%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP097-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:37:52 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.53s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of clauses : 35 ( 30 unt; 0 nHn; 7 RR)
% Number of literals : 48 ( 47 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(X1,inverse(divide(divide(X2,X3),divide(X1,X3)))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| 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(X1,inverse(divide(divide(X2,X3),divide(X1,X3)))) = X2,
single_axiom ).
cnf(c_0_4,plain,
divide(X1,inverse(divide(X2,divide(X1,inverse(divide(divide(X2,X3),divide(X4,X3))))))) = X4,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
divide(X1,inverse(divide(X2,X2))) = X1,
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_6,plain,
divide(X1,inverse(divide(X2,X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_5]),c_0_5]) ).
cnf(c_0_7,plain,
divide(inverse(divide(X1,X2)),inverse(X1)) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_8,plain,
inverse(divide(divide(X1,X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_9,plain,
divide(X1,divide(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_8]) ).
cnf(c_0_10,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_9,c_0_6]) ).
cnf(c_0_11,plain,
divide(divide(X1,X2),inverse(X2)) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| 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_13,plain,
divide(divide(X1,X1),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
divide(X1,inverse(divide(divide(X2,inverse(divide(divide(X3,X4),divide(X1,X4)))),X3))) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_15,plain,
divide(inverse(X1),divide(X2,X1)) = inverse(X2),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| 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_12 ).
cnf(c_0_17,axiom,
multiply(X1,X2) = divide(X1,inverse(X2)),
multiply ).
cnf(c_0_18,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_19,plain,
divide(divide(X1,X2),X1) = inverse(X2),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_20,plain,
divide(X1,divide(X2,divide(X3,divide(divide(X1,X4),divide(X2,X4))))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_10]),c_0_10]) ).
cnf(c_0_21,plain,
divide(divide(X1,X2),divide(X3,divide(X2,X1))) = inverse(X3),
inference(spm,[status(thm)],[c_0_15,c_0_10]) ).
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
| divide(b4,inverse(a4)) != divide(a4,inverse(b4)) ),
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)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]),c_0_17]),c_0_17]),c_0_17]),c_0_17]),c_0_17]),c_0_17]),c_0_17]),c_0_17]) ).
cnf(c_0_23,plain,
divide(X1,X1) = divide(X2,X2),
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_24,plain,
divide(divide(X1,inverse(X2)),X2) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_25,plain,
divide(inverse(X1),inverse(X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_11,c_0_19]) ).
cnf(c_0_26,plain,
divide(X1,divide(X2,divide(X3,X1))) = divide(X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_10]) ).
cnf(c_0_27,negated_conjecture,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[c_0_22,c_0_23]),c_0_10]),c_0_13]),c_0_18])]) ).
cnf(c_0_28,plain,
divide(inverse(X1),X2) = divide(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_24,c_0_19]) ).
cnf(c_0_29,plain,
divide(divide(X1,X2),inverse(X3)) = divide(X3,divide(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_10]) ).
cnf(c_0_30,plain,
divide(X1,divide(X2,X3)) = divide(X3,divide(X2,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_26]) ).
cnf(c_0_31,plain,
divide(X1,inverse(X2)) = divide(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_32,negated_conjecture,
divide(b3,divide(inverse(a3),c3)) != divide(a3,divide(inverse(b3),c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_28]),c_0_30]),c_0_31])]) ).
cnf(c_0_33,plain,
divide(X1,divide(inverse(X2),X3)) = divide(X3,divide(inverse(X1),X2)),
inference(spm,[status(thm)],[c_0_30,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP097-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Sun Sep 20 19:57:07 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.43 Running first-order theorem proving
% 0.03/0.43 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
% 0.20/0.53 % Version: 3.5.1
% 0.20/0.53 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.20/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.20/0.53 % Starting new_bool_3 with 300s (1) cores
% 0.20/0.53 % Starting new_bool_1 with 300s (1) cores
% 0.20/0.53 % Starting sh5l with 300s (1) cores
% 0.20/0.53 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 3278802 completed with status 0
% 0.20/0.53 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.20/0.53 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.20/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.20/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.53 % No SInE strategy applied
% 0.20/0.53 % Search class: FUHPF-FFSF21-MFFFFFNN
% 0.20/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.53 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.20/0.53 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.20/0.53 % Starting new_bool_3 with 136s (1) cores
% 0.20/0.53 % Starting new_bool_1 with 136s (1) cores
% 0.20/0.53 % SubtermCWHack with pid 3278806 completed with status 0
% 0.20/0.53 % Result found by SubtermCWHack
% 0.20/0.53 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.20/0.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.53 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.20/0.53 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.53 % No SInE strategy applied
% 0.20/0.53 % Search class: FUHPF-FFSF21-MFFFFFNN
% 0.20/0.53 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.53 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.53 % Preprocessing time : 0.002 s
% 0.20/0.53
% 0.20/0.53 % Proof found!
% 0.20/0.53 % SZS status Unsatisfiable
% 0.20/0.53 % SZS output start CNFRefutation
% See solution above
% 0.20/0.53 % Parsed axioms : 3
% 0.20/0.53 % Removed by relevancy pruning/SinE : 0
% 0.20/0.53 % Initial clauses : 3
% 0.20/0.53 % Removed in clause preprocessing : 1
% 0.20/0.53 % Initial clauses in saturation : 2
% 0.20/0.53 % Processed clauses : 404
% 0.20/0.53 % ...of these trivial : 130
% 0.20/0.53 % ...subsumed : 213
% 0.20/0.53 % ...remaining for further processing : 61
% 0.20/0.53 % Other redundant clauses eliminated : 0
% 0.20/0.53 % Clauses deleted for lack of memory : 0
% 0.20/0.53 % Backward-subsumed : 0
% 0.20/0.53 % Backward-rewritten : 31
% 0.20/0.53 % Generated clauses : 3671
% 0.20/0.53 % ...of the previous two non-redundant : 2489
% 0.20/0.53 % ...aggressively subsumed : 0
% 0.20/0.53 % Contextual simplify-reflections : 0
% 0.20/0.53 % Paramodulations : 3670
% 0.20/0.53 % Factorizations : 0
% 0.20/0.53 % NegExts : 0
% 0.20/0.53 % Equation resolutions : 0
% 0.20/0.53 % Disequality decompositions : 0
% 0.20/0.53 % Total rewrite steps : 4145
% 0.20/0.53 % ...of those cached : 3061
% 0.20/0.53 % Propositional unsat checks : 0
% 0.20/0.53 % Propositional check models : 0
% 0.20/0.53 % Propositional check unsatisfiable : 0
% 0.20/0.53 % Propositional clauses : 0
% 0.20/0.53 % Propositional clauses after purity: 0
% 0.20/0.53 % Propositional unsat core size : 0
% 0.20/0.53 % Propositional preprocessing time : 0.000
% 0.20/0.53 % Propositional encoding time : 0.000
% 0.20/0.53 % Propositional solver time : 0.000
% 0.20/0.53 % Success case prop preproc time : 0.000
% 0.20/0.53 % Success case prop encoding time : 0.000
% 0.20/0.53 % Success case prop solver time : 0.000
% 0.20/0.53 % Current number of processed clauses : 29
% 0.20/0.53 % Positive orientable unit clauses : 22
% 0.20/0.53 % Positive unorientable unit clauses: 7
% 0.20/0.53 % Negative unit clauses : 0
% 0.20/0.53 % Non-unit-clauses : 0
% 0.20/0.53 % Current number of unprocessed clauses: 1217
% 0.20/0.53 % ...number of literals in the above : 1217
% 0.20/0.53 % Current number of archived formulas : 0
% 0.20/0.53 % Current number of archived clauses : 33
% 0.20/0.53 % Clause-clause subsumption calls (NU) : 0
% 0.20/0.53 % Rec. Clause-clause subsumption calls : 0
% 0.20/0.53 % Non-unit clause-clause subsumptions : 0
% 0.20/0.53 % Unit Clause-clause subsumption calls : 42
% 0.20/0.53 % Rewrite failures with RHS unbound : 53
% 0.20/0.53 % BW rewrite match attempts : 215
% 0.20/0.53 % BW rewrite match successes : 107
% 0.20/0.53 % Condensation attempts : 0
% 0.20/0.53 % Condensation successes : 0
% 0.20/0.53 % Termbank termtop insertions : 32766
% 0.20/0.53 % Search garbage collected termcells : 11
% 0.20/0.53
% 0.20/0.53 % -------------------------------------------------
% 0.20/0.53 % User time : 0.065 s
% 0.20/0.53 % System time : 0.007 s
% 0.20/0.53 % Total time : 0.073 s
% 0.20/0.53 % Maximum resident set size: 3380 pages
% 0.20/0.53
% 0.20/0.53 % -------------------------------------------------
% 0.20/0.53 % User time : 0.311 s
% 0.20/0.53 % System time : 0.037 s
% 0.20/0.53 % Total time : 0.349 s
% 0.20/0.53 % Maximum resident set size: 4608 pages
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------