%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP067-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 0.15s 5.63s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of clauses : 29 ( 25 unt; 0 nHn; 7 RR)
% Number of literals : 37 ( 36 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(divide(divide(X1,X1),divide(X1,divide(X2,divide(divide(identity,X1),X3)))),X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(identity,axiom,
identity = divide(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(inverse,axiom,
inverse(X1) = divide(identity,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_5,axiom,
divide(divide(divide(X1,X1),divide(X1,divide(X2,divide(divide(identity,X1),X3)))),X3) = X2,
single_axiom ).
cnf(c_0_6,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_7,plain,
divide(divide(identity,divide(X1,divide(X2,divide(divide(identity,X1),X3)))),X3) = X2,
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
divide(divide(identity,divide(X1,divide(X2,identity))),divide(identity,X1)) = X2,
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
divide(identity,divide(identity,divide(X1,identity))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_6]),c_0_6]) ).
cnf(c_0_10,plain,
divide(divide(identity,divide(identity,divide(X1,divide(identity,X2)))),X2) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_11,plain,
divide(identity,divide(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_6]),c_0_9]) ).
cnf(c_0_12,plain,
divide(divide(identity,divide(identity,divide(X1,identity))),identity) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_6]) ).
cnf(c_0_13,plain,
divide(divide(X1,divide(identity,X2)),X2) = X1,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
divide(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(fof_simplification,[status(thm)],[prove_these_axioms]) ).
cnf(c_0_16,plain,
divide(identity,divide(X1,X2)) = divide(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_8]),c_0_14]) ).
cnf(c_0_17,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
c_0_15 ).
cnf(c_0_18,axiom,
inverse(X1) = divide(identity,X1),
inverse ).
cnf(c_0_19,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
multiply ).
cnf(c_0_20,plain,
divide(divide(divide(X1,divide(divide(identity,X2),X3)),X2),X3) = X1,
inference(rw,[status(thm)],[c_0_7,c_0_16]) ).
cnf(c_0_21,plain,
divide(X1,divide(X2,divide(identity,X1))) = divide(identity,X2),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_22,negated_conjecture,
( divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(divide(identity,a1),divide(identity,a1)) != identity
| divide(identity,divide(identity,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)],[c_0_17,c_0_18]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_23,plain,
divide(divide(divide(X1,divide(identity,X2)),X3),divide(X2,X3)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_11]) ).
cnf(c_0_24,negated_conjecture,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_11]),c_0_6])]) ).
cnf(c_0_25,plain,
divide(divide(X1,X2),divide(X3,X2)) = divide(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_23]),c_0_6]),c_0_14]) ).
cnf(c_0_26,negated_conjecture,
divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(divide(identity,c3),b3)),
inference(rw,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_27,plain,
divide(divide(X1,divide(identity,X2)),X3) = divide(X1,divide(X3,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP067-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/5.56 % Computer : n003.cluster.edu
% 0.11/5.56 % Model : x86_64 x86_64
% 0.11/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.56 % Memory : 8046.5625MB
% 0.11/5.56 % OS : Linux 6.8.0-71-generic
% 0.11/5.56 % CPULimit : 300
% 0.11/5.56 % WCLimit : 300
% 0.11/5.56 % DateTime : Sun Sep 20 19:58:21 UTC 2026
% 0.11/5.56 % CPUTime :
% 0.11/5.56 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/5.61 Running first-order theorem proving
% 0.15/5.61 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
% 0.15/5.63 % Version: 3.5.1
% 0.15/5.63 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.63 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.63 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.63 % Starting sh5l with 300s (1) cores
% 0.15/5.63 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2443794 completed with status 0
% 0.15/5.63 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.15/5.63 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.63 % No SInE strategy applied
% 0.15/5.63 % Search class: FUHPS-FFSF22-DFFFFFNN
% 0.15/5.63 % partial match(1): FUUPS-FFSF22-DFFFFFNN
% 0.15/5.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.63 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.15/5.63 % Starting G-E--_107_B42_F1_PI_SE_Q4_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/5.63 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 0.15/5.63 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/5.63 % SubtermCWHack with pid 2443799 completed with status 0
% 0.15/5.63 % Result found by SubtermCWHack
% 0.15/5.63 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.63 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/5.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.63 % No SInE strategy applied
% 0.15/5.63 % Search class: FUHPS-FFSF22-DFFFFFNN
% 0.15/5.63 % partial match(1): FUUPS-FFSF22-DFFFFFNN
% 0.15/5.63 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.63 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.63 % Preprocessing time : 0.001 s
% 0.15/5.63
% 0.15/5.63 % Proof found!
% 0.15/5.63 % SZS status Unsatisfiable
% 0.15/5.63 % SZS output start CNFRefutation
% See solution above
% 0.15/5.63 % Parsed axioms : 5
% 0.15/5.63 % Removed by relevancy pruning/SinE : 0
% 0.15/5.63 % Initial clauses : 5
% 0.15/5.63 % Removed in clause preprocessing : 2
% 0.15/5.63 % Initial clauses in saturation : 3
% 0.15/5.63 % Processed clauses : 35
% 0.15/5.63 % ...of these trivial : 13
% 0.15/5.63 % ...subsumed : 0
% 0.15/5.63 % ...remaining for further processing : 22
% 0.15/5.63 % Other redundant clauses eliminated : 0
% 0.15/5.63 % Clauses deleted for lack of memory : 0
% 0.15/5.63 % Backward-subsumed : 0
% 0.15/5.63 % Backward-rewritten : 13
% 0.15/5.63 % Generated clauses : 355
% 0.15/5.63 % ...of the previous two non-redundant : 132
% 0.15/5.63 % ...aggressively subsumed : 0
% 0.15/5.63 % Contextual simplify-reflections : 0
% 0.15/5.63 % Paramodulations : 355
% 0.15/5.63 % Factorizations : 0
% 0.15/5.63 % NegExts : 0
% 0.15/5.63 % Equation resolutions : 0
% 0.15/5.63 % Disequality decompositions : 0
% 0.15/5.63 % Total rewrite steps : 490
% 0.15/5.63 % ...of those cached : 365
% 0.15/5.63 % Propositional unsat checks : 0
% 0.15/5.63 % Propositional check models : 0
% 0.15/5.63 % Propositional check unsatisfiable : 0
% 0.15/5.63 % Propositional clauses : 0
% 0.15/5.63 % Propositional clauses after purity: 0
% 0.15/5.63 % Propositional unsat core size : 0
% 0.15/5.63 % Propositional preprocessing time : 0.000
% 0.15/5.63 % Propositional encoding time : 0.000
% 0.15/5.63 % Propositional solver time : 0.000
% 0.15/5.63 % Success case prop preproc time : 0.000
% 0.15/5.63 % Success case prop encoding time : 0.000
% 0.15/5.63 % Success case prop solver time : 0.000
% 0.15/5.63 % Current number of processed clauses : 9
% 0.15/5.63 % Positive orientable unit clauses : 9
% 0.15/5.63 % Positive unorientable unit clauses: 0
% 0.15/5.63 % Negative unit clauses : 0
% 0.15/5.63 % Non-unit-clauses : 0
% 0.15/5.63 % Current number of unprocessed clauses: 50
% 0.15/5.63 % ...number of literals in the above : 50
% 0.15/5.63 % Current number of archived formulas : 0
% 0.15/5.63 % Current number of archived clauses : 15
% 0.15/5.63 % Clause-clause subsumption calls (NU) : 0
% 0.15/5.63 % Rec. Clause-clause subsumption calls : 0
% 0.15/5.63 % Non-unit clause-clause subsumptions : 0
% 0.15/5.63 % Unit Clause-clause subsumption calls : 0
% 0.15/5.63 % Rewrite failures with RHS unbound : 0
% 0.15/5.63 % BW rewrite match attempts : 25
% 0.15/5.63 % BW rewrite match successes : 13
% 0.15/5.63 % Condensation attempts : 0
% 0.15/5.63 % Condensation successes : 0
% 0.15/5.63 % Termbank termtop insertions : 3434
% 0.15/5.63 % Search garbage collected termcells : 8
% 0.15/5.63
% 0.15/5.63 % -------------------------------------------------
% 0.15/5.63 % User time : 0.005 s
% 0.15/5.63 % System time : 0.004 s
% 0.15/5.63 % Total time : 0.009 s
% 0.15/5.63 % Maximum resident set size: 3584 pages
% 0.15/5.63
% 0.15/5.63 % -------------------------------------------------
% 0.15/5.63 % User time : 0.030 s
% 0.15/5.63 % System time : 0.010 s
% 0.15/5.63 % Total time : 0.040 s
% 0.15/5.63 % Maximum resident set size: 4608 pages
% 0.15/5.63 % E exiting
%------------------------------------------------------------------------------