93 % OS : Linux 6.8.0-71-generic
% 0.12/10.93 % CPULimit : 300
% 0.12/10.93 % WCLimit : 300
% 0.12/10.93 % DateTime : Sun Sep 20 19:57:22 UTC 2026
% 0.12/10.94 % CPUTime :
% 0.12/10.94 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/10.97 Running first-order theorem proving
% 0.12/10.97 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
% 0.12/11.05 % Version: 3.5.1
% 0.12/11.05 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/11.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/11.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/11.05 % Starting new_bool_3 with 300s (1) cores
% 0.12/11.05 % Starting new_bool_1 with 300s (1) cores
% 0.12/11.05 % Starting sh5l with 300s (1) cores
% 0.12/11.05 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3381255 completed with status 0
% 0.12/11.05 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.12/11.05 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/11.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/11.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/11.05 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/11.05 % No SInE strategy applied
% 0.12/11.05 % Search class: FUHPS-FFSF22-MFFFFFNN
% 0.12/11.05 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 0.12/11.05 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/11.05 % Starting SubtermCWHack with 136s (1) cores
% 0.12/11.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.12/11.05 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 0.12/11.05 % Starting new_bool_3 with 136s (1) cores
% 0.12/11.05 % Starting new_bool_1 with 136s (1) cores
% 0.12/11.05 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3381261 completed with status 0
% 0.12/11.05 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.12/11.05 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/11.05 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/11.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/11.05 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/11.05 % No SInE strategy applied
% 0.12/11.05 % Search class: FUHPS-FFSF22-MFFFFFNN
% 0.12/11.05 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 0.12/11.05 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/11.05 % Starting SubtermCWHack with 136s (1) cores
% 0.12/11.05 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.12/11.05 % Preprocessing time : 0.002 s
% 0.12/11.05
% 0.12/11.05 % Proof found!
% 0.12/11.05 % SZS status Unsatisfiable
% 0.12/11.05 % SZS output start CNFRefutation
% See solution above
% 0.12/11.05 % Parsed axioms : 5
% 0.12/11.05 % Removed by relevancy pruning/SinE : 0
% 0.12/11.05 % Initial clauses : 5
% 0.12/11.05 % Removed in clause preprocessing : 2
% 0.12/11.05 % Initial clauses in saturation : 3
% 0.12/11.05 % Processed clauses : 409
% 0.12/11.05 % ...of these trivial : 143
% 0.12/11.05 % ...subsumed : 172
% 0.12/11.05 % ...remaining for further processing : 94
% 0.12/11.05 % Other redundant clauses eliminated : 0
% 0.12/11.05 % Clauses deleted for lack of memory : 0
% 0.12/11.05 % Backward-subsumed : 0
% 0.12/11.05 % Backward-rewritten : 55
% 0.12/11.05 % Generated clauses : 6015
% 0.12/11.05 % ...of the previous two non-redundant : 3287
% 0.12/11.05 % ...aggressively subsumed : 0
% 0.12/11.05 % Contextual simplify-reflections : 0
% 0.12/11.05 % Paramodulations : 6015
% 0.12/11.05 % Factorizations : 0
% 0.12/11.05 % NegExts : 0
% 0.12/11.05 % Equation resolutions : 0
% 0.12/11.05 % Disequality decompositions : 0
% 0.12/11.05 % Total rewrite steps : 14199
% 0.12/11.05 % ...of those cached : 11247
% 0.12/11.05 % Propositional unsat checks : 0
% 0.12/11.05 % Propositional check models : 0
% 0.12/11.05 % Propositional check unsatisfiable : 0
% 0.12/11.05 % Propositional clauses : 0
% 0.12/11.05 % Propositional clauses after purity: 0
% 0.12/11.05 % Propositional unsat core size : 0
% 0.12/11.05 % Propositional preprocessing time : 0.000
% 0.12/11.05 % Propositional encoding time : 0.000
% 0.12/11.05 % Propositional solver time : 0.000
% 0.12/11.05 % Success case prop preproc time : 0.000
% 0.12/11.05 % Success case prop encoding time : 0.000
% 0.12/11.05 % Success case prop solver time : 0.000
% 0.12/11.05 % Current number of processed clauses : 39
% 0.12/11.05 % Positive orientable unit clauses : 33
% 0.12/11.05 % Positive unorientable unit clauses: 6
% 0.12/11.05 % Negative unit clauses : 0
% 0.12/11.05 % Non-unit-clauses : 0
% 0.12/11.05 % Current number of unprocessed clauses: 1841
% 0.12/11.05 % ...number of literals in the above : 1841
% 0.12/11.05 % Current number of archived formulas : 0
% 0.12/11.05 % Current number of archived clauses : 57
% 0.12/11.05 % Clause-clause subsumption calls (NU) : 0
% 0.12/11.05 % Rec. Clause-clause subsumption calls : 0
% 0.12/11.05 % Non-unit clause-clause subsumptions : 0
% 0.12/11.05 % Unit Clause-clause subsumption calls : 79
% 0.12/11.05 % Rewrite failures with RHS unbound : 0
% 0.12/11.05 % BW rewrite match attempts : 280
% 0.12/11.05 % BW rewrite match successes : 100
% 0.12/11.05 % Condensation attempts : 0
% 0.12/11.05 % Condensation successes : 0
% 0.12/11.05 % Termbank termtop insertions : 102944
% 0.12/11.05 % Search garbage collected termcells : 8
% 0.12/11.05
% 0.12/11.05 % -------------------------------------------------
% 0.12/11.05 % User time : 0.052 s
% 0.12/11.05 % System time : 0.005 s
% 0.12/11.05 % Total time : 0.057 s
% 0.12/11.05 % Maximum resident set size: 3636 pages
% 0.12/11.05
% 0.12/11.05 % -------------------------------------------------
% 0.12/11.05 % User time : 0.241 s
% 0.12/11.05 % System time : 0.023 s
% 0.12/11.05 % Total time : 0.264 s
% 0.12/11.05 % Maximum resident set size: 4608 pages
% 0.12/11.05 % E exiting
%------------------------------------------------------------------------------