%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP098-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 12:41:47 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.67s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of clauses : 31 ( 26 unt; 0 nHn; 6 RR)
% Number of literals : 44 ( 43 equ; 18 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 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 : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(divide(X1,inverse(X2)),X3),divide(X1,X3)) = X2,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,inverse(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_3,axiom,
divide(divide(divide(X1,inverse(X2)),X3),divide(X1,X3)) = X2,
single_axiom ).
cnf(c_0_4,plain,
divide(divide(divide(divide(divide(X1,inverse(X2)),X3),inverse(X4)),divide(X1,X3)),X2) = X4,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
divide(divide(X1,inverse(X2)),X1) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_4]),c_0_3]) ).
cnf(c_0_6,plain,
divide(X1,divide(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_7,plain,
divide(divide(X1,X1),inverse(X2)) = X2,
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
divide(X1,divide(divide(X2,inverse(X1)),divide(X2,inverse(X3)))) = X3,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_9,plain,
divide(divide(X1,inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_7]),c_0_7]) ).
cnf(c_0_10,plain,
divide(X1,divide(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_7]),c_0_7]) ).
cnf(c_0_11,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_10]) ).
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,X2),divide(divide(divide(divide(divide(X3,X4),X5),inverse(X1)),divide(X3,X5)),X2)) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_11]) ).
cnf(c_0_14,plain,
divide(X1,X1) = divide(X2,X2),
inference(spm,[status(thm)],[c_0_10,c_0_6]) ).
cnf(c_0_15,plain,
divide(divide(X1,X1),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_16,plain,
divide(divide(X1,X2),X1) = inverse(X2),
inference(spm,[status(thm)],[c_0_5,c_0_11]) ).
cnf(c_0_17,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_18,axiom,
multiply(X1,X2) = divide(X1,inverse(X2)),
multiply ).
cnf(c_0_19,plain,
divide(divide(X1,X2),inverse(X2)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_20,plain,
divide(divide(X1,X2),divide(divide(X1,X3),X2)) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_11]),c_0_10]) ).
cnf(c_0_21,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_16,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_17,c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_23,plain,
divide(inverse(X1),inverse(X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_24,plain,
divide(X1,divide(X2,X3)) = divide(X3,divide(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_20]),c_0_21]) ).
cnf(c_0_25,plain,
divide(inverse(X1),X2) = divide(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_9,c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( divide(a4,inverse(b4)) != divide(b4,inverse(a4))
| divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_7])]),c_0_14]) ).
cnf(c_0_27,plain,
divide(divide(X1,X2),inverse(X3)) = divide(X3,divide(X2,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_28,plain,
divide(X1,divide(inverse(X2),X3)) = divide(X3,divide(inverse(X1),X2)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
divide(X1,inverse(X2)) = divide(X2,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_25]),c_0_21]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[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_26,c_0_21]),c_0_27]),c_0_25]),c_0_24]),c_0_28]),c_0_25]),c_0_25]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP098-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.47 % Computer : n006.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Sun Sep 20 19:57:28 UTC 2026
% 0.20/0.48 % CPUTime :
% 0.20/0.48 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.55 Running first-order theorem proving
% 0.24/0.55 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.24/0.67 % Version: 3.5.1
% 0.24/0.67 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.24/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.67 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.24/0.67 % Starting new_bool_3 with 300s (1) cores
% 0.24/0.67 % Starting new_bool_1 with 300s (1) cores
% 0.24/0.67 % Starting sh5l with 300s (1) cores
% 0.24/0.67 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 1132648 completed with status 0
% 0.24/0.67 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.24/0.67 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.24/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.67 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.24/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.67 % No SInE strategy applied
% 0.24/0.67 % Search class: FUHPF-FFSF21-MFFFFFNN
% 0.24/0.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.67 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.67 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.24/0.67 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.24/0.67 % Starting new_bool_3 with 136s (1) cores
% 0.24/0.67 % Starting new_bool_1 with 136s (1) cores
% 0.24/0.67 % SubtermCWHack with pid 1132652 completed with status 0
% 0.24/0.67 % Result found by SubtermCWHack
% 0.24/0.67 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.24/0.67 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.24/0.67 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.24/0.67 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.24/0.67 % No SInE strategy applied
% 0.24/0.67 % Search class: FUHPF-FFSF21-MFFFFFNN
% 0.24/0.67 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.24/0.67 % Starting SubtermCWHack with 136s (1) cores
% 0.24/0.67 % Preprocessing time : 0.002 s
% 0.24/0.67
% 0.24/0.67 % Proof found!
% 0.24/0.67 % SZS status Unsatisfiable
% 0.24/0.67 % SZS output start CNFRefutation
% See solution above
% 0.24/0.67 % Parsed axioms : 3
% 0.24/0.67 % Removed by relevancy pruning/SinE : 0
% 0.24/0.67 % Initial clauses : 3
% 0.24/0.67 % Removed in clause preprocessing : 1
% 0.24/0.67 % Initial clauses in saturation : 2
% 0.24/0.67 % Processed clauses : 352
% 0.24/0.67 % ...of these trivial : 126
% 0.24/0.67 % ...subsumed : 171
% 0.24/0.67 % ...remaining for further processing : 54
% 0.24/0.67 % Other redundant clauses eliminated : 0
% 0.24/0.67 % Clauses deleted for lack of memory : 0
% 0.24/0.67 % Backward-subsumed : 0
% 0.24/0.67 % Backward-rewritten : 30
% 0.24/0.67 % Generated clauses : 3571
% 0.24/0.67 % ...of the previous two non-redundant : 2871
% 0.24/0.67 % ...aggressively subsumed : 0
% 0.24/0.67 % Contextual simplify-reflections : 0
% 0.24/0.67 % Paramodulations : 3571
% 0.24/0.67 % Factorizations : 0
% 0.24/0.67 % NegExts : 0
% 0.24/0.67 % Equation resolutions : 0
% 0.24/0.67 % Disequality decompositions : 0
% 0.24/0.67 % Total rewrite steps : 3910
% 0.24/0.67 % ...of those cached : 2895
% 0.24/0.67 % Propositional unsat checks : 0
% 0.24/0.67 % Propositional check models : 0
% 0.24/0.67 % Propositional check unsatisfiable : 0
% 0.24/0.67 % Propositional clauses : 0
% 0.24/0.67 % Propositional clauses after purity: 0
% 0.24/0.67 % Propositional unsat core size : 0
% 0.24/0.67 % Propositional preprocessing time : 0.000
% 0.24/0.67 % Propositional encoding time : 0.000
% 0.24/0.67 % Propositional solver time : 0.000
% 0.24/0.67 % Success case prop preproc time : 0.000
% 0.24/0.67 % Success case prop encoding time : 0.000
% 0.24/0.67 % Success case prop solver time : 0.000
% 0.24/0.67 % Current number of processed clauses : 24
% 0.24/0.67 % Positive orientable unit clauses : 17
% 0.24/0.67 % Positive unorientable unit clauses: 7
% 0.24/0.67 % Negative unit clauses : 0
% 0.24/0.67 % Non-unit-clauses : 0
% 0.24/0.67 % Current number of unprocessed clauses: 1955
% 0.24/0.67 % ...number of literals in the above : 1955
% 0.24/0.67 % Current number of archived formulas : 0
% 0.24/0.67 % Current number of archived clauses : 31
% 0.24/0.67 % Clause-clause subsumption calls (NU) : 0
% 0.24/0.67 % Rec. Clause-clause subsumption calls : 0
% 0.24/0.67 % Non-unit clause-clause subsumptions : 0
% 0.24/0.67 % Unit Clause-clause subsumption calls : 60
% 0.24/0.67 % Rewrite failures with RHS unbound : 61
% 0.24/0.67 % BW rewrite match attempts : 292
% 0.24/0.67 % BW rewrite match successes : 128
% 0.24/0.67 % Condensation attempts : 0
% 0.24/0.67 % Condensation successes : 0
% 0.24/0.67 % Termbank termtop insertions : 40717
% 0.24/0.67 % Search garbage collected termcells : 11
% 0.24/0.67
% 0.24/0.67 % -------------------------------------------------
% 0.24/0.67 % User time : 0.079 s
% 0.24/0.67 % System time : 0.009 s
% 0.24/0.67 % Total time : 0.088 s
% 0.24/0.67 % Maximum resident set size: 3580 pages
% 0.24/0.67
% 0.24/0.67 % -------------------------------------------------
% 0.24/0.67 % User time : 0.402 s
% 0.24/0.67 % System time : 0.039 s
% 0.24/0.67 % Total time : 0.441 s
% 0.24/0.67 % Maximum resident set size: 4608 pages
% 0.24/0.67 % E exiting
%------------------------------------------------------------------------------