%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP777+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:41:14 PM UTC 2026
% Result : Theorem 1.05s 0.81s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 66 unt; 0 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 126 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos08,axiom,
! [X4,X1,X2] : bigC(X2,X1,X4) = product(product(X2,X1),product(X4,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
fof(sos06,axiom,
! [X2] : product(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
fof(sos05,axiom,
! [X3,X4,X1,X2] : product(product(X2,X1),product(X4,X3)) = product(product(X2,X4),product(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
fof(sos02,axiom,
! [X1,X2] : product(X2,difference(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
fof(sos01,axiom,
! [X1,X2] : difference(X2,product(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
fof(sos04,axiom,
! [X1,X2] : product(quotient(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
fof(sos07,axiom,
! [X1,X2] : product(product(product(X2,X1),X1),product(X1,product(X1,X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
fof(sos03,axiom,
! [X1,X2] : quotient(product(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
fof(sos09,axiom,
product(product(a,c),product(c,b)) = product(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
fof(goals,conjecture,
! [X5] : bigC(a,b,X5) = bigC(c,c,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_10,plain,
! [X7,X8,X9] : bigC(X9,X8,X7) = product(product(X9,X8),product(X7,X9)),
inference(variable_rename,[status(thm)],[sos08]) ).
fof(c_0_11,plain,
! [X22] : product(X22,X22) = X22,
inference(variable_rename,[status(thm)],[sos06]) ).
fof(c_0_12,plain,
! [X18,X19,X20,X21] : product(product(X21,X20),product(X19,X18)) = product(product(X21,X19),product(X20,X18)),
inference(variable_rename,[status(thm)],[sos05]) ).
cnf(c_0_13,plain,
bigC(X1,X2,X3) = product(product(X1,X2),product(X3,X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
product(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
bigC(X1,X2,X1) = product(product(X1,X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
bigC(X1,X2,X3) = bigC(X1,X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_15]),c_0_13]) ).
cnf(c_0_18,plain,
bigC(X1,X1,X2) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_19,plain,
! [X12,X13] : product(X13,difference(X13,X12)) = X12,
inference(variable_rename,[status(thm)],[sos02]) ).
fof(c_0_20,plain,
! [X10,X11] : difference(X11,product(X11,X10)) = X10,
inference(variable_rename,[status(thm)],[sos01]) ).
cnf(c_0_21,plain,
product(product(X1,X2),X1) = product(X1,product(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_22,plain,
product(X1,difference(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
difference(X1,product(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
product(X1,product(difference(X1,X2),X1)) = product(X2,X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_25,plain,
! [X16,X17] : product(quotient(X17,X16),X16) = X17,
inference(variable_rename,[status(thm)],[sos04]) ).
fof(c_0_26,plain,
! [X23,X24] : product(product(product(X24,X23),X23),product(X23,product(X23,X24))) = X23,
inference(variable_rename,[status(thm)],[sos07]) ).
cnf(c_0_27,plain,
difference(X1,product(X2,X1)) = product(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
product(quotient(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_29,plain,
! [X14,X15] : quotient(product(X15,X14),X14) = X15,
inference(variable_rename,[status(thm)],[sos03]) ).
cnf(c_0_30,plain,
product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
product(difference(X1,quotient(X2,X1)),X1) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
bigC(X1,difference(X1,X2),X3) = product(X2,product(X3,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_22]) ).
cnf(c_0_33,plain,
quotient(product(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,plain,
product(product(X1,X2),product(X3,X2)) = product(product(X1,X3),X2),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_35,plain,
product(product(difference(X1,X2),X1),product(X1,quotient(X2,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_22]) ).
cnf(c_0_36,plain,
bigC(X1,X2,difference(X1,X3)) = product(X3,product(X2,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_32]) ).
cnf(c_0_37,plain,
quotient(product(X1,product(X2,X1)),X1) = product(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_21]) ).
cnf(c_0_38,plain,
difference(product(product(X1,X2),X2),X2) = product(X2,product(X2,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_39,plain,
product(product(a,c),product(c,b)) = product(a,b),
inference(split_conjunct,[status(thm)],[sos09]) ).
cnf(c_0_40,plain,
quotient(product(product(X1,X2),X3),product(X2,X3)) = product(X1,X3),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,plain,
product(product(difference(X1,X2),X1),X2) = product(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_35]),c_0_24]),c_0_13]),c_0_36]),c_0_28]),c_0_14]) ).
cnf(c_0_42,plain,
quotient(product(X1,X2),X1) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_43,plain,
product(X1,product(X1,quotient(X2,X1))) = difference(product(X2,X1),X1),
inference(spm,[status(thm)],[c_0_38,c_0_28]) ).
cnf(c_0_44,plain,
quotient(product(a,b),product(c,b)) = product(a,c),
inference(spm,[status(thm)],[c_0_33,c_0_39]) ).
cnf(c_0_45,plain,
quotient(product(X1,X2),product(X3,X2)) = product(quotient(X1,X3),X2),
inference(spm,[status(thm)],[c_0_40,c_0_28]) ).
cnf(c_0_46,plain,
product(difference(X1,X2),quotient(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_31]),c_0_28]) ).
cnf(c_0_47,plain,
quotient(difference(product(X1,X2),X2),X2) = difference(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_42]),c_0_43]),c_0_28]) ).
fof(c_0_48,negated_conjecture,
~ ! [X5] : bigC(a,b,X5) = bigC(c,c,X5),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_49,plain,
product(product(quotient(X1,X2),X3),X2) = product(X1,product(X3,X2)),
inference(spm,[status(thm)],[c_0_34,c_0_28]) ).
cnf(c_0_50,plain,
product(quotient(a,c),b) = product(a,c),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,plain,
product(product(X1,X2),product(X1,X3)) = product(X1,product(X2,X3)),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_52,plain,
difference(difference(X1,X2),X2) = quotient(X2,X1),
inference(spm,[status(thm)],[c_0_23,c_0_46]) ).
cnf(c_0_53,plain,
difference(product(X1,X2),X2) = product(difference(X1,X2),X2),
inference(spm,[status(thm)],[c_0_28,c_0_47]) ).
cnf(c_0_54,plain,
difference(quotient(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
fof(c_0_55,negated_conjecture,
bigC(a,b,esk1_0) != bigC(c,c,esk1_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])]) ).
cnf(c_0_56,plain,
product(product(a,c),c) = product(a,product(b,c)),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,plain,
quotient(product(X1,product(X2,X3)),product(X1,X3)) = product(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_51]) ).
cnf(c_0_58,plain,
quotient(X1,product(X2,X1)) = product(quotient(X1,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_53]),c_0_52]) ).
cnf(c_0_59,plain,
product(product(X1,quotient(X2,X1)),X2) = product(X2,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_41,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
bigC(a,b,esk1_0) != bigC(c,c,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,plain,
product(product(X1,quotient(X2,X3)),product(X4,X3)) = product(product(X1,X4),X2),
inference(spm,[status(thm)],[c_0_15,c_0_28]) ).
cnf(c_0_62,plain,
product(c,quotient(c,a)) = product(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_56]),c_0_57]),c_0_58]),c_0_34]),c_0_59]) ).
cnf(c_0_63,negated_conjecture,
bigC(a,b,esk1_0) != product(c,product(esk1_0,c)),
inference(rw,[status(thm)],[c_0_60,c_0_18]) ).
cnf(c_0_64,plain,
bigC(a,b,X1) = product(c,product(X1,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_13]),c_0_21]) ).
cnf(c_0_65,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP777+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 20:42:50 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
% 1.05/0.81 % Version: 3.5.1
% 1.05/0.81 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.05/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.05/0.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.05/0.81 % Starting new_bool_3 with 300s (1) cores
% 1.05/0.81 % Starting new_bool_1 with 300s (1) cores
% 1.05/0.81 % Starting sh5l with 300s (1) cores
% 1.05/0.81 % sh5l with pid 3899776 completed with status 0
% 1.05/0.81 % Result found by sh5l
% 1.05/0.81 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.05/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.05/0.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.05/0.81 % Starting new_bool_3 with 300s (1) cores
% 1.05/0.81 % Starting new_bool_1 with 300s (1) cores
% 1.05/0.81 % Starting sh5l with 300s (1) cores
% 1.05/0.81 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 1.05/0.81 % SinE strategy is gf500_gu_R04_F100_L20000
% 1.05/0.81 % Search class: FUUPM-FFSF32-MFFFFFNN
% 1.05/0.81 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.05/0.81 % Starting SubtermCWHack with 28s (1) cores
% 1.05/0.81 % SubtermCWHack with pid 3899784 completed with status 0
% 1.05/0.81 % Result found by SubtermCWHack
% 1.05/0.81 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.05/0.81 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.05/0.81 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.05/0.81 % Starting new_bool_3 with 300s (1) cores
% 1.05/0.81 % Starting new_bool_1 with 300s (1) cores
% 1.05/0.81 % Starting sh5l with 300s (1) cores
% 1.05/0.81 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 1.05/0.81 % SinE strategy is gf500_gu_R04_F100_L20000
% 1.05/0.81 % Search class: FUUPM-FFSF32-MFFFFFNN
% 1.05/0.81 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 1.05/0.81 % Starting SubtermCWHack with 28s (1) cores
% 1.05/0.81 % Preprocessing time : 0.001 s
% 1.05/0.81
% 1.05/0.81 % Proof found!
% 1.05/0.81 % SZS status Theorem
% 1.05/0.81 % SZS output start CNFRefutation
% See solution above
% 1.05/0.81 % Parsed axioms : 10
% 1.05/0.81 % Removed by relevancy pruning/SinE : 0
% 1.05/0.81 % Initial clauses : 10
% 1.05/0.81 % Removed in clause preprocessing : 0
% 1.05/0.81 % Initial clauses in saturation : 10
% 1.05/0.81 % Processed clauses : 611
% 1.05/0.81 % ...of these trivial : 267
% 1.05/0.81 % ...subsumed : 79
% 1.05/0.81 % ...remaining for further processing : 265
% 1.05/0.81 % Other redundant clauses eliminated : 0
% 1.05/0.81 % Clauses deleted for lack of memory : 0
% 1.05/0.81 % Backward-subsumed : 0
% 1.05/0.81 % Backward-rewritten : 64
% 1.05/0.81 % Generated clauses : 20096
% 1.05/0.81 % ...of the previous two non-redundant : 18273
% 1.05/0.81 % ...aggressively subsumed : 0
% 1.05/0.81 % Contextual simplify-reflections : 0
% 1.05/0.81 % Paramodulations : 20096
% 1.05/0.81 % Factorizations : 0
% 1.05/0.81 % NegExts : 0
% 1.05/0.81 % Equation resolutions : 0
% 1.05/0.81 % Disequality decompositions : 0
% 1.05/0.81 % Total rewrite steps : 12095
% 1.05/0.81 % ...of those cached : 10185
% 1.05/0.81 % Propositional unsat checks : 0
% 1.05/0.81 % Propositional check models : 0
% 1.05/0.81 % Propositional check unsatisfiable : 0
% 1.05/0.81 % Propositional clauses : 0
% 1.05/0.81 % Propositional clauses after purity: 0
% 1.05/0.81 % Propositional unsat core size : 0
% 1.05/0.81 % Propositional preprocessing time : 0.000
% 1.05/0.81 % Propositional encoding time : 0.000
% 1.05/0.81 % Propositional solver time : 0.000
% 1.05/0.81 % Success case prop preproc time : 0.000
% 1.05/0.81 % Success case prop encoding time : 0.000
% 1.05/0.81 % Success case prop solver time : 0.000
% 1.05/0.81 % Current number of processed clauses : 201
% 1.05/0.81 % Positive orientable unit clauses : 191
% 1.05/0.81 % Positive unorientable unit clauses: 10
% 1.05/0.81 % Negative unit clauses : 0
% 1.05/0.81 % Non-unit-clauses : 0
% 1.05/0.81 % Current number of unprocessed clauses: 17561
% 1.05/0.81 % ...number of literals in the above : 17561
% 1.05/0.81 % Current number of archived formulas : 0
% 1.05/0.81 % Current number of archived clauses : 64
% 1.05/0.81 % Clause-clause subsumption calls (NU) : 0
% 1.05/0.81 % Rec. Clause-clause subsumption calls : 0
% 1.05/0.81 % Non-unit clause-clause subsumptions : 0
% 1.05/0.81 % Unit Clause-clause subsumption calls : 34
% 1.05/0.81 % Rewrite failures with RHS unbound : 0
% 1.05/0.81 % BW rewrite match attempts : 676
% 1.05/0.81 % BW rewrite match successes : 258
% 1.05/0.81 % Condensation attempts : 0
% 1.05/0.81 % Condensation successes : 0
% 1.05/0.81 % Termbank termtop insertions : 246413
% 1.05/0.81 % Search garbage collected termcells : 10
% 1.05/0.81
% 1.05/0.81 % -------------------------------------------------
% 1.05/0.81 % User time : 0.301 s
% 1.05/0.81 % System time : 0.018 s
% 1.05/0.81 % Total time : 0.319 s
% 1.05/0.81 % Maximum resident set size: 3636 pages
% 1.05/0.81
% 1.05/0.81 % -------------------------------------------------
% 1.05/0.81 % User time : 0.304 s
% 1.05/0.81 % System time : 0.021 s
% 1.05/0.81 % Total time : 0.325 s
% 1.05/0.81 % Maximum resident set size: 4608 pages
% 1.05/0.81 % E exiting
%------------------------------------------------------------------------------