%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP711+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/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 12:41:01 PM UTC 2026
% Result : Theorem 0.15s 0.64s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 31 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 25 ( 8 ~; 8 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [X1] : mult(X1,unit) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f03,axiom,
! [X2,X3,X1] : mult(X1,mult(X3,mult(X3,X2))) = mult(mult(mult(X1,X3),X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f05,axiom,
! [X1] : mult(i(X1),X1) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f02,axiom,
! [X1] : mult(unit,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f04,axiom,
! [X1] : mult(X1,i(X1)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( ( mult(X5,X4) = mult(X6,X4)
=> X5 = X6 )
& ( mult(X4,X5) = mult(X4,X6)
=> X5 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_6,plain,
! [X7] : mult(X7,unit) = X7,
inference(variable_rename,[status(thm)],[f01]) ).
fof(c_0_7,plain,
! [X9,X10,X11] : mult(X11,mult(X10,mult(X10,X9))) = mult(mult(mult(X11,X10),X10),X9),
inference(variable_rename,[status(thm)],[f03]) ).
cnf(c_0_8,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_8]) ).
fof(c_0_11,plain,
! [X13] : mult(i(X13),X13) = unit,
inference(variable_rename,[status(thm)],[f05]) ).
fof(c_0_12,plain,
! [X8] : mult(unit,X8) = X8,
inference(variable_rename,[status(thm)],[f02]) ).
cnf(c_0_13,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
mult(i(X1),X1) = unit,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
mult(unit,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X12] : mult(X12,i(X12)) = unit,
inference(variable_rename,[status(thm)],[f04]) ).
cnf(c_0_17,plain,
mult(i(mult(X1,X1)),mult(X1,mult(X1,X2))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
mult(X1,i(X1)) = unit,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
mult(i(X1),mult(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_14]),c_0_15]) ).
cnf(c_0_20,plain,
mult(i(mult(X1,X1)),X1) = i(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_8]) ).
cnf(c_0_21,plain,
i(mult(i(X1),i(X1))) = mult(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_14]),c_0_8]) ).
cnf(c_0_22,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_15]),c_0_15]) ).
cnf(c_0_23,plain,
mult(i(X1),mult(X1,mult(X1,X2))) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_24,plain,
i(i(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_18]),c_0_8]) ).
fof(c_0_25,negated_conjecture,
~ ! [X4,X5,X6] :
( ( mult(X5,X4) = mult(X6,X4)
=> X5 = X6 )
& ( mult(X4,X5) = mult(X4,X6)
=> X5 = X6 ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_26,plain,
mult(X1,mult(i(X1),mult(X1,X2))) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_23]),c_0_24]) ).
fof(c_0_27,negated_conjecture,
( ( esk2_0 != esk3_0
| esk2_0 != esk3_0 )
& ( esk2_0 != esk3_0
| mult(esk2_0,esk1_0) = mult(esk3_0,esk1_0) )
& ( mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0)
| esk2_0 != esk3_0 )
& ( mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0)
| mult(esk2_0,esk1_0) = mult(esk3_0,esk1_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])]) ).
cnf(c_0_28,plain,
mult(i(X1),mult(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_26]),c_0_17]) ).
cnf(c_0_29,plain,
mult(X1,mult(X2,mult(X2,i(mult(X1,mult(X2,X2)))))) = unit,
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_30,negated_conjecture,
( mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0)
| mult(esk2_0,esk1_0) = mult(esk3_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
mult(X1,mult(X1,i(mult(X2,mult(X1,X1))))) = i(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_8]) ).
cnf(c_0_32,negated_conjecture,
( mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0)
| mult(esk2_0,mult(esk1_0,esk1_0)) = mult(esk3_0,mult(esk1_0,esk1_0)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_30]),c_0_10]) ).
cnf(c_0_33,negated_conjecture,
( esk2_0 != esk3_0
| esk2_0 != esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
( i(esk2_0) = i(esk3_0)
| mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_31]) ).
cnf(c_0_35,negated_conjecture,
esk3_0 != esk2_0,
inference(cn,[status(thm)],[c_0_33]) ).
cnf(c_0_36,negated_conjecture,
mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_34]),c_0_24]),c_0_35]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_36]),c_0_28]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP711+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.58 % Computer : n003.cluster.edu
% 0.12/0.58 % Model : x86_64 x86_64
% 0.12/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.58 % Memory : 8046.5625MB
% 0.12/0.58 % OS : Linux 6.8.0-71-generic
% 0.12/0.58 % CPULimit : 300
% 0.12/0.58 % WCLimit : 300
% 0.12/0.58 % DateTime : Sun Sep 20 20:36:30 UTC 2026
% 0.12/0.58 % CPUTime :
% 0.12/0.58 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.62 Running first-order theorem proving
% 0.12/0.62 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
% 0.15/0.64 % Version: 3.5.1
% 0.15/0.64 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.64 % Starting sh5l with 300s (1) cores
% 0.15/0.64 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2561967 completed with status 0
% 0.15/0.64 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.15/0.64 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.64 % No SInE strategy applied
% 0.15/0.64 % Search class: FGUPM-FFSF21-MFFFFFNN
% 0.15/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.15/0.64 % Starting C12_02_nc_SAT001_MinMin_p005000_rr with 136s (1) cores
% 0.15/0.64 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.64 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.64 % SubtermCWHack with pid 2561971 completed with status 0
% 0.15/0.64 % Result found by SubtermCWHack
% 0.15/0.64 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.15/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.64 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.15/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.64 % No SInE strategy applied
% 0.15/0.64 % Search class: FGUPM-FFSF21-MFFFFFNN
% 0.15/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.64 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.64 % Preprocessing time : 0.001 s
% 0.15/0.64
% 0.15/0.64 % Proof found!
% 0.15/0.64 % SZS status Theorem
% 0.15/0.64 % SZS output start CNFRefutation
% See solution above
% 0.15/0.64 % Parsed axioms : 6
% 0.15/0.64 % Removed by relevancy pruning/SinE : 0
% 0.15/0.64 % Initial clauses : 9
% 0.15/0.64 % Removed in clause preprocessing : 2
% 0.15/0.64 % Initial clauses in saturation : 7
% 0.15/0.64 % Processed clauses : 40
% 0.15/0.64 % ...of these trivial : 5
% 0.15/0.64 % ...subsumed : 0
% 0.15/0.64 % ...remaining for further processing : 35
% 0.15/0.64 % Other redundant clauses eliminated : 0
% 0.15/0.64 % Clauses deleted for lack of memory : 0
% 0.15/0.64 % Backward-subsumed : 0
% 0.15/0.64 % Backward-rewritten : 14
% 0.15/0.64 % Generated clauses : 495
% 0.15/0.64 % ...of the previous two non-redundant : 280
% 0.15/0.64 % ...aggressively subsumed : 0
% 0.15/0.64 % Contextual simplify-reflections : 0
% 0.15/0.64 % Paramodulations : 495
% 0.15/0.64 % Factorizations : 0
% 0.15/0.64 % NegExts : 0
% 0.15/0.64 % Equation resolutions : 0
% 0.15/0.64 % Disequality decompositions : 0
% 0.15/0.64 % Total rewrite steps : 915
% 0.15/0.64 % ...of those cached : 766
% 0.15/0.64 % Propositional unsat checks : 0
% 0.15/0.64 % Propositional check models : 0
% 0.15/0.64 % Propositional check unsatisfiable : 0
% 0.15/0.64 % Propositional clauses : 0
% 0.15/0.64 % Propositional clauses after purity: 0
% 0.15/0.64 % Propositional unsat core size : 0
% 0.15/0.64 % Propositional preprocessing time : 0.000
% 0.15/0.64 % Propositional encoding time : 0.000
% 0.15/0.64 % Propositional solver time : 0.000
% 0.15/0.64 % Success case prop preproc time : 0.000
% 0.15/0.64 % Success case prop encoding time : 0.000
% 0.15/0.64 % Success case prop solver time : 0.000
% 0.15/0.64 % Current number of processed clauses : 21
% 0.15/0.64 % Positive orientable unit clauses : 20
% 0.15/0.64 % Positive unorientable unit clauses: 0
% 0.15/0.64 % Negative unit clauses : 1
% 0.15/0.64 % Non-unit-clauses : 0
% 0.15/0.64 % Current number of unprocessed clauses: 232
% 0.15/0.64 % ...number of literals in the above : 253
% 0.15/0.64 % Current number of archived formulas : 0
% 0.15/0.64 % Current number of archived clauses : 14
% 0.15/0.64 % Clause-clause subsumption calls (NU) : 1
% 0.15/0.64 % Rec. Clause-clause subsumption calls : 1
% 0.15/0.64 % Non-unit clause-clause subsumptions : 0
% 0.15/0.64 % Unit Clause-clause subsumption calls : 2
% 0.15/0.64 % Rewrite failures with RHS unbound : 0
% 0.15/0.64 % BW rewrite match attempts : 29
% 0.15/0.64 % BW rewrite match successes : 11
% 0.15/0.64 % Condensation attempts : 0
% 0.15/0.64 % Condensation successes : 0
% 0.15/0.64 % Termbank termtop insertions : 5966
% 0.15/0.64 % Search garbage collected termcells : 55
% 0.15/0.64
% 0.15/0.64 % -------------------------------------------------
% 0.15/0.64 % User time : 0.004 s
% 0.15/0.64 % System time : 0.004 s
% 0.15/0.64 % Total time : 0.008 s
% 0.15/0.64 % Maximum resident set size: 3632 pages
% 0.15/0.64
% 0.15/0.64 % -------------------------------------------------
% 0.15/0.64 % User time : 0.018 s
% 0.15/0.64 % System time : 0.015 s
% 0.15/0.64 % Total time : 0.034 s
% 0.15/0.64 % Maximum resident set size: 4608 pages
% 0.15/0.64 % E exiting
%------------------------------------------------------------------------------