%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP068-1 : 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 : n006.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 12:37:47 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of clauses : 30 ( 25 unt; 0 nHn; 8 RR)
% Number of literals : 39 ( 38 equ; 16 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 : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(X1,divide(divide(divide(identity,X2),X3),divide(divide(divide(X1,X1),X1),X3))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(identity,axiom,
identity = divide(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
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(inverse,axiom,
inverse(X1) = divide(identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_5,axiom,
divide(X1,divide(divide(divide(identity,X2),X3),divide(divide(divide(X1,X1),X1),X3))) = X2,
single_axiom ).
cnf(c_0_6,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_7,plain,
divide(X1,divide(divide(divide(identity,X2),X3),divide(divide(identity,X1),X3))) = X2,
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
divide(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
divide(X1,divide(divide(identity,X2),divide(identity,X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_10,plain,
divide(X1,divide(X2,divide(identity,X1))) = divide(identity,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_9]),c_0_6]),c_0_8]) ).
cnf(c_0_11,plain,
divide(identity,divide(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_8]),c_0_8]) ).
cnf(c_0_12,plain,
divide(divide(identity,X1),divide(X2,X1)) = divide(identity,X2),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,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_14,plain,
divide(divide(identity,divide(X1,X2)),divide(identity,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_12]),c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
c_0_13 ).
cnf(c_0_16,axiom,
inverse(X1) = divide(identity,X1),
inverse ).
cnf(c_0_17,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
multiply ).
cnf(c_0_18,plain,
divide(divide(identity,divide(divide(identity,X1),X2)),X1) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
cnf(c_0_19,plain,
divide(X1,divide(X2,divide(divide(identity,X1),divide(divide(divide(identity,X2),X3),divide(X4,X3))))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_7]),c_0_11]) ).
cnf(c_0_20,negated_conjecture,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(divide(identity,a1),divide(identity,a1)) != identity
| divide(identity,divide(identity,a2)) != 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_15,c_0_16]),c_0_17]),c_0_17]),c_0_17]),c_0_17]),c_0_17]),c_0_17]) ).
cnf(c_0_21,plain,
divide(identity,divide(divide(X1,X2),divide(X3,X2))) = divide(X3,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_6]),c_0_11]) ).
cnf(c_0_22,negated_conjecture,
( divide(identity,divide(identity,a2)) != a2
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_6])]) ).
cnf(c_0_23,plain,
divide(identity,divide(X1,X2)) = divide(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_8]),c_0_8]) ).
cnf(c_0_24,negated_conjecture,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_11])]) ).
cnf(c_0_25,plain,
divide(divide(X1,X2),divide(X3,X2)) = divide(X1,X3),
inference(rw,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_26,plain,
divide(divide(X1,divide(identity,X2)),X2) = X1,
inference(rw,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(divide(identity,c3),b3)),
inference(rw,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_28,plain,
divide(divide(X1,divide(identity,X2)),X3) = divide(X1,divide(X3,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP068-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n006.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 19:56:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1129729 completed with status 0
% 0.10/0.44 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.10/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.10/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.44 % No SInE strategy applied
% 0.10/0.44 % Search class: FUHPS-FFSF22-MFFFFFNN
% 0.10/0.44 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 0.10/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 0.10/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.44 % new_bool_1 with pid 1129737 completed with status 0
% 0.10/0.44 % Result found by new_bool_1
% 0.10/0.44 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.10/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.44 % No SInE strategy applied
% 0.10/0.44 % Search class: FUHPS-FFSF22-MFFFFFNN
% 0.10/0.44 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 0.10/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.44 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.10/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 0.10/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.10/0.44 % Preprocessing time : 0.001 s
% 0.10/0.44 % Presaturation interreduction done
% 0.10/0.44
% 0.10/0.44 % Proof found!
% 0.10/0.44 % SZS status Unsatisfiable
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44 % Parsed axioms : 5
% 0.10/0.44 % Removed by relevancy pruning/SinE : 0
% 0.10/0.44 % Initial clauses : 5
% 0.10/0.44 % Removed in clause preprocessing : 2
% 0.10/0.44 % Initial clauses in saturation : 3
% 0.10/0.44 % Processed clauses : 33
% 0.10/0.44 % ...of these trivial : 9
% 0.10/0.44 % ...subsumed : 0
% 0.10/0.44 % ...remaining for further processing : 24
% 0.10/0.44 % Other redundant clauses eliminated : 0
% 0.10/0.44 % Clauses deleted for lack of memory : 0
% 0.10/0.44 % Backward-subsumed : 0
% 0.10/0.44 % Backward-rewritten : 13
% 0.10/0.44 % Generated clauses : 362
% 0.10/0.44 % ...of the previous two non-redundant : 192
% 0.10/0.44 % ...aggressively subsumed : 0
% 0.10/0.44 % Contextual simplify-reflections : 0
% 0.10/0.44 % Paramodulations : 362
% 0.10/0.44 % Factorizations : 0
% 0.10/0.44 % NegExts : 0
% 0.10/0.44 % Equation resolutions : 0
% 0.10/0.44 % Disequality decompositions : 0
% 0.10/0.44 % Total rewrite steps : 443
% 0.10/0.44 % ...of those cached : 333
% 0.10/0.44 % Propositional unsat checks : 0
% 0.10/0.44 % Propositional check models : 0
% 0.10/0.44 % Propositional check unsatisfiable : 0
% 0.10/0.44 % Propositional clauses : 0
% 0.10/0.44 % Propositional clauses after purity: 0
% 0.10/0.44 % Propositional unsat core size : 0
% 0.10/0.44 % Propositional preprocessing time : 0.000
% 0.10/0.44 % Propositional encoding time : 0.000
% 0.10/0.44 % Propositional solver time : 0.000
% 0.10/0.44 % Success case prop preproc time : 0.000
% 0.10/0.44 % Success case prop encoding time : 0.000
% 0.10/0.44 % Success case prop solver time : 0.000
% 0.10/0.44 % Current number of processed clauses : 8
% 0.10/0.44 % Positive orientable unit clauses : 8
% 0.10/0.44 % Positive unorientable unit clauses: 0
% 0.10/0.44 % Negative unit clauses : 0
% 0.10/0.44 % Non-unit-clauses : 0
% 0.10/0.44 % Current number of unprocessed clauses: 155
% 0.10/0.44 % ...number of literals in the above : 155
% 0.10/0.44 % Current number of archived formulas : 0
% 0.10/0.44 % Current number of archived clauses : 18
% 0.10/0.44 % Clause-clause subsumption calls (NU) : 0
% 0.10/0.44 % Rec. Clause-clause subsumption calls : 0
% 0.10/0.44 % Non-unit clause-clause subsumptions : 0
% 0.10/0.44 % Unit Clause-clause subsumption calls : 0
% 0.10/0.44 % Rewrite failures with RHS unbound : 0
% 0.10/0.44 % BW rewrite match attempts : 36
% 0.10/0.44 % BW rewrite match successes : 13
% 0.10/0.44 % Condensation attempts : 0
% 0.10/0.44 % Condensation successes : 0
% 0.10/0.44 % Termbank termtop insertions : 4006
% 0.10/0.44 % Search garbage collected termcells : 8
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.003 s
% 0.10/0.44 % System time : 0.003 s
% 0.10/0.44 % Total time : 0.006 s
% 0.10/0.44 % Maximum resident set size: 3636 pages
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.022 s
% 0.10/0.44 % System time : 0.009 s
% 0.10/0.44 % Total time : 0.032 s
% 0.10/0.44 % Maximum resident set size: 4608 pages
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------