%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP094-1 : 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 : n007.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 0.12s 0.46s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of clauses : 29 ( 24 unt; 0 nHn; 7 RR)
% Number of literals : 42 ( 41 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(identity,divide(X1,X2)),divide(divide(X2,X3),X1)) = X3,
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(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(inverse,axiom,
inverse(X1) = divide(identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_5,axiom,
divide(divide(identity,divide(X1,X2)),divide(divide(X2,X3),X1)) = X3,
single_axiom ).
cnf(c_0_6,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_7,plain,
divide(identity,divide(divide(X1,X2),X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_6]) ).
cnf(c_0_8,plain,
divide(identity,divide(identity,X1)) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
divide(identity,divide(X1,identity)) = divide(identity,X1),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
divide(X1,identity) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_9]),c_0_9]),c_0_8]) ).
cnf(c_0_11,plain,
divide(X1,divide(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_10]),c_0_8]) ).
cnf(c_0_12,plain,
divide(identity,divide(X1,X2)) = divide(X2,X1),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_13,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_14,plain,
divide(divide(X1,X2),X1) = divide(identity,X2),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_15,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_13 ).
cnf(c_0_16,axiom,
inverse(X1) = divide(identity,X1),
inverse ).
cnf(c_0_17,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
multiply ).
cnf(c_0_18,plain,
divide(divide(X1,X2),divide(identity,X2)) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(divide(identity,b1),divide(identity,b1)) != divide(divide(identity,a1),divide(identity,a1))
| divide(divide(divide(identity,b2),divide(identity,b2)),divide(identity,a2)) != a2
| divide(b4,divide(identity,a4)) != divide(a4,divide(identity,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]),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_20,plain,
divide(divide(X1,divide(identity,X2)),X2) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_21,plain,
divide(divide(X1,X2),divide(divide(X1,X3),X2)) = X3,
inference(rw,[status(thm)],[c_0_5,c_0_12]) ).
cnf(c_0_22,negated_conjecture,
( divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4))
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(divide(identity,c3),b3)) ),
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_19,c_0_6]),c_0_11]),c_0_6]),c_0_6]),c_0_12])]) ).
cnf(c_0_23,plain,
divide(divide(identity,X1),X2) = divide(divide(identity,X2),X1),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
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_14,c_0_21]),c_0_12]) ).
cnf(c_0_25,plain,
divide(divide(X1,X2),X3) = divide(divide(X1,X3),X2),
inference(spm,[status(thm)],[c_0_11,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
divide(b3,divide(divide(identity,a3),c3)) != divide(a3,divide(divide(identity,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)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_12]),c_0_25]),c_0_24]),c_0_24])]) ).
cnf(c_0_27,plain,
divide(X1,divide(divide(X2,X3),X4)) = divide(X4,divide(divide(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP094-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 19:54:50 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.45 % Version: 3.5.1
% 0.12/0.45 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.12/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.45 % Starting sh5l with 300s (1) cores
% 0.12/0.45 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 3444015 completed with status 0
% 0.12/0.45 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 0.12/0.45 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.12/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.45 % No SInE strategy applied
% 0.12/0.45 % Search class: FUHPS-FFSF22-MFFFFFNN
% 0.12/0.45 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 0.12/0.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.45 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 0.12/0.45 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 0.12/0.45 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.46 % Starting new_bool_1 with 136s (1) cores
% 0.12/0.46 % SubtermCWHack with pid 3444020 completed with status 0
% 0.12/0.46 % Result found by SubtermCWHack
% 0.12/0.46 % Preprocessing class: FSSSSMSMSSSNFFN.
% 0.12/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.46 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 0.12/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.46 % No SInE strategy applied
% 0.12/0.46 % Search class: FUHPS-FFSF22-MFFFFFNN
% 0.12/0.46 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 0.12/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.46 % Preprocessing time : 0.001 s
% 0.12/0.46
% 0.12/0.46 % Proof found!
% 0.12/0.46 % SZS status Unsatisfiable
% 0.12/0.46 % SZS output start CNFRefutation
% See solution above
% 0.12/0.46 % Parsed axioms : 5
% 0.12/0.46 % Removed by relevancy pruning/SinE : 0
% 0.12/0.46 % Initial clauses : 5
% 0.12/0.46 % Removed in clause preprocessing : 2
% 0.12/0.46 % Initial clauses in saturation : 3
% 0.12/0.46 % Processed clauses : 179
% 0.12/0.46 % ...of these trivial : 53
% 0.12/0.46 % ...subsumed : 88
% 0.12/0.46 % ...remaining for further processing : 38
% 0.12/0.46 % Other redundant clauses eliminated : 0
% 0.12/0.46 % Clauses deleted for lack of memory : 0
% 0.12/0.46 % Backward-subsumed : 1
% 0.12/0.46 % Backward-rewritten : 20
% 0.12/0.46 % Generated clauses : 1714
% 0.12/0.46 % ...of the previous two non-redundant : 1058
% 0.12/0.46 % ...aggressively subsumed : 0
% 0.12/0.46 % Contextual simplify-reflections : 0
% 0.12/0.46 % Paramodulations : 1714
% 0.12/0.46 % Factorizations : 0
% 0.12/0.46 % NegExts : 0
% 0.12/0.46 % Equation resolutions : 0
% 0.12/0.46 % Disequality decompositions : 0
% 0.12/0.46 % Total rewrite steps : 2064
% 0.12/0.46 % ...of those cached : 1253
% 0.12/0.46 % Propositional unsat checks : 0
% 0.12/0.46 % Propositional check models : 0
% 0.12/0.46 % Propositional check unsatisfiable : 0
% 0.12/0.46 % Propositional clauses : 0
% 0.12/0.46 % Propositional clauses after purity: 0
% 0.12/0.46 % Propositional unsat core size : 0
% 0.12/0.46 % Propositional preprocessing time : 0.000
% 0.12/0.46 % Propositional encoding time : 0.000
% 0.12/0.46 % Propositional solver time : 0.000
% 0.12/0.46 % Success case prop preproc time : 0.000
% 0.12/0.46 % Success case prop encoding time : 0.000
% 0.12/0.46 % Success case prop solver time : 0.000
% 0.12/0.46 % Current number of processed clauses : 17
% 0.12/0.46 % Positive orientable unit clauses : 12
% 0.12/0.46 % Positive unorientable unit clauses: 5
% 0.12/0.46 % Negative unit clauses : 0
% 0.12/0.46 % Non-unit-clauses : 0
% 0.12/0.46 % Current number of unprocessed clauses: 670
% 0.12/0.46 % ...number of literals in the above : 670
% 0.12/0.46 % Current number of archived formulas : 0
% 0.12/0.46 % Current number of archived clauses : 23
% 0.12/0.46 % Clause-clause subsumption calls (NU) : 0
% 0.12/0.46 % Rec. Clause-clause subsumption calls : 0
% 0.12/0.46 % Non-unit clause-clause subsumptions : 0
% 0.12/0.46 % Unit Clause-clause subsumption calls : 21
% 0.12/0.46 % Rewrite failures with RHS unbound : 0
% 0.12/0.46 % BW rewrite match attempts : 104
% 0.12/0.46 % BW rewrite match successes : 82
% 0.12/0.46 % Condensation attempts : 0
% 0.12/0.46 % Condensation successes : 0
% 0.12/0.46 % Termbank termtop insertions : 15990
% 0.12/0.46 % Search garbage collected termcells : 11
% 0.12/0.46
% 0.12/0.46 % -------------------------------------------------
% 0.12/0.46 % User time : 0.010 s
% 0.12/0.46 % System time : 0.003 s
% 0.12/0.46 % Total time : 0.014 s
% 0.12/0.46 % Maximum resident set size: 3584 pages
% 0.12/0.46
% 0.12/0.46 % -------------------------------------------------
% 0.12/0.46 % User time : 0.041 s
% 0.12/0.46 % System time : 0.014 s
% 0.12/0.46 % Total time : 0.055 s
% 0.12/0.46 % Maximum resident set size: 4864 pages
% 0.12/0.46 % E exiting
%------------------------------------------------------------------------------