%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP066-1 : 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 : n005.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 0.26s 0.63s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 35 ( 31 unt; 0 nHn; 6 RR)
% Number of literals : 42 ( 41 equ; 12 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 : 60 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(identity,divide(X1,divide(X2,divide(divide(divide(X1,X1),X1),X3)))),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(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
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(c_0_5,axiom,
divide(divide(identity,divide(X1,divide(X2,divide(divide(divide(X1,X1),X1),X3)))),X3) = X2,
single_axiom ).
cnf(c_0_6,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_7,plain,
divide(divide(identity,divide(X1,divide(X2,divide(divide(identity,X1),X3)))),X3) = X2,
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
multiply ).
cnf(c_0_9,plain,
divide(multiply(identity,multiply(X1,X2)),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_6]),c_0_8]),c_0_8]) ).
cnf(c_0_10,plain,
multiply(X1,identity) = divide(X1,identity),
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_11,plain,
multiply(divide(identity,divide(X1,divide(X2,identity))),X1) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_6]),c_0_8]) ).
cnf(c_0_12,plain,
divide(multiply(identity,divide(X1,identity)),identity) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
multiply(identity,divide(X1,identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_6]),c_0_6]) ).
cnf(c_0_14,plain,
divide(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,plain,
multiply(identity,X1) = X1,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
divide(multiply(X1,X2),X2) = X1,
inference(rw,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_17,plain,
multiply(X1,divide(identity,X2)) = divide(X1,multiply(identity,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_18,plain,
divide(identity,divide(X1,multiply(X2,X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_14]),c_0_14]),c_0_8]) ).
cnf(c_0_19,plain,
multiply(divide(X1,X2),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_16]),c_0_17]),c_0_15]) ).
cnf(c_0_20,plain,
divide(identity,divide(X1,divide(X2,divide(divide(identity,X1),divide(divide(identity,X3),X4))))) = divide(divide(identity,divide(X3,X2)),X4),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_21,plain,
divide(identity,divide(X1,X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
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 ),
inference(fof_simplification,[status(thm)],[prove_these_axioms]) ).
cnf(c_0_23,plain,
divide(divide(X1,divide(divide(identity,X2),divide(divide(identity,X3),X4))),X2) = divide(divide(X1,X3),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
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_22 ).
cnf(c_0_25,axiom,
inverse(X1) = divide(identity,X1),
inverse ).
cnf(c_0_26,plain,
multiply(divide(identity,X1),X1) = identity,
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_27,plain,
divide(X1,multiply(X2,X3)) = divide(divide(X1,X3),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_23]),c_0_6]),c_0_21]),c_0_8]) ).
cnf(c_0_28,negated_conjecture,
( multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_29,plain,
multiply(X1,divide(X2,X3)) = divide(X1,divide(X3,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_21]) ).
cnf(c_0_30,plain,
divide(multiply(X1,X2),X3) = divide(X1,divide(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_27]),c_0_21]) ).
cnf(c_0_31,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_15])]) ).
cnf(c_0_32,plain,
multiply(X1,multiply(X2,X3)) = divide(X1,divide(divide(identity,X3),X2)),
inference(spm,[status(thm)],[c_0_29,c_0_8]) ).
cnf(c_0_33,plain,
multiply(multiply(X1,X2),X3) = divide(X1,divide(divide(identity,X3),X2)),
inference(spm,[status(thm)],[c_0_8,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP066-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.09 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.48 % Computer : n005.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Sun Sep 20 19:56:33 UTC 2026
% 0.23/0.48 % CPUTime :
% 0.23/0.48 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.56 Running first-order theorem proving
% 0.26/0.56 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
% 0.26/0.63 % Version: 3.5.1
% 0.26/0.63 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.26/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.26/0.63 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.63 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.63 % Starting sh5l with 300s (1) cores
% 0.26/0.63 % new_bool_3 with pid 1626999 completed with status 0
% 0.26/0.63 % Result found by new_bool_3
% 0.26/0.63 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.26/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.26/0.63 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.63 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.63 % Search class: FUHPM-FFSF21-DFFFFFNN
% 0.26/0.63 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.63 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.63 % SubtermCWHack with pid 1627004 completed with status 0
% 0.26/0.63 % Result found by SubtermCWHack
% 0.26/0.63 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.26/0.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.26/0.63 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.63 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.63 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.63 % Search class: FUHPM-FFSF21-DFFFFFNN
% 0.26/0.63 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.63 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.63 % Preprocessing time : 0.001 s
% 0.26/0.63
% 0.26/0.63 % Proof found!
% 0.26/0.63 % SZS status Unsatisfiable
% 0.26/0.63 % SZS output start CNFRefutation
% See solution above
% 0.26/0.63 % Parsed axioms : 5
% 0.26/0.63 % Removed by relevancy pruning/SinE : 0
% 0.26/0.63 % Initial clauses : 5
% 0.26/0.63 % Removed in clause preprocessing : 0
% 0.26/0.63 % Initial clauses in saturation : 5
% 0.26/0.63 % Processed clauses : 78
% 0.26/0.63 % ...of these trivial : 29
% 0.26/0.63 % ...subsumed : 0
% 0.26/0.63 % ...remaining for further processing : 48
% 0.26/0.63 % Other redundant clauses eliminated : 0
% 0.26/0.63 % Clauses deleted for lack of memory : 0
% 0.26/0.63 % Backward-subsumed : 0
% 0.26/0.63 % Backward-rewritten : 30
% 0.26/0.63 % Generated clauses : 684
% 0.26/0.63 % ...of the previous two non-redundant : 317
% 0.26/0.63 % ...aggressively subsumed : 0
% 0.26/0.63 % Contextual simplify-reflections : 0
% 0.26/0.63 % Paramodulations : 684
% 0.26/0.63 % Factorizations : 0
% 0.26/0.63 % NegExts : 0
% 0.26/0.63 % Equation resolutions : 0
% 0.26/0.63 % Disequality decompositions : 0
% 0.26/0.63 % Total rewrite steps : 1266
% 0.26/0.63 % ...of those cached : 888
% 0.26/0.63 % Propositional unsat checks : 0
% 0.26/0.63 % Propositional check models : 0
% 0.26/0.63 % Propositional check unsatisfiable : 0
% 0.26/0.63 % Propositional clauses : 0
% 0.26/0.63 % Propositional clauses after purity: 0
% 0.26/0.63 % Propositional unsat core size : 0
% 0.26/0.63 % Propositional preprocessing time : 0.000
% 0.26/0.63 % Propositional encoding time : 0.000
% 0.26/0.63 % Propositional solver time : 0.000
% 0.26/0.63 % Success case prop preproc time : 0.000
% 0.26/0.63 % Success case prop encoding time : 0.000
% 0.26/0.63 % Success case prop solver time : 0.000
% 0.26/0.63 % Current number of processed clauses : 18
% 0.26/0.63 % Positive orientable unit clauses : 18
% 0.26/0.63 % Positive unorientable unit clauses: 0
% 0.26/0.63 % Negative unit clauses : 0
% 0.26/0.63 % Non-unit-clauses : 0
% 0.26/0.63 % Current number of unprocessed clauses: 140
% 0.26/0.63 % ...number of literals in the above : 140
% 0.26/0.63 % Current number of archived formulas : 0
% 0.26/0.63 % Current number of archived clauses : 30
% 0.26/0.63 % Clause-clause subsumption calls (NU) : 0
% 0.26/0.63 % Rec. Clause-clause subsumption calls : 0
% 0.26/0.63 % Non-unit clause-clause subsumptions : 0
% 0.26/0.63 % Unit Clause-clause subsumption calls : 0
% 0.26/0.63 % Rewrite failures with RHS unbound : 0
% 0.26/0.63 % BW rewrite match attempts : 36
% 0.26/0.63 % BW rewrite match successes : 30
% 0.26/0.63 % Condensation attempts : 0
% 0.26/0.63 % Condensation successes : 0
% 0.26/0.63 % Termbank termtop insertions : 6588
% 0.26/0.63 % Search garbage collected termcells : 8
% 0.26/0.63
% 0.26/0.63 % -------------------------------------------------
% 0.26/0.63 % User time : 0.009 s
% 0.26/0.63 % System time : 0.003 s
% 0.26/0.63 % Total time : 0.012 s
% 0.26/0.63 % Maximum resident set size: 3636 pages
% 0.26/0.63
% 0.26/0.63 % -------------------------------------------------
% 0.26/0.63 % User time : 0.014 s
% 0.26/0.63 % System time : 0.007 s
% 0.26/0.63 % Total time : 0.021 s
% 0.26/0.63 % Maximum resident set size: 4608 pages
% 0.26/0.63 % E exiting
%------------------------------------------------------------------------------