%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP660+2 : 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 : n014.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 12:44:39 PM UTC 2026
% Result : Theorem 0.18s 0.59s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 45 unt; 0 def)
% Number of atoms : 53 ( 52 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 2 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f04,axiom,
! [X1,X2] : rd(mult(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f05,axiom,
! [X3,X1,X2] : mult(mult(mult(X2,X1),X3),X2) = mult(X2,mult(X1,mult(X3,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f03,axiom,
! [X1,X2] : mult(rd(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f01,axiom,
! [X1,X2] : mult(X2,ld(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f02,axiom,
! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(goals,conjecture,
! [X4,X5] :
( mult(rd(X5,X5),X4) = X4
& mult(X4,rd(X5,X5)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_6,plain,
! [X12,X13] : rd(mult(X13,X12),X12) = X13,
inference(variable_rename,[status(thm)],[f04]) ).
fof(c_0_7,plain,
! [X14,X15,X16] : mult(mult(mult(X16,X15),X14),X16) = mult(X16,mult(X15,mult(X14,X16))),
inference(variable_rename,[status(thm)],[f05]) ).
cnf(c_0_8,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
mult(mult(mult(X1,X2),X3),X1) = mult(X1,mult(X2,mult(X3,X1))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X10,X11] : mult(rd(X11,X10),X10) = X11,
inference(variable_rename,[status(thm)],[f03]) ).
cnf(c_0_11,plain,
rd(mult(X1,mult(X2,mult(X3,X1))),X1) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
rd(mult(X1,mult(X2,X3)),X1) = mult(mult(X1,X2),rd(X3,X1)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_14,plain,
! [X6,X7] : mult(X7,ld(X7,X6)) = X6,
inference(variable_rename,[status(thm)],[f01]) ).
cnf(c_0_15,plain,
mult(mult(X1,rd(X2,X3)),rd(X3,X1)) = rd(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
fof(c_0_16,plain,
! [X8,X9] : ld(X9,mult(X9,X8)) = X8,
inference(variable_rename,[status(thm)],[f02]) ).
cnf(c_0_17,plain,
mult(mult(mult(X1,X2),X1),rd(X2,mult(X1,X2))) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_18,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
rd(rd(mult(X1,X2),X1),rd(X3,X1)) = mult(X1,rd(X2,X3)),
inference(spm,[status(thm)],[c_0_8,c_0_15]) ).
cnf(c_0_20,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
mult(mult(X1,X2),rd(ld(X2,X1),X1)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
rd(X1,rd(X2,X1)) = mult(X1,rd(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_8]) ).
cnf(c_0_23,plain,
rd(ld(X1,X2),X2) = ld(mult(X2,X1),X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
mult(X1,rd(X1,mult(X2,X1))) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_8]) ).
cnf(c_0_25,plain,
mult(mult(X1,X2),rd(ld(X2,X3),X1)) = rd(mult(X1,X3),X1),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_26,plain,
mult(ld(mult(X1,X2),X1),X1) = ld(X2,X1),
inference(spm,[status(thm)],[c_0_12,c_0_23]) ).
cnf(c_0_27,plain,
ld(X1,rd(X1,X2)) = rd(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_24]) ).
cnf(c_0_28,plain,
ld(mult(X1,X2),rd(mult(X1,X3),X1)) = rd(ld(X2,X3),X1),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_29,plain,
ld(ld(X1,X2),X1) = mult(ld(X2,X1),X1),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_30,plain,
rd(mult(X1,X2),mult(X1,mult(X1,X2))) = rd(ld(X2,X2),X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
mult(ld(X1,X2),mult(ld(X2,X1),X1)) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_32,plain,
rd(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_8]) ).
cnf(c_0_33,plain,
mult(rd(mult(X1,X2),X1),rd(X1,mult(X1,X3))) = rd(mult(mult(X1,X3),ld(X3,X2)),mult(X1,X3)),
inference(spm,[status(thm)],[c_0_15,c_0_25]) ).
cnf(c_0_34,plain,
mult(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_32]),c_0_32]),c_0_32]) ).
cnf(c_0_35,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_18]) ).
cnf(c_0_36,plain,
rd(X1,ld(X2,X2)) = mult(ld(X2,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_32]),c_0_12]),c_0_18]) ).
cnf(c_0_37,plain,
mult(ld(X1,X1),X1) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
ld(X1,X1) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_8,c_0_37]) ).
fof(c_0_39,negated_conjecture,
~ ! [X4,X5] :
( mult(rd(X5,X5),X4) = X4
& mult(X4,rd(X5,X5)) = X4 ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_40,plain,
mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_38]),c_0_38]),c_0_38]) ).
cnf(c_0_41,plain,
rd(X1,rd(X2,X2)) = mult(rd(X2,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_38]),c_0_38]) ).
fof(c_0_42,negated_conjecture,
( mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0
| mult(esk1_0,rd(esk2_0,esk2_0)) != esk1_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])]) ).
cnf(c_0_43,plain,
mult(rd(X1,X1),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_40]),c_0_41]),c_0_20]),c_0_41]),c_0_18]) ).
cnf(c_0_44,negated_conjecture,
( mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0
| mult(esk1_0,rd(esk2_0,esk2_0)) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_45,plain,
rd(X1,rd(X2,X2)) = X1,
inference(rw,[status(thm)],[c_0_41,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
mult(esk1_0,rd(esk2_0,esk2_0)) != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_43])]) ).
cnf(c_0_47,plain,
mult(X1,rd(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_45]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP660+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n014.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 20:29:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.18/0.59 % Version: 3.5.1
% 0.18/0.59 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.18/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.59 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.18/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.59 % Starting sh5l with 300s (1) cores
% 0.18/0.59 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2305535 completed with status 0
% 0.18/0.59 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.18/0.59 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.18/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.59 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.18/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.59 % No SInE strategy applied
% 0.18/0.59 % Search class: FUHPM-FFSF22-MFFFFFNN
% 0.18/0.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.59 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.18/0.59 % Starting H----_102_C18_F1_PI_AE_Q4_CS_SP_PS_S5PRR_S2S with 136s (1) cores
% 0.18/0.59 % Starting new_bool_3 with 136s (1) cores
% 0.18/0.59 % Starting new_bool_1 with 136s (1) cores
% 0.18/0.59 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2305540 completed with status 0
% 0.18/0.59 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.18/0.59 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.18/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.59 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.18/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.59 % No SInE strategy applied
% 0.18/0.59 % Search class: FUHPM-FFSF22-MFFFFFNN
% 0.18/0.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.59 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.18/0.59 % Preprocessing time : 0.001 s
% 0.18/0.59
% 0.18/0.59 % Proof found!
% 0.18/0.59 % SZS status Theorem
% 0.18/0.59 % SZS output start CNFRefutation
% See solution above
% 0.18/0.59 % Parsed axioms : 6
% 0.18/0.59 % Removed by relevancy pruning/SinE : 0
% 0.18/0.59 % Initial clauses : 6
% 0.18/0.59 % Removed in clause preprocessing : 0
% 0.18/0.59 % Initial clauses in saturation : 6
% 0.18/0.59 % Processed clauses : 165
% 0.18/0.59 % ...of these trivial : 52
% 0.18/0.59 % ...subsumed : 6
% 0.18/0.59 % ...remaining for further processing : 107
% 0.18/0.59 % Other redundant clauses eliminated : 0
% 0.18/0.59 % Clauses deleted for lack of memory : 0
% 0.18/0.59 % Backward-subsumed : 0
% 0.18/0.59 % Backward-rewritten : 24
% 0.18/0.59 % Generated clauses : 7348
% 0.18/0.59 % ...of the previous two non-redundant : 6348
% 0.18/0.59 % ...aggressively subsumed : 0
% 0.18/0.59 % Contextual simplify-reflections : 0
% 0.18/0.59 % Paramodulations : 7348
% 0.18/0.59 % Factorizations : 0
% 0.18/0.59 % NegExts : 0
% 0.18/0.59 % Equation resolutions : 0
% 0.18/0.59 % Disequality decompositions : 0
% 0.18/0.59 % Total rewrite steps : 4071
% 0.18/0.59 % ...of those cached : 2885
% 0.18/0.59 % Propositional unsat checks : 0
% 0.18/0.59 % Propositional check models : 0
% 0.18/0.59 % Propositional check unsatisfiable : 0
% 0.18/0.59 % Propositional clauses : 0
% 0.18/0.59 % Propositional clauses after purity: 0
% 0.18/0.59 % Propositional unsat core size : 0
% 0.18/0.59 % Propositional preprocessing time : 0.000
% 0.18/0.59 % Propositional encoding time : 0.000
% 0.18/0.59 % Propositional solver time : 0.000
% 0.18/0.59 % Success case prop preproc time : 0.000
% 0.18/0.59 % Success case prop encoding time : 0.000
% 0.18/0.59 % Success case prop solver time : 0.000
% 0.18/0.59 % Current number of processed clauses : 83
% 0.18/0.59 % Positive orientable unit clauses : 78
% 0.18/0.59 % Positive unorientable unit clauses: 5
% 0.18/0.59 % Negative unit clauses : 0
% 0.18/0.59 % Non-unit-clauses : 0
% 0.18/0.59 % Current number of unprocessed clauses: 6138
% 0.18/0.59 % ...number of literals in the above : 6138
% 0.18/0.59 % Current number of archived formulas : 0
% 0.18/0.59 % Current number of archived clauses : 24
% 0.18/0.59 % Clause-clause subsumption calls (NU) : 0
% 0.18/0.59 % Rec. Clause-clause subsumption calls : 0
% 0.18/0.59 % Non-unit clause-clause subsumptions : 0
% 0.18/0.59 % Unit Clause-clause subsumption calls : 10
% 0.18/0.59 % Rewrite failures with RHS unbound : 0
% 0.18/0.59 % BW rewrite match attempts : 268
% 0.18/0.59 % BW rewrite match successes : 22
% 0.18/0.59 % Condensation attempts : 0
% 0.18/0.59 % Condensation successes : 0
% 0.18/0.59 % Termbank termtop insertions : 119126
% 0.18/0.59 % Search garbage collected termcells : 25
% 0.18/0.59
% 0.18/0.59 % -------------------------------------------------
% 0.18/0.59 % User time : 0.126 s
% 0.18/0.59 % System time : 0.013 s
% 0.18/0.59 % Total time : 0.139 s
% 0.18/0.59 % Maximum resident set size: 3376 pages
% 0.18/0.59
% 0.18/0.59 % -------------------------------------------------
% 0.18/0.59 % User time : 0.519 s
% 0.18/0.59 % System time : 0.049 s
% 0.18/0.59 % Total time : 0.568 s
% 0.18/0.59 % Maximum resident set size: 4608 pages
% 0.18/0.59 % E exiting
%------------------------------------------------------------------------------