%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP079-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of clauses : 36 ( 31 unt; 0 nHn; 8 RR)
% Number of literals : 45 ( 44 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 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 : 50 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity,axiom,
identity = double_divide(X1,inverse(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
cnf(inverse,axiom,
inverse(X1) = double_divide(X1,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(single_axiom,axiom,
double_divide(double_divide(identity,X1),double_divide(double_divide(double_divide(X2,X3),double_divide(identity,identity)),double_divide(X1,X3))) = X2,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(multiply,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
file('/export/starexec/sandbox2/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(identity,X1),double_divide(double_divide(double_divide(X2,X3),double_divide(identity,identity)),double_divide(X1,X3))) = X2,
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(identity,X1),double_divide(identity,double_divide(X1,double_divide(X2,identity)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_10,plain,
double_divide(double_divide(identity,X1),double_divide(identity,identity)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_11,plain,
double_divide(identity,identity) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_8]),c_0_8]) ).
cnf(c_0_12,plain,
double_divide(double_divide(identity,X1),identity) = X1,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,plain,
double_divide(double_divide(identity,X1),X1) = identity,
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_14,plain,
double_divide(identity,double_divide(X1,identity)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_13]),c_0_11]),c_0_12]) ).
cnf(c_0_15,plain,
double_divide(identity,double_divide(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_14]),c_0_11]) ).
cnf(c_0_16,plain,
double_divide(X1,identity) = double_divide(identity,X1),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_17,plain,
double_divide(double_divide(X1,identity),X1) = identity,
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_18,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_17]),c_0_14]),c_0_11]),c_0_16]),c_0_16]),c_0_15]) ).
cnf(c_0_19,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_20,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
cnf(c_0_21,plain,
double_divide(double_divide(identity,X1),double_divide(identity,double_divide(X1,X2))) = double_divide(identity,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_13]),c_0_8]) ).
cnf(c_0_22,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
c_0_19 ).
cnf(c_0_23,axiom,
multiply(X1,X2) = double_divide(double_divide(X2,X1),identity),
multiply ).
cnf(c_0_24,plain,
double_divide(double_divide(identity,X1),double_divide(identity,X2)) = double_divide(identity,double_divide(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,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_22,c_0_6]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_26,plain,
double_divide(X1,double_divide(double_divide(identity,double_divide(X2,double_divide(double_divide(identity,double_divide(X3,X4)),double_divide(X1,X4)))),X3)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_7]),c_0_15]),c_0_11]),c_0_16]),c_0_11]),c_0_16]) ).
cnf(c_0_27,plain,
double_divide(double_divide(identity,double_divide(X1,X2)),double_divide(X3,X2)) = double_divide(X1,double_divide(identity,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_7]),c_0_11]),c_0_16]) ).
cnf(c_0_28,plain,
double_divide(identity,double_divide(X1,double_divide(identity,X2))) = double_divide(X2,double_divide(identity,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_29,negated_conjecture,
( double_divide(identity,double_divide(a1,double_divide(identity,a1))) != identity
| 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(cn,[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)],[inference(rw,[status(thm)],[c_0_25,c_0_16]),c_0_16]),c_0_15]),c_0_16]),c_0_16]),c_0_16]),c_0_16]),c_0_16]),c_0_16])]) ).
cnf(c_0_30,plain,
double_divide(X1,double_divide(identity,X1)) = identity,
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_31,plain,
double_divide(identity,double_divide(double_divide(identity,X1),X2)) = double_divide(double_divide(identity,X2),X1),
inference(spm,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_32,plain,
double_divide(identity,double_divide(X1,double_divide(X2,double_divide(identity,X3)))) = double_divide(X2,double_divide(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_26]),c_0_27]),c_0_24]),c_0_18]),c_0_28]) ).
cnf(c_0_33,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)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_11])]),c_0_31]),c_0_28]) ).
cnf(c_0_34,plain,
double_divide(double_divide(X1,X2),double_divide(identity,X3)) = double_divide(double_divide(identity,X2),double_divide(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_24]),c_0_28]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP079-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 19:57:33 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.17/0.51 % Version: 3.5.1
% 0.17/0.51 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.17/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.17/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.17/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.17/0.51 % Starting sh5l with 300s (1) cores
% 0.17/0.51 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1087659 completed with status 0
% 0.17/0.51 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.17/0.51 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.17/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.17/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.51 % No SInE strategy applied
% 0.17/0.51 % Search class: FUHPS-FFSF22-MFFFFFNN
% 0.17/0.51 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 0.17/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.51 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.17/0.51 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 0.17/0.51 % Starting new_bool_3 with 136s (1) cores
% 0.17/0.51 % Starting new_bool_1 with 136s (1) cores
% 0.17/0.51 % SubtermCWHack with pid 1087663 completed with status 0
% 0.17/0.51 % Result found by SubtermCWHack
% 0.17/0.51 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.17/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.17/0.51 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.17/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.17/0.51 % No SInE strategy applied
% 0.17/0.51 % Search class: FUHPS-FFSF22-MFFFFFNN
% 0.17/0.51 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 0.17/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.17/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.17/0.51 % Preprocessing time : 0.001 s
% 0.17/0.51
% 0.17/0.51 % Proof found!
% 0.17/0.51 % SZS status Unsatisfiable
% 0.17/0.51 % SZS output start CNFRefutation
% See solution above
% 0.17/0.51 % Parsed axioms : 5
% 0.17/0.51 % Removed by relevancy pruning/SinE : 0
% 0.17/0.51 % Initial clauses : 5
% 0.17/0.51 % Removed in clause preprocessing : 2
% 0.17/0.51 % Initial clauses in saturation : 3
% 0.17/0.51 % Processed clauses : 676
% 0.17/0.51 % ...of these trivial : 131
% 0.17/0.51 % ...subsumed : 447
% 0.17/0.51 % ...remaining for further processing : 98
% 0.17/0.51 % Other redundant clauses eliminated : 0
% 0.17/0.51 % Clauses deleted for lack of memory : 0
% 0.17/0.51 % Backward-subsumed : 0
% 0.17/0.51 % Backward-rewritten : 66
% 0.17/0.51 % Generated clauses : 9717
% 0.17/0.51 % ...of the previous two non-redundant : 5531
% 0.17/0.51 % ...aggressively subsumed : 0
% 0.17/0.51 % Contextual simplify-reflections : 0
% 0.17/0.51 % Paramodulations : 9717
% 0.17/0.51 % Factorizations : 0
% 0.17/0.51 % NegExts : 0
% 0.17/0.51 % Equation resolutions : 0
% 0.17/0.51 % Disequality decompositions : 0
% 0.17/0.51 % Total rewrite steps : 20812
% 0.17/0.51 % ...of those cached : 18403
% 0.17/0.51 % Propositional unsat checks : 0
% 0.17/0.51 % Propositional check models : 0
% 0.17/0.51 % Propositional check unsatisfiable : 0
% 0.17/0.51 % Propositional clauses : 0
% 0.17/0.51 % Propositional clauses after purity: 0
% 0.17/0.51 % Propositional unsat core size : 0
% 0.17/0.51 % Propositional preprocessing time : 0.000
% 0.17/0.51 % Propositional encoding time : 0.000
% 0.17/0.51 % Propositional solver time : 0.000
% 0.17/0.51 % Success case prop preproc time : 0.000
% 0.17/0.51 % Success case prop encoding time : 0.000
% 0.17/0.51 % Success case prop solver time : 0.000
% 0.17/0.51 % Current number of processed clauses : 32
% 0.17/0.51 % Positive orientable unit clauses : 28
% 0.17/0.51 % Positive unorientable unit clauses: 4
% 0.17/0.51 % Negative unit clauses : 0
% 0.17/0.51 % Non-unit-clauses : 0
% 0.17/0.51 % Current number of unprocessed clauses: 3892
% 0.17/0.51 % ...number of literals in the above : 3892
% 0.17/0.51 % Current number of archived formulas : 0
% 0.17/0.51 % Current number of archived clauses : 68
% 0.17/0.51 % Clause-clause subsumption calls (NU) : 0
% 0.17/0.51 % Rec. Clause-clause subsumption calls : 0
% 0.17/0.51 % Non-unit clause-clause subsumptions : 0
% 0.17/0.51 % Unit Clause-clause subsumption calls : 39
% 0.17/0.51 % Rewrite failures with RHS unbound : 0
% 0.17/0.51 % BW rewrite match attempts : 346
% 0.17/0.51 % BW rewrite match successes : 94
% 0.17/0.51 % Condensation attempts : 0
% 0.17/0.51 % Condensation successes : 0
% 0.17/0.51 % Termbank termtop insertions : 162463
% 0.17/0.51 % Search garbage collected termcells : 8
% 0.17/0.51
% 0.17/0.51 % -------------------------------------------------
% 0.17/0.51 % User time : 0.059 s
% 0.17/0.51 % System time : 0.009 s
% 0.17/0.51 % Total time : 0.069 s
% 0.17/0.51 % Maximum resident set size: 3608 pages
% 0.17/0.51
% 0.17/0.51 % -------------------------------------------------
% 0.17/0.51 % User time : 0.265 s
% 0.17/0.51 % System time : 0.037 s
% 0.17/0.51 % Total time : 0.301 s
% 0.17/0.51 % Maximum resident set size: 4608 pages
% 0.17/0.51 % E exiting
%------------------------------------------------------------------------------