%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP777+1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:27:16 PM UTC 2026
% Result : Theorem 3.73s 3.04s
% Output : CNFRefutation 3.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 88 ( 88 unt; 0 def)
% Number of atoms : 88 ( 87 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 5 ( 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 : 116 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos05,axiom,
! [X3,X4,X1,X2] : product(product(X2,X1),product(X4,X3)) = product(product(X2,X4),product(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
fof(sos06,axiom,
! [X2] : product(X2,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
fof(sos09,axiom,
product(product(a,c),product(c,b)) = product(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
fof(sos03,axiom,
! [X1,X2] : quotient(product(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
fof(sos01,axiom,
! [X1,X2] : difference(X2,product(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
fof(sos07,axiom,
! [X1,X2] : product(product(product(X2,X1),X1),product(X1,product(X1,X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
fof(sos04,axiom,
! [X1,X2] : product(quotient(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
fof(sos02,axiom,
! [X1,X2] : product(X2,difference(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
fof(goals,conjecture,
! [X5] : bigC(a,b,X5) = bigC(c,c,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(sos08,axiom,
! [X4,X1,X2] : bigC(X2,X1,X4) = product(product(X2,X1),product(X4,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
fof(c_0_10,plain,
! [X33,X34,X35,X36] : product(product(X36,X35),product(X34,X33)) = product(product(X36,X34),product(X35,X33)),
inference(variable_rename,[status(thm)],[sos05]) ).
fof(c_0_11,plain,
! [X37] : product(X37,X37) = X37,
inference(variable_rename,[status(thm)],[sos06]) ).
cnf(c_0_12,plain,
product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
product(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,plain,
product(product(X1,X2),product(X1,X3)) = product(X1,product(X2,X3)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,plain,
product(product(a,c),product(c,b)) = product(a,b),
inference(split_conjunct,[status(thm)],[sos09]) ).
fof(c_0_16,plain,
! [X29,X30] : quotient(product(X30,X29),X29) = X30,
inference(variable_rename,[status(thm)],[sos03]) ).
fof(c_0_17,plain,
! [X25,X26] : difference(X26,product(X26,X25)) = X25,
inference(variable_rename,[status(thm)],[sos01]) ).
cnf(c_0_18,plain,
product(product(product(a,c),X1),product(a,b)) = product(product(a,c),product(X1,product(c,b))),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
product(product(X1,X2),X1) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
fof(c_0_20,plain,
! [X38,X39] : product(product(product(X39,X38),X38),product(X38,product(X38,X39))) = X38,
inference(variable_rename,[status(thm)],[sos07]) ).
cnf(c_0_21,plain,
quotient(product(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
difference(X1,product(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
product(a,product(product(c,a),b)) = product(a,product(c,product(c,b))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_14]),c_0_14]) ).
cnf(c_0_24,plain,
product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
product(product(X1,X2),product(X3,X2)) = product(product(X1,X3),X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_26,plain,
quotient(product(X1,product(X2,X1)),X1) = product(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_27,plain,
product(product(c,a),b) = product(c,product(c,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_22]) ).
cnf(c_0_28,plain,
product(product(product(a,c),b),product(product(c,b),product(product(c,a),product(b,c)))) = product(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_15]),c_0_25]),c_0_12]) ).
cnf(c_0_29,plain,
product(product(product(a,c),X1),product(product(c,b),X2)) = product(product(a,b),product(X1,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_30,plain,
product(product(product(X1,X2),X3),product(product(X4,X5),X6)) = product(product(product(X1,X4),product(X2,X5)),product(X3,X6)),
inference(spm,[status(thm)],[c_0_12,c_0_12]) ).
cnf(c_0_31,plain,
product(product(c,a),product(b,c)) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_15]),c_0_25]),c_0_27]),c_0_21]),c_0_12]) ).
cnf(c_0_32,plain,
product(product(a,b),product(b,product(product(c,a),product(b,c)))) = product(c,b),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
product(product(product(product(c,a),product(b,c)),a),product(a,b)) = product(a,c),
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(spm,[status(thm)],[c_0_24,c_0_15]),c_0_12]),c_0_30]),c_0_14]),c_0_30]),c_0_12]),c_0_15]) ).
cnf(c_0_34,plain,
product(product(a,c),product(product(c,a),product(b,c))) = product(a,product(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_15]),c_0_14]),c_0_12]) ).
fof(c_0_35,plain,
! [X31,X32] : product(quotient(X32,X31),X31) = X32,
inference(variable_rename,[status(thm)],[sos04]) ).
cnf(c_0_36,plain,
product(product(c,a),product(X1,product(b,c))) = product(product(product(c,a),X1),c),
inference(spm,[status(thm)],[c_0_14,c_0_31]) ).
cnf(c_0_37,plain,
product(product(a,b),product(b,c)) = product(c,b),
inference(rw,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_38,plain,
product(product(c,a),product(a,b)) = product(a,c),
inference(rw,[status(thm)],[c_0_33,c_0_31]) ).
cnf(c_0_39,plain,
product(product(a,c),c) = product(a,product(b,c)),
inference(rw,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_40,plain,
product(quotient(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
product(a,product(b,c)) = product(c,product(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_14]),c_0_38]),c_0_39]) ).
cnf(c_0_42,plain,
product(product(X1,X2),product(X2,product(X2,quotient(X1,X2)))) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_40]) ).
cnf(c_0_43,plain,
product(product(a,c),c) = product(c,product(a,b)),
inference(rw,[status(thm)],[c_0_39,c_0_41]) ).
cnf(c_0_44,plain,
product(product(X1,product(X2,X3)),product(X4,product(X5,X6))) = product(product(X1,X4),product(product(X2,X5),product(X3,X6))),
inference(spm,[status(thm)],[c_0_12,c_0_12]) ).
fof(c_0_45,plain,
! [X27,X28] : product(X28,difference(X28,X27)) = X27,
inference(variable_rename,[status(thm)],[sos02]) ).
cnf(c_0_46,plain,
product(c,product(product(a,c),product(b,a))) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_21]),c_0_14]),c_0_12]) ).
cnf(c_0_47,plain,
difference(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_48,plain,
product(product(a,c),product(product(b,c),product(c,a))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_39]),c_0_44]) ).
cnf(c_0_49,plain,
product(X1,difference(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,plain,
product(product(a,c),product(b,a)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_46]),c_0_47]) ).
cnf(c_0_51,plain,
difference(product(a,c),c) = product(product(b,c),product(c,a)),
inference(spm,[status(thm)],[c_0_22,c_0_48]) ).
cnf(c_0_52,plain,
product(X1,product(X2,difference(X1,X3))) = product(product(X1,X2),X3),
inference(spm,[status(thm)],[c_0_14,c_0_49]) ).
cnf(c_0_53,plain,
product(product(b,c),product(c,a)) = product(b,a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_50]),c_0_51]) ).
cnf(c_0_54,plain,
product(product(X1,quotient(X2,X3)),X3) = product(product(X1,X3),X2),
inference(spm,[status(thm)],[c_0_25,c_0_40]) ).
cnf(c_0_55,plain,
difference(X1,product(product(X1,X2),X3)) = product(X2,difference(X1,X3)),
inference(spm,[status(thm)],[c_0_22,c_0_52]) ).
cnf(c_0_56,plain,
product(product(b,c),c) = product(b,product(a,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_53]),c_0_14]),c_0_31]) ).
cnf(c_0_57,plain,
product(product(X1,product(a,c)),product(X2,product(c,b))) = product(product(X1,X2),product(a,b)),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_58,plain,
quotient(product(product(X1,X2),X3),X2) = product(X1,quotient(X3,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_54]) ).
cnf(c_0_59,plain,
product(c,difference(b,product(c,a))) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_53]),c_0_22]) ).
cnf(c_0_60,plain,
product(product(b,c),product(a,b)) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_56]),c_0_21]),c_0_57]) ).
cnf(c_0_61,plain,
quotient(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_62,plain,
product(a,quotient(product(b,c),b)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_37]),c_0_21]) ).
cnf(c_0_63,plain,
difference(b,product(c,a)) = difference(c,a),
inference(spm,[status(thm)],[c_0_22,c_0_59]) ).
cnf(c_0_64,plain,
product(b,quotient(product(a,b),c)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_60]),c_0_61]) ).
cnf(c_0_65,plain,
quotient(product(b,c),b) = difference(a,c),
inference(spm,[status(thm)],[c_0_22,c_0_62]) ).
cnf(c_0_66,plain,
product(product(X1,X2),product(X3,difference(X2,X4))) = product(product(X1,X3),X4),
inference(spm,[status(thm)],[c_0_12,c_0_49]) ).
cnf(c_0_67,plain,
product(b,difference(c,a)) = product(c,a),
inference(spm,[status(thm)],[c_0_49,c_0_63]) ).
cnf(c_0_68,plain,
quotient(product(a,b),c) = difference(b,c),
inference(spm,[status(thm)],[c_0_22,c_0_64]) ).
fof(c_0_69,negated_conjecture,
~ ! [X5] : bigC(a,b,X5) = bigC(c,c,X5),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_70,plain,
product(product(X1,X2),product(difference(X1,X3),X4)) = product(X3,product(X2,X4)),
inference(spm,[status(thm)],[c_0_12,c_0_49]) ).
cnf(c_0_71,plain,
product(difference(a,c),b) = product(b,c),
inference(spm,[status(thm)],[c_0_40,c_0_65]) ).
cnf(c_0_72,plain,
product(product(X1,c),product(c,a)) = product(product(X1,b),a),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,plain,
product(difference(b,c),c) = product(a,b),
inference(spm,[status(thm)],[c_0_40,c_0_68]) ).
fof(c_0_74,negated_conjecture,
bigC(a,b,esk1_0) != bigC(c,c,esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])]) ).
fof(c_0_75,plain,
! [X40,X41,X42] : bigC(X42,X41,X40) = product(product(X42,X41),product(X40,X42)),
inference(variable_rename,[status(thm)],[sos08]) ).
cnf(c_0_76,plain,
product(product(X1,quotient(X2,X3)),product(X4,X3)) = product(product(X1,X4),X2),
inference(spm,[status(thm)],[c_0_12,c_0_40]) ).
cnf(c_0_77,plain,
product(product(a,X1),product(b,c)) = product(c,product(X1,b)),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_78,plain,
product(product(difference(b,c),b),a) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_12]),c_0_50]) ).
cnf(c_0_79,negated_conjecture,
bigC(a,b,esk1_0) != bigC(c,c,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_80,plain,
bigC(X1,X2,X3) = product(product(X1,X2),product(X3,X1)),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_81,plain,
product(c,product(quotient(X1,c),b)) = product(product(a,b),X1),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_82,plain,
product(difference(b,c),b) = quotient(c,a),
inference(spm,[status(thm)],[c_0_21,c_0_78]) ).
cnf(c_0_83,negated_conjecture,
product(product(c,c),product(esk1_0,c)) != product(product(a,b),product(esk1_0,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80]),c_0_80]) ).
cnf(c_0_84,plain,
product(c,quotient(c,a)) = product(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_68]),c_0_82]),c_0_14]),c_0_13]) ).
cnf(c_0_85,negated_conjecture,
product(product(a,b),product(esk1_0,a)) != product(c,product(esk1_0,c)),
inference(rw,[status(thm)],[c_0_83,c_0_13]) ).
cnf(c_0_86,plain,
product(product(a,b),product(X1,a)) = product(c,product(X1,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_84]),c_0_19]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP777+1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon May 4 19:05:35 EDT 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.34 % start to proof: theBenchmark
% 3.73/3.04 % Version : CSE_E---1.7
% 3.73/3.04 % Problem : theBenchmark.p
% 3.73/3.04 % SZS status Theorem for theBenchmark.p
% 3.73/3.04 % SZS output start CNFRefutation
% See solution above
% 3.73/3.05 % Total time : 2.371s
%------------------------------------------------------------------------------