%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP074-1 : 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 : n017.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 0.14s 0.50s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of clauses : 37 ( 31 unt; 0 nHn; 9 RR)
% Number of literals : 48 ( 47 equ; 19 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 : 95 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(inverse(divide(divide(divide(X1,X1),X2),divide(X3,divide(X2,X4)))),X4) = 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(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(divide(divide(X1,X1),X2),divide(X3,divide(X2,X4)))),X4) = X3,
single_axiom ).
cnf(c_0_4,plain,
divide(inverse(divide(divide(divide(X1,X1),X2),X3)),X4) = inverse(divide(divide(divide(X5,X5),X6),divide(X3,divide(X6,divide(X2,X4))))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
divide(inverse(divide(divide(divide(X1,X1),inverse(divide(divide(divide(X2,X2),X3),divide(X4,divide(X3,X5))))),divide(X6,X4))),X5) = X6,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_6,plain,
divide(divide(inverse(divide(divide(divide(X1,X1),X2),X3)),X4),divide(X2,X4)) = X3,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_7,plain,
inverse(divide(divide(divide(X1,X1),X2),divide(divide(X3,X4),divide(X2,X4)))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_4]),c_0_3]) ).
cnf(c_0_8,plain,
divide(divide(X1,X2),divide(X3,X2)) = divide(divide(X1,X4),divide(X3,X4)),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
divide(divide(inverse(divide(divide(divide(X1,X1),X2),divide(X3,X2))),X4),divide(X5,X4)) = divide(X3,X5),
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_10,plain,
divide(divide(inverse(divide(X1,X2)),X3),divide(divide(X4,inverse(divide(divide(divide(X5,X5),X4),X1))),X3)) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_11,plain,
divide(divide(inverse(divide(divide(divide(X1,X2),divide(X3,X2)),X4)),X5),divide(divide(X3,X1),X5)) = X4,
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_12,plain,
divide(X1,divide(X2,inverse(divide(divide(divide(X3,X3),X2),divide(divide(X4,X4),X5))))) = divide(X1,X5),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
divide(X1,inverse(divide(divide(divide(X2,X2),X1),divide(divide(X3,X3),X4)))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_11]) ).
cnf(c_0_14,plain,
divide(inverse(divide(divide(divide(X1,X1),X2),divide(X3,divide(X4,X4)))),X2) = X3,
inference(spm,[status(thm)],[c_0_5,c_0_13]) ).
cnf(c_0_15,plain,
divide(X1,divide(X2,divide(X3,X3))) = divide(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_16,plain,
divide(X1,divide(X2,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_15]),c_0_11]) ).
cnf(c_0_17,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_18,plain,
inverse(divide(divide(X1,X1),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_16]),c_0_16]),c_0_16]) ).
cnf(c_0_19,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_17 ).
cnf(c_0_20,axiom,
multiply(X1,X2) = divide(X1,inverse(X2)),
multiply ).
cnf(c_0_21,plain,
divide(divide(X1,X1),X2) = inverse(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_13]),c_0_16]),c_0_18]) ).
cnf(c_0_22,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_19,c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]),c_0_20]) ).
cnf(c_0_23,plain,
divide(X1,inverse(divide(X2,X2))) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_24,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( inverse(inverse(a2)) != a2
| divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(rw,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_26,plain,
divide(inverse(divide(divide(divide(X1,X2),divide(X3,X2)),divide(X4,divide(divide(X3,X1),X5)))),X5) = X4,
inference(spm,[status(thm)],[c_0_3,c_0_8]) ).
cnf(c_0_27,plain,
divide(X1,X1) = divide(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_23]),c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( divide(inverse(a1),inverse(a1)) != divide(inverse(b1),inverse(b1))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_24])]) ).
cnf(c_0_29,plain,
divide(divide(X1,inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_21]),c_0_21]),c_0_24]) ).
cnf(c_0_30,negated_conjecture,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(sr,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_31,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_14]),c_0_21]),c_0_24]),c_0_16]) ).
cnf(c_0_32,plain,
divide(divide(X1,X2),divide(X3,X2)) = divide(X1,X3),
inference(spm,[status(thm)],[c_0_8,c_0_16]) ).
cnf(c_0_33,plain,
divide(divide(X1,X2),inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_27]),c_0_21]),c_0_24]),c_0_21]) ).
cnf(c_0_34,negated_conjecture,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3)),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
divide(divide(X1,inverse(X2)),X3) = divide(X1,divide(X3,X2)),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP074-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 19:52:13 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.50 % Version: 3.5.1
% 0.14/0.50 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.50 % Starting sh5l with 300s (1) cores
% 0.14/0.50 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 487279 completed with status 0
% 0.14/0.50 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.14/0.50 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.50 % No SInE strategy applied
% 0.14/0.50 % Search class: FUHPF-FFSF21-MFFFFFNN
% 0.14/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.14/0.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/0.50 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.50 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.50 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 487286 completed with status 0
% 0.14/0.50 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.14/0.50 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.50 % No SInE strategy applied
% 0.14/0.50 % Search class: FUHPF-FFSF21-MFFFFFNN
% 0.14/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.50 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.14/0.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.14/0.50 % Preprocessing time : 0.001 s
% 0.14/0.50 % Presaturation interreduction done
% 0.14/0.50
% 0.14/0.50 % Proof found!
% 0.14/0.50 % SZS status Unsatisfiable
% 0.14/0.50 % SZS output start CNFRefutation
% See solution above
% 0.14/0.50 % Parsed axioms : 3
% 0.14/0.50 % Removed by relevancy pruning/SinE : 0
% 0.14/0.50 % Initial clauses : 3
% 0.14/0.50 % Removed in clause preprocessing : 1
% 0.14/0.50 % Initial clauses in saturation : 2
% 0.14/0.50 % Processed clauses : 123
% 0.14/0.50 % ...of these trivial : 36
% 0.14/0.50 % ...subsumed : 38
% 0.14/0.50 % ...remaining for further processing : 49
% 0.14/0.50 % Other redundant clauses eliminated : 0
% 0.14/0.50 % Clauses deleted for lack of memory : 0
% 0.14/0.50 % Backward-subsumed : 1
% 0.14/0.50 % Backward-rewritten : 32
% 0.14/0.50 % Generated clauses : 3603
% 0.14/0.50 % ...of the previous two non-redundant : 3058
% 0.14/0.50 % ...aggressively subsumed : 0
% 0.14/0.50 % Contextual simplify-reflections : 0
% 0.14/0.50 % Paramodulations : 3602
% 0.14/0.50 % Factorizations : 0
% 0.14/0.50 % NegExts : 0
% 0.14/0.50 % Equation resolutions : 0
% 0.14/0.50 % Disequality decompositions : 0
% 0.14/0.50 % Total rewrite steps : 3647
% 0.14/0.50 % ...of those cached : 2258
% 0.14/0.50 % Propositional unsat checks : 0
% 0.14/0.50 % Propositional check models : 0
% 0.14/0.50 % Propositional check unsatisfiable : 0
% 0.14/0.50 % Propositional clauses : 0
% 0.14/0.50 % Propositional clauses after purity: 0
% 0.14/0.50 % Propositional unsat core size : 0
% 0.14/0.50 % Propositional preprocessing time : 0.000
% 0.14/0.50 % Propositional encoding time : 0.000
% 0.14/0.50 % Propositional solver time : 0.000
% 0.14/0.50 % Success case prop preproc time : 0.000
% 0.14/0.50 % Success case prop encoding time : 0.000
% 0.14/0.50 % Success case prop solver time : 0.000
% 0.14/0.50 % Current number of processed clauses : 13
% 0.14/0.50 % Positive orientable unit clauses : 12
% 0.14/0.50 % Positive unorientable unit clauses: 1
% 0.14/0.50 % Negative unit clauses : 0
% 0.14/0.50 % Non-unit-clauses : 0
% 0.14/0.50 % Current number of unprocessed clauses: 2839
% 0.14/0.50 % ...number of literals in the above : 2839
% 0.14/0.50 % Current number of archived formulas : 0
% 0.14/0.50 % Current number of archived clauses : 37
% 0.14/0.50 % Clause-clause subsumption calls (NU) : 0
% 0.14/0.50 % Rec. Clause-clause subsumption calls : 0
% 0.14/0.50 % Non-unit clause-clause subsumptions : 0
% 0.14/0.50 % Unit Clause-clause subsumption calls : 35
% 0.14/0.50 % Rewrite failures with RHS unbound : 263
% 0.14/0.50 % BW rewrite match attempts : 325
% 0.14/0.50 % BW rewrite match successes : 62
% 0.14/0.50 % Condensation attempts : 0
% 0.14/0.50 % Condensation successes : 0
% 0.14/0.50 % Termbank termtop insertions : 63946
% 0.14/0.50 % Search garbage collected termcells : 8
% 0.14/0.50
% 0.14/0.50 % -------------------------------------------------
% 0.14/0.50 % User time : 0.063 s
% 0.14/0.50 % System time : 0.008 s
% 0.14/0.50 % Total time : 0.071 s
% 0.14/0.50 % Maximum resident set size: 3636 pages
% 0.14/0.50
% 0.14/0.50 % -------------------------------------------------
% 0.14/0.50 % User time : 0.308 s
% 0.14/0.50 % System time : 0.035 s
% 0.14/0.50 % Total time : 0.342 s
% 0.14/0.50 % Maximum resident set size: 4608 pages
% 0.14/0.50 % E exiting
%------------------------------------------------------------------------------