%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP071-1 : 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 : n004.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 2.19s 0.84s
% Output : CNFRefutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 3
% Syntax : Number of clauses : 50 ( 46 unt; 0 nHn; 5 RR)
% Number of literals : 58 ( 57 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 157 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(inverse(divide(X1,divide(X2,divide(X3,X4)))),divide(divide(X4,X3),X1)) = X2,
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(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,inverse(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_3,axiom,
divide(inverse(divide(X1,divide(X2,divide(X3,X4)))),divide(divide(X4,X3),X1)) = X2,
single_axiom ).
cnf(c_0_4,plain,
divide(inverse(divide(X1,X2)),divide(divide(X3,divide(X4,X5)),X1)) = inverse(divide(X3,divide(X2,divide(X5,X4)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
inverse(divide(X1,divide(divide(X2,divide(divide(X3,X4),X1)),divide(X4,X3)))) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,plain,
inverse(inverse(divide(X1,divide(X2,divide(inverse(divide(divide(X3,X4),X2)),divide(X4,X3)))))) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_7,plain,
inverse(divide(divide(inverse(divide(divide(X1,X2),divide(X3,X4))),divide(X2,X1)),divide(X5,divide(X4,X3)))) = inverse(inverse(X5)),
inference(spm,[status(thm)],[c_0_6,c_0_3]) ).
cnf(c_0_8,plain,
divide(inverse(inverse(X1)),divide(divide(X2,X3),divide(inverse(divide(divide(X4,X5),divide(X2,X3))),divide(X5,X4)))) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_7]) ).
cnf(c_0_9,plain,
divide(inverse(X1),divide(divide(X2,X3),inverse(divide(divide(X3,X2),divide(X1,divide(X4,X5)))))) = divide(X5,X4),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_10,plain,
divide(inverse(inverse(X1)),divide(X2,divide(inverse(divide(divide(X3,X4),X2)),divide(X4,X3)))) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_8]) ).
cnf(c_0_11,plain,
divide(divide(divide(X1,X2),inverse(divide(divide(X2,X1),divide(X3,divide(X4,X5))))),inverse(X3)) = divide(X4,X5),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_9]),c_0_9]) ).
cnf(c_0_12,plain,
divide(inverse(X1),divide(divide(divide(X2,X3),inverse(divide(divide(X3,X2),X4))),inverse(inverse(X1)))) = X4,
inference(spm,[status(thm)],[c_0_3,c_0_10]) ).
cnf(c_0_13,plain,
divide(divide(divide(X1,X2),inverse(divide(divide(X2,X1),divide(X3,X4)))),inverse(X3)) = X4,
inference(spm,[status(thm)],[c_0_11,c_0_3]) ).
cnf(c_0_14,plain,
divide(X1,divide(divide(divide(X2,X3),inverse(divide(divide(X3,X2),X4))),inverse(X1))) = X4,
inference(spm,[status(thm)],[c_0_12,c_0_6]) ).
cnf(c_0_15,plain,
divide(divide(divide(X1,X2),X3),inverse(divide(X3,divide(divide(X4,X5),divide(X2,X1))))) = divide(X5,X4),
inference(spm,[status(thm)],[c_0_13,c_0_5]) ).
cnf(c_0_16,plain,
divide(divide(inverse(divide(divide(X1,X2),X3)),divide(divide(X4,X5),divide(X1,X2))),divide(X5,X4)) = X3,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
divide(divide(inverse(divide(X1,X2)),divide(divide(X3,X4),X1)),divide(X4,X3)) = X2,
inference(spm,[status(thm)],[c_0_16,c_0_16]) ).
cnf(c_0_18,plain,
divide(divide(divide(divide(divide(X1,X2),X3),inverse(divide(X3,X4))),inverse(X4)),inverse(X2)) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_19,plain,
divide(divide(X1,inverse(X2)),inverse(inverse(divide(X3,X4)))) = divide(divide(X1,divide(inverse(X4),X2)),X3),
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
cnf(c_0_20,plain,
inverse(divide(divide(X1,X2),divide(X3,divide(divide(divide(X2,X1),X4),inverse(X3))))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_19]),c_0_4]) ).
cnf(c_0_21,plain,
divide(X1,divide(divide(inverse(X2),divide(divide(X3,X4),X1)),divide(X4,X3))) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_20]) ).
cnf(c_0_22,plain,
divide(divide(X1,X2),divide(X3,divide(divide(divide(X2,X1),inverse(X4)),inverse(X3)))) = X4,
inference(spm,[status(thm)],[c_0_21,c_0_21]) ).
cnf(c_0_23,plain,
divide(divide(X1,X2),inverse(divide(divide(X2,X1),divide(X3,divide(X4,inverse(X3)))))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_4]) ).
cnf(c_0_24,plain,
divide(X1,divide(X2,inverse(X1))) = divide(X3,divide(X2,inverse(X3))),
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_25,plain,
divide(divide(divide(divide(divide(X1,inverse(X2)),X2),X3),inverse(divide(X3,X4))),inverse(X4)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_26,plain,
divide(divide(X1,inverse(X2)),X2) = divide(divide(X1,inverse(X3)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_24]),c_0_9]) ).
cnf(c_0_27,plain,
divide(divide(X1,divide(divide(X2,inverse(X3)),X3)),divide(X4,X2)) = divide(X1,X4),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_28,plain,
divide(divide(X1,X2),divide(X3,divide(divide(divide(X2,X1),inverse(X4)),X4))) = inverse(X3),
inference(spm,[status(thm)],[c_0_22,c_0_26]) ).
cnf(c_0_29,plain,
divide(inverse(divide(X1,X2)),inverse(X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_27]),c_0_28]) ).
cnf(c_0_30,plain,
divide(inverse(divide(X1,divide(X2,X3))),divide(divide(divide(divide(X4,X5),X6),inverse(divide(X6,divide(X3,divide(X5,X4))))),X1)) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_31,plain,
divide(inverse(X1),inverse(inverse(divide(X2,X1)))) = inverse(X2),
inference(spm,[status(thm)],[c_0_29,c_0_29]) ).
cnf(c_0_32,plain,
inverse(inverse(divide(X1,divide(X2,inverse(inverse(X2)))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_27]),c_0_28]) ).
cnf(c_0_33,plain,
divide(inverse(divide(inverse(divide(X1,divide(X2,divide(X3,inverse(X2))))),divide(X4,X1))),X3) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_23]),c_0_3]) ).
cnf(c_0_34,plain,
divide(inverse(divide(X1,inverse(inverse(X1)))),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
inverse(divide(X1,divide(X2,inverse(X1)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_27]),c_0_28]) ).
cnf(c_0_36,plain,
divide(X1,X1) = inverse(divide(X2,inverse(inverse(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]),c_0_35]) ).
cnf(c_0_37,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(fof_simplification,[status(thm)],[prove_these_axioms]) ).
cnf(c_0_38,plain,
divide(inverse(divide(divide(X1,divide(divide(X2,inverse(X3)),inverse(X1))),divide(X4,X2))),X3) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_22]),c_0_3]) ).
cnf(c_0_39,plain,
divide(X1,divide(X2,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_36]),c_0_34]),c_0_29]) ).
cnf(c_0_40,plain,
divide(divide(X1,X1),X2) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_36]),c_0_32]) ).
cnf(c_0_41,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
c_0_37 ).
cnf(c_0_42,axiom,
multiply(X1,X2) = divide(X1,inverse(X2)),
multiply ).
cnf(c_0_43,plain,
divide(divide(X1,inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_35]) ).
cnf(c_0_44,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_40]),c_0_39]),c_0_29]),c_0_39]) ).
cnf(c_0_45,negated_conjecture,
( divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3))))
| divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1))
| divide(divide(inverse(b2),inverse(b2)),inverse(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)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_42]),c_0_42]),c_0_42]),c_0_42]),c_0_42]),c_0_42]),c_0_42]) ).
cnf(c_0_46,plain,
divide(X1,X1) = divide(X2,X2),
inference(spm,[status(thm)],[c_0_36,c_0_36]) ).
cnf(c_0_47,plain,
divide(divide(X1,inverse(X2)),X3) = divide(X1,divide(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_43]),c_0_43]) ).
cnf(c_0_48,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_43]),c_0_44]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48]),c_0_40]),c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP071-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 % Computer : n004.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 20 19:56:20 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.47 Running first-order theorem proving
% 0.18/0.47 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
% 2.19/0.84 % Version: 3.5.1
% 2.19/0.84 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.19/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.19/0.84 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.19/0.84 % Starting new_bool_3 with 300s (1) cores
% 2.19/0.84 % Starting new_bool_1 with 300s (1) cores
% 2.19/0.84 % Starting sh5l with 300s (1) cores
% 2.19/0.84 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1351338 completed with status 0
% 2.19/0.84 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 2.19/0.84 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.19/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.19/0.84 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.19/0.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.19/0.84 % No SInE strategy applied
% 2.19/0.84 % Search class: FUHPF-FFSF21-MFFFFFNN
% 2.19/0.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.19/0.84 % Starting SubtermCWHack with 136s (1) cores
% 2.19/0.84 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.19/0.84 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 2.19/0.84 % Starting new_bool_3 with 136s (1) cores
% 2.19/0.84 % Starting new_bool_1 with 136s (1) cores
% 2.19/0.84 % SubtermCWHack with pid 1351343 completed with status 0
% 2.19/0.84 % Result found by SubtermCWHack
% 2.19/0.84 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.19/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.19/0.84 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.19/0.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.19/0.84 % No SInE strategy applied
% 2.19/0.84 % Search class: FUHPF-FFSF21-MFFFFFNN
% 2.19/0.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.19/0.84 % Starting SubtermCWHack with 136s (1) cores
% 2.19/0.84 % Preprocessing time : 0.002 s
% 2.19/0.84
% 2.19/0.84 % Proof found!
% 2.19/0.84 % SZS status Unsatisfiable
% 2.19/0.84 % SZS output start CNFRefutation
% See solution above
% 2.19/0.84 % Parsed axioms : 3
% 2.19/0.84 % Removed by relevancy pruning/SinE : 0
% 2.19/0.84 % Initial clauses : 3
% 2.19/0.84 % Removed in clause preprocessing : 1
% 2.19/0.84 % Initial clauses in saturation : 2
% 2.19/0.84 % Processed clauses : 385
% 2.19/0.84 % ...of these trivial : 189
% 2.19/0.84 % ...subsumed : 105
% 2.19/0.84 % ...remaining for further processing : 90
% 2.19/0.84 % Other redundant clauses eliminated : 0
% 2.19/0.84 % Clauses deleted for lack of memory : 0
% 2.19/0.84 % Backward-subsumed : 0
% 2.19/0.84 % Backward-rewritten : 73
% 2.19/0.84 % Generated clauses : 12286
% 2.19/0.84 % ...of the previous two non-redundant : 10321
% 2.19/0.84 % ...aggressively subsumed : 0
% 2.19/0.84 % Contextual simplify-reflections : 0
% 2.19/0.84 % Paramodulations : 12285
% 2.19/0.84 % Factorizations : 0
% 2.19/0.84 % NegExts : 0
% 2.19/0.84 % Equation resolutions : 0
% 2.19/0.84 % Disequality decompositions : 0
% 2.19/0.84 % Total rewrite steps : 12882
% 2.19/0.84 % ...of those cached : 8664
% 2.19/0.84 % Propositional unsat checks : 0
% 2.19/0.84 % Propositional check models : 0
% 2.19/0.84 % Propositional check unsatisfiable : 0
% 2.19/0.84 % Propositional clauses : 0
% 2.19/0.84 % Propositional clauses after purity: 0
% 2.19/0.84 % Propositional unsat core size : 0
% 2.19/0.84 % Propositional preprocessing time : 0.000
% 2.19/0.84 % Propositional encoding time : 0.000
% 2.19/0.84 % Propositional solver time : 0.000
% 2.19/0.84 % Success case prop preproc time : 0.000
% 2.19/0.84 % Success case prop encoding time : 0.000
% 2.19/0.84 % Success case prop solver time : 0.000
% 2.19/0.84 % Current number of processed clauses : 16
% 2.19/0.84 % Positive orientable unit clauses : 15
% 2.19/0.84 % Positive unorientable unit clauses: 1
% 2.19/0.84 % Negative unit clauses : 0
% 2.19/0.84 % Non-unit-clauses : 0
% 2.19/0.84 % Current number of unprocessed clauses: 4929
% 2.19/0.84 % ...number of literals in the above : 4929
% 2.19/0.84 % Current number of archived formulas : 0
% 2.19/0.84 % Current number of archived clauses : 75
% 2.19/0.84 % Clause-clause subsumption calls (NU) : 0
% 2.19/0.84 % Rec. Clause-clause subsumption calls : 0
% 2.19/0.84 % Non-unit clause-clause subsumptions : 0
% 2.19/0.84 % Unit Clause-clause subsumption calls : 178
% 2.19/0.84 % Rewrite failures with RHS unbound : 282
% 2.19/0.84 % BW rewrite match attempts : 765
% 2.19/0.84 % BW rewrite match successes : 120
% 2.19/0.84 % Condensation attempts : 0
% 2.19/0.84 % Condensation successes : 0
% 2.19/0.84 % Termbank termtop insertions : 194456
% 2.19/0.84 % Search garbage collected termcells : 8
% 2.19/0.84
% 2.19/0.84 % -------------------------------------------------
% 2.19/0.84 % User time : 0.293 s
% 2.19/0.84 % System time : 0.021 s
% 2.19/0.84 % Total time : 0.314 s
% 2.19/0.84 % Maximum resident set size: 3584 pages
% 2.19/0.84
% 2.19/0.84 % -------------------------------------------------
% 2.19/0.84 % User time : 1.131 s
% 2.19/0.84 % System time : 0.082 s
% 2.19/0.84 % Total time : 1.213 s
% 2.19/0.84 % Maximum resident set size: 4608 pages
% 2.19/0.84 % E exiting
%------------------------------------------------------------------------------