%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP069-1 : 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 : n008.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 12:41:42 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.62s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 30 ( 26 unt; 0 nHn; 6 RR)
% Number of literals : 38 ( 37 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 49 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(X1,divide(divide(divide(divide(X1,X1),X2),X3),divide(divide(identity,X1),X3))) = X2,
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(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
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(X1,divide(divide(divide(divide(X1,X1),X2),X3),divide(divide(identity,X1),X3))) = X2,
single_axiom ).
cnf(c_0_6,axiom,
identity = divide(X1,X1),
identity ).
cnf(c_0_7,plain,
divide(X1,divide(divide(divide(identity,X2),X3),divide(divide(identity,X1),X3))) = X2,
inference(rw,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
divide(X1,identity) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
divide(X1,divide(divide(identity,X2),divide(identity,X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_10,plain,
divide(divide(identity,X1),divide(divide(identity,X2),X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_9]),c_0_6]),c_0_8]) ).
cnf(c_0_11,plain,
divide(divide(identity,divide(divide(identity,X1),X2)),X1) = X2,
inference(spm,[status(thm)],[c_0_10,c_0_10]) ).
cnf(c_0_12,plain,
divide(identity,divide(identity,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_8]),c_0_8]) ).
cnf(c_0_13,plain,
divide(identity,divide(divide(divide(identity,X1),X2),divide(identity,X2))) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_14,plain,
divide(divide(identity,divide(X1,X2)),divide(identity,X1)) = X2,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
divide(identity,divide(X1,X2)) = divide(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_12]) ).
cnf(c_0_16,plain,
divide(divide(X1,X2),divide(identity,X2)) = X1,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
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 ),
inference(fof_simplification,[status(thm)],[prove_these_axioms]) ).
cnf(c_0_18,plain,
divide(divide(identity,X1),divide(X2,X1)) = divide(identity,X2),
inference(spm,[status(thm)],[c_0_10,c_0_12]) ).
cnf(c_0_19,plain,
divide(divide(identity,X1),divide(divide(divide(identity,X2),X3),divide(X1,X3))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_7]),c_0_6]),c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
c_0_17 ).
cnf(c_0_21,axiom,
inverse(X1) = divide(identity,X1),
inverse ).
cnf(c_0_22,axiom,
multiply(X1,X2) = divide(X1,divide(identity,X2)),
multiply ).
cnf(c_0_23,plain,
divide(divide(X1,divide(identity,X2)),X2) = X1,
inference(rw,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_24,plain,
divide(divide(divide(X1,X2),divide(divide(identity,X3),X2)),X3) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_15]),c_0_12]) ).
cnf(c_0_25,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_20,c_0_21]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_22]),c_0_22]) ).
cnf(c_0_26,plain,
divide(divide(X1,X2),divide(X3,X2)) = divide(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_12]) ).
cnf(c_0_27,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_25,c_0_12]),c_0_6])]) ).
cnf(c_0_28,plain,
divide(divide(X1,divide(identity,X2)),X3) = divide(X1,divide(X3,X2)),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_15]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP069-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.55 % Computer : n008.cluster.edu
% 0.08/0.55 % Model : x86_64 x86_64
% 0.08/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.55 % Memory : 8046.5625MB
% 0.08/0.55 % OS : Linux 6.8.0-71-generic
% 0.08/0.55 % CPULimit : 300
% 0.08/0.55 % WCLimit : 300
% 0.08/0.55 % DateTime : Sun Sep 20 19:57:25 UTC 2026
% 0.14/0.56 % CPUTime :
% 0.14/0.56 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.60 Running first-order theorem proving
% 0.14/0.60 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
% 0.14/0.62 % Version: 3.5.1
% 0.14/0.62 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.62 % Starting sh5l with 300s (1) cores
% 0.14/0.62 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3476783 completed with status 0
% 0.14/0.62 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.14/0.62 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.62 % No SInE strategy applied
% 0.14/0.62 % Search class: FUHPS-FFSF22-MFFFFFNN
% 0.14/0.62 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 0.14/0.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.14/0.62 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S0Y_ni with 136s (1) cores
% 0.14/0.62 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.62 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.62 % SubtermCWHack with pid 3476787 completed with status 0
% 0.14/0.62 % Result found by SubtermCWHack
% 0.14/0.62 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.14/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.62 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.14/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.62 % No SInE strategy applied
% 0.14/0.62 % Search class: FUHPS-FFSF22-MFFFFFNN
% 0.14/0.62 % partial match(1): FUUPS-FFSF22-MFFFFFNN
% 0.14/0.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.62 % Preprocessing time : 0.001 s
% 0.14/0.62
% 0.14/0.62 % Proof found!
% 0.14/0.62 % SZS status Unsatisfiable
% 0.14/0.62 % SZS output start CNFRefutation
% See solution above
% 0.14/0.62 % Parsed axioms : 5
% 0.14/0.62 % Removed by relevancy pruning/SinE : 0
% 0.14/0.62 % Initial clauses : 5
% 0.14/0.62 % Removed in clause preprocessing : 2
% 0.14/0.62 % Initial clauses in saturation : 3
% 0.14/0.62 % Processed clauses : 44
% 0.14/0.62 % ...of these trivial : 19
% 0.14/0.62 % ...subsumed : 0
% 0.14/0.62 % ...remaining for further processing : 24
% 0.14/0.62 % Other redundant clauses eliminated : 0
% 0.14/0.62 % Clauses deleted for lack of memory : 0
% 0.14/0.62 % Backward-subsumed : 0
% 0.14/0.62 % Backward-rewritten : 15
% 0.14/0.62 % Generated clauses : 512
% 0.14/0.62 % ...of the previous two non-redundant : 222
% 0.14/0.62 % ...aggressively subsumed : 0
% 0.14/0.62 % Contextual simplify-reflections : 0
% 0.14/0.62 % Paramodulations : 512
% 0.14/0.62 % Factorizations : 0
% 0.14/0.62 % NegExts : 0
% 0.14/0.62 % Equation resolutions : 0
% 0.14/0.62 % Disequality decompositions : 0
% 0.14/0.62 % Total rewrite steps : 794
% 0.14/0.62 % ...of those cached : 617
% 0.14/0.62 % Propositional unsat checks : 0
% 0.14/0.62 % Propositional check models : 0
% 0.14/0.62 % Propositional check unsatisfiable : 0
% 0.14/0.62 % Propositional clauses : 0
% 0.14/0.62 % Propositional clauses after purity: 0
% 0.14/0.62 % Propositional unsat core size : 0
% 0.14/0.62 % Propositional preprocessing time : 0.000
% 0.14/0.62 % Propositional encoding time : 0.000
% 0.14/0.62 % Propositional solver time : 0.000
% 0.14/0.62 % Success case prop preproc time : 0.000
% 0.14/0.62 % Success case prop encoding time : 0.000
% 0.14/0.62 % Success case prop solver time : 0.000
% 0.14/0.62 % Current number of processed clauses : 9
% 0.14/0.62 % Positive orientable unit clauses : 9
% 0.14/0.62 % Positive unorientable unit clauses: 0
% 0.14/0.62 % Negative unit clauses : 0
% 0.14/0.62 % Non-unit-clauses : 0
% 0.14/0.62 % Current number of unprocessed clauses: 113
% 0.14/0.62 % ...number of literals in the above : 113
% 0.14/0.62 % Current number of archived formulas : 0
% 0.14/0.62 % Current number of archived clauses : 17
% 0.14/0.62 % Clause-clause subsumption calls (NU) : 0
% 0.14/0.62 % Rec. Clause-clause subsumption calls : 0
% 0.14/0.62 % Non-unit clause-clause subsumptions : 0
% 0.14/0.62 % Unit Clause-clause subsumption calls : 0
% 0.14/0.62 % Rewrite failures with RHS unbound : 0
% 0.14/0.62 % BW rewrite match attempts : 26
% 0.14/0.62 % BW rewrite match successes : 15
% 0.14/0.62 % Condensation attempts : 0
% 0.14/0.62 % Condensation successes : 0
% 0.14/0.62 % Termbank termtop insertions : 5325
% 0.14/0.62 % Search garbage collected termcells : 8
% 0.14/0.62
% 0.14/0.62 % -------------------------------------------------
% 0.14/0.62 % User time : 0.003 s
% 0.14/0.62 % System time : 0.004 s
% 0.14/0.62 % Total time : 0.007 s
% 0.14/0.62 % Maximum resident set size: 3636 pages
% 0.14/0.62
% 0.14/0.62 % -------------------------------------------------
% 0.14/0.62 % User time : 0.011 s
% 0.14/0.62 % System time : 0.017 s
% 0.14/0.62 % Total time : 0.027 s
% 0.14/0.62 % Maximum resident set size: 4608 pages
% 0.14/0.62 % E exiting
%------------------------------------------------------------------------------