%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP780+1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 2.41s 2.12s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 73 ( 69 unt; 0 def)
% Number of atoms : 79 ( 63 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 4 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 100 ( 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/sandbox/benchmark/theBenchmark.p',sos05) ).
fof(sos06,axiom,
! [X2] : product(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
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(sos08,axiom,
! [X5,X6,X7] :
( d(X5,X6,X7)
<=> product(X5,X6) = product(X6,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
fof(sos03,axiom,
! [X1,X2] : quotient(product(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
fof(sos01,axiom,
! [X1,X2] : difference(X2,product(X2,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
fof(sos11,axiom,
d(b1,b2,b3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
fof(sos12,axiom,
d(c1,c2,c3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
fof(sos04,axiom,
! [X1,X2] : product(quotient(X2,X1),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
fof(goals,conjecture,
d(bigC(a1,b3,c2),bigC(a2,b1,c3),bigC(a3,b2,c1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(sos09,axiom,
! [X4,X1,X2] : bigC(X2,X1,X4) = product(product(X2,X1),product(X4,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
fof(sos10,axiom,
d(a1,a2,a3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
fof(c_0_12,plain,
! [X37,X38,X39,X40] : product(product(X40,X39),product(X38,X37)) = product(product(X40,X38),product(X39,X37)),
inference(variable_rename,[status(thm)],[sos05]) ).
fof(c_0_13,plain,
! [X41] : product(X41,X41) = X41,
inference(variable_rename,[status(thm)],[sos06]) ).
cnf(c_0_14,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_15,plain,
product(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X42,X43] : product(product(product(X43,X42),X42),product(X42,product(X42,X43))) = X42,
inference(variable_rename,[status(thm)],[sos07]) ).
fof(c_0_17,plain,
! [X44,X45,X46] :
( ( ~ d(X44,X45,X46)
| product(X44,X45) = product(X45,X46) )
& ( product(X44,X45) != product(X45,X46)
| d(X44,X45,X46) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos08])]) ).
fof(c_0_18,plain,
! [X33,X34] : quotient(product(X34,X33),X33) = X34,
inference(variable_rename,[status(thm)],[sos03]) ).
cnf(c_0_19,plain,
product(product(X1,X2),product(X3,X2)) = product(product(X1,X3),X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_20,plain,
! [X29,X30] : difference(X30,product(X30,X29)) = X29,
inference(variable_rename,[status(thm)],[sos01]) ).
cnf(c_0_21,plain,
product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,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_14,c_0_14]) ).
cnf(c_0_23,plain,
( product(X1,X2) = product(X2,X3)
| ~ d(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
d(b1,b2,b3),
inference(split_conjunct,[status(thm)],[sos11]) ).
cnf(c_0_25,plain,
d(c1,c2,c3),
inference(split_conjunct,[status(thm)],[sos12]) ).
cnf(c_0_26,plain,
quotient(product(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
product(product(X1,X2),X1) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
fof(c_0_28,plain,
! [X35,X36] : product(quotient(X36,X35),X35) = X36,
inference(variable_rename,[status(thm)],[sos04]) ).
cnf(c_0_29,plain,
difference(X1,product(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
product(product(product(product(X1,X2),X3),product(X3,X4)),product(product(product(X3,X4),X4),product(product(X3,X4),product(X1,X2)))) = product(X3,X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_14]),c_0_22]),c_0_22]) ).
cnf(c_0_31,plain,
product(product(X1,X2),product(X1,X3)) = product(X1,product(X2,X3)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_32,plain,
product(b2,b3) = product(b1,b2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_33,plain,
product(c2,c3) = product(c1,c2),
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).
cnf(c_0_34,plain,
quotient(product(X1,product(X2,X1)),X1) = product(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,plain,
product(quotient(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_36,plain,
difference(product(product(X1,X2),X2),X2) = product(X2,product(X2,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_37,plain,
product(product(product(product(X1,X2),X3),product(X3,X4)),product(product(X3,X4),product(X4,product(X1,X2)))) = product(X3,X4),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
product(product(product(b3,b2),b2),product(b2,product(b1,b2))) = b2,
inference(spm,[status(thm)],[c_0_21,c_0_32]) ).
cnf(c_0_39,plain,
product(product(product(c3,c2),c2),product(c2,product(c1,c2))) = c2,
inference(spm,[status(thm)],[c_0_21,c_0_33]) ).
cnf(c_0_40,plain,
quotient(product(X1,X2),X1) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
product(X1,product(X1,quotient(X2,X1))) = difference(product(X2,X1),X1),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_42,plain,
product(product(product(product(b1,b3),product(b3,b2)),b2),b2) = product(product(b3,b2),b2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_19]),c_0_19]) ).
cnf(c_0_43,plain,
product(product(product(product(c1,c3),product(c3,c2)),c2),c2) = product(product(c3,c2),c2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_39]),c_0_19]),c_0_19]) ).
fof(c_0_44,negated_conjecture,
~ d(bigC(a1,b3,c2),bigC(a2,b1,c3),bigC(a3,b2,c1)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
fof(c_0_45,plain,
! [X47,X48,X49] : bigC(X49,X48,X47) = product(product(X49,X48),product(X47,X49)),
inference(variable_rename,[status(thm)],[sos09]) ).
cnf(c_0_46,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_40,c_0_41]),c_0_40]),c_0_41]),c_0_35]) ).
cnf(c_0_47,plain,
product(product(product(b1,b3),product(b3,b2)),b2) = product(b3,b2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_42]),c_0_26]) ).
cnf(c_0_48,plain,
product(product(product(c1,c3),product(c3,c2)),c2) = product(c3,c2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_43]),c_0_26]) ).
cnf(c_0_49,negated_conjecture,
~ d(bigC(a1,b3,c2),bigC(a2,b1,c3),bigC(a3,b2,c1)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,plain,
bigC(X1,X2,X3) = product(product(X1,X2),product(X3,X1)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
difference(product(X1,X2),X2) = product(difference(X1,X2),X2),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_52,plain,
product(product(b1,b3),product(b3,b2)) = b3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_47]),c_0_26]) ).
cnf(c_0_53,plain,
product(product(c1,c3),product(c3,c2)) = c3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_48]),c_0_26]) ).
cnf(c_0_54,negated_conjecture,
~ d(product(product(a1,b3),product(c2,a1)),product(product(a2,b1),product(c3,a2)),product(product(a3,b2),product(c1,a3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_50]),c_0_50]) ).
cnf(c_0_55,plain,
( d(X1,X2,X3)
| product(X1,X2) != product(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_56,plain,
d(a1,a2,a3),
inference(split_conjunct,[status(thm)],[sos10]) ).
cnf(c_0_57,plain,
product(product(difference(X1,X2),X2),X2) = product(X2,product(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_51]),c_0_51]) ).
cnf(c_0_58,plain,
product(difference(b1,b3),b3) = product(b3,b2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_52]),c_0_51]) ).
cnf(c_0_59,plain,
product(difference(c1,c3),c3) = product(c3,c2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_53]),c_0_51]) ).
cnf(c_0_60,negated_conjecture,
product(product(product(a2,b1),product(c3,a2)),product(product(a3,b2),product(c1,a3))) != product(product(product(a1,b3),product(c2,a1)),product(product(a2,b1),product(c3,a2))),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
product(a2,a3) = product(a1,a2),
inference(spm,[status(thm)],[c_0_23,c_0_56]) ).
cnf(c_0_62,plain,
product(b3,product(b3,b1)) = product(b3,product(b1,b2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_27]),c_0_32]) ).
cnf(c_0_63,plain,
product(c3,product(c3,c1)) = product(c3,product(c1,c2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_59]),c_0_27]),c_0_33]) ).
cnf(c_0_64,negated_conjecture,
product(product(product(a1,a2),product(b3,b1)),product(product(c2,a1),product(c3,a2))) != product(product(product(a1,a2),product(b1,b2)),product(product(c3,a2),product(c1,a3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_14]),c_0_14]),c_0_61]),c_0_14]),c_0_14]) ).
cnf(c_0_65,plain,
product(b3,b1) = product(b1,b2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_62]),c_0_29]) ).
cnf(c_0_66,plain,
product(product(X1,a2),product(X2,a3)) = product(product(X1,X2),product(a1,a2)),
inference(spm,[status(thm)],[c_0_14,c_0_61]) ).
cnf(c_0_67,plain,
product(c3,c1) = product(c1,c2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_63]),c_0_29]) ).
cnf(c_0_68,negated_conjecture,
product(product(product(a1,a2),product(b1,b2)),product(product(c3,a2),product(c1,a3))) != product(product(product(a1,a2),product(b1,b2)),product(product(c2,a1),product(c3,a2))),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,plain,
product(product(c3,a2),product(c1,a3)) = product(product(c1,a2),product(c2,a3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_66]) ).
cnf(c_0_70,negated_conjecture,
product(product(product(a1,a2),product(b1,b2)),product(product(c2,a1),product(c3,a2))) != product(product(product(a1,a2),product(b1,b2)),product(product(c1,a2),product(c2,a3))),
inference(rw,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_71,plain,
product(product(c2,X1),product(c3,X2)) = product(product(c1,c2),product(X1,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_33]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_71]),c_0_66])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP780+1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n018.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 19:05:02 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 2.41/2.12 % Version : CSE_E---1.7
% 2.41/2.12 % Problem : theBenchmark.p
% 2.41/2.12 % SZS status Theorem for theBenchmark.p
% 2.41/2.12 % SZS output start CNFRefutation
% See solution above
% 2.41/2.13 % Total time : 1.371s
%------------------------------------------------------------------------------