%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP774+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 : n024.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 04:27:15 PM UTC 2026
% Result : Theorem 42.71s 29.05s
% Output : CNFRefutation 42.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 54 ( 36 unt; 0 def)
% Number of atoms : 86 ( 52 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 58 ( 26 ~; 22 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos02,axiom,
! [X3] : product(X3,X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
fof(sos01,axiom,
! [X1,X2,X3] : product(product(X3,X2),X1) = product(X3,product(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
fof(goals,conjecture,
! [X6,X7,X8,X9] :
( ( d(X6,X7)
& d(X8,X9) )
=> d(product(X6,X8),product(X7,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(sos03,axiom,
! [X4,X5] :
( d(X4,X5)
<=> ( product(X4,product(X5,X4)) = X4
& product(X5,product(X4,X5)) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
fof(c_0_4,plain,
! [X23] : product(X23,X23) = X23,
inference(variable_rename,[status(thm)],[sos02]) ).
fof(c_0_5,plain,
! [X20,X21,X22] : product(product(X22,X21),X20) = product(X22,product(X21,X20)),
inference(variable_rename,[status(thm)],[sos01]) ).
fof(c_0_6,negated_conjecture,
~ ! [X6,X7,X8,X9] :
( ( d(X6,X7)
& d(X8,X9) )
=> d(product(X6,X8),product(X7,X9)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_7,plain,
! [X24,X25] :
( ( product(X24,product(X25,X24)) = X24
| ~ d(X24,X25) )
& ( product(X25,product(X24,X25)) = X25
| ~ d(X24,X25) )
& ( product(X24,product(X25,X24)) != X24
| product(X25,product(X24,X25)) != X25
| d(X24,X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos03])])]) ).
cnf(c_0_8,plain,
product(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
product(product(X1,X2),X3) = product(X1,product(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_10,negated_conjecture,
( d(esk1_0,esk2_0)
& d(esk3_0,esk4_0)
& ~ d(product(esk1_0,esk3_0),product(esk2_0,esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_11,plain,
( d(X1,X2)
| product(X1,product(X2,X1)) != X1
| product(X2,product(X1,X2)) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
product(X1,product(X2,product(X1,X2))) = product(X1,X2),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( product(X1,product(X2,X1)) = X1
| ~ d(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
d(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( d(product(X1,X2),X3)
| product(X1,product(X2,product(X3,product(X1,X2)))) != product(X1,X2)
| product(X3,product(X1,product(X2,X3))) != X3 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_9]),c_0_9]) ).
cnf(c_0_16,plain,
product(X1,product(X1,X2)) = product(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_17,plain,
product(X1,product(X2,product(X1,product(X2,X3)))) = product(X1,product(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_12]),c_0_9]),c_0_9]),c_0_9]) ).
cnf(c_0_18,negated_conjecture,
product(esk2_0,product(esk1_0,esk2_0)) = esk2_0,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
product(X1,product(X2,product(X3,product(X1,product(X2,X3))))) = product(X1,product(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_12]),c_0_9]),c_0_9]) ).
cnf(c_0_20,negated_conjecture,
d(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,plain,
( product(X1,product(X2,X1)) = X1
| ~ d(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,plain,
( d(product(X1,X2),X2)
| product(X2,product(X1,X2)) != X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_8]),c_0_16]),c_0_12])]) ).
cnf(c_0_23,plain,
( d(product(X1,X2),product(X3,product(X2,X3)))
| product(X3,product(X2,product(X3,product(X1,product(X2,X3))))) != product(X3,product(X2,X3))
| product(X1,product(X2,product(X3,product(X1,X2)))) != product(X1,X2) ),
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_15,c_0_12]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_17]) ).
cnf(c_0_24,negated_conjecture,
product(esk2_0,product(esk1_0,product(esk2_0,X1))) = product(esk2_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_18]),c_0_9]) ).
cnf(c_0_25,plain,
product(X1,product(X2,product(X3,product(X1,product(X2,product(X3,X4)))))) = product(X1,product(X2,product(X3,X4))),
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_9,c_0_19]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_9]) ).
cnf(c_0_26,negated_conjecture,
product(esk4_0,product(esk3_0,esk4_0)) = esk4_0,
inference(spm,[status(thm)],[c_0_13,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
product(esk1_0,product(esk2_0,esk1_0)) = esk1_0,
inference(spm,[status(thm)],[c_0_21,c_0_14]) ).
cnf(c_0_28,plain,
( d(product(X1,product(X2,X3)),X3)
| product(X3,product(X1,product(X2,X3))) != X3 ),
inference(spm,[status(thm)],[c_0_22,c_0_9]) ).
cnf(c_0_29,negated_conjecture,
( d(product(esk2_0,X1),product(X2,product(esk1_0,product(esk2_0,product(X1,X2)))))
| product(esk2_0,product(X1,product(X2,product(esk2_0,X1)))) != product(esk2_0,X1) ),
inference(cn,[status(thm)],[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(rw,[status(thm)],[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_23,c_0_24]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_24]),c_0_9]),c_0_9]),c_0_19]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_24])]) ).
cnf(c_0_30,negated_conjecture,
product(X1,product(esk4_0,product(esk3_0,product(X1,esk4_0)))) = product(X1,esk4_0),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
product(esk1_0,product(esk2_0,product(esk1_0,X1))) = product(esk1_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_27]),c_0_9]) ).
cnf(c_0_32,negated_conjecture,
product(esk3_0,product(esk4_0,esk3_0)) = esk3_0,
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_33,plain,
( d(product(X1,product(X2,product(X3,X4))),X4)
| product(X4,product(X1,product(X2,product(X3,X4)))) != X4 ),
inference(spm,[status(thm)],[c_0_28,c_0_9]) ).
cnf(c_0_34,negated_conjecture,
d(product(esk2_0,esk4_0),product(esk3_0,product(esk1_0,product(esk2_0,product(esk4_0,esk3_0))))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( d(product(esk1_0,X1),product(X2,product(esk2_0,product(esk1_0,product(X1,X2)))))
| product(esk1_0,product(X1,product(X2,product(esk1_0,X1)))) != product(esk1_0,X1) ),
inference(cn,[status(thm)],[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(rw,[status(thm)],[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_23,c_0_31]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_31]),c_0_9]),c_0_9]),c_0_19]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_31])]) ).
cnf(c_0_36,negated_conjecture,
product(X1,product(esk3_0,product(esk4_0,product(X1,esk3_0)))) = product(X1,esk3_0),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_37,plain,
( d(product(X1,product(X2,product(X3,product(X4,X5)))),product(X4,product(X3,product(X4,X5))))
| product(X4,product(X3,product(X4,product(X5,product(X1,product(X2,product(X3,product(X4,X5)))))))) != product(X4,product(X3,product(X4,X5))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_17]),c_0_9]),c_0_9]),c_0_9]) ).
cnf(c_0_38,negated_conjecture,
product(esk2_0,product(esk4_0,product(esk3_0,product(esk1_0,product(esk2_0,esk4_0))))) = product(esk2_0,esk4_0),
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_21,c_0_34]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_30]),c_0_9]) ).
cnf(c_0_39,negated_conjecture,
d(product(esk1_0,esk3_0),product(esk4_0,product(esk2_0,product(esk1_0,product(esk3_0,esk4_0))))),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
product(X1,product(X2,product(X3,product(X4,product(X1,product(X2,product(X3,X4))))))) = product(X1,product(X2,product(X3,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_19]),c_0_9]),c_0_9]) ).
cnf(c_0_41,negated_conjecture,
d(product(esk2_0,esk4_0),product(esk1_0,product(esk3_0,product(esk1_0,product(esk2_0,esk4_0))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_9]),c_0_12])]) ).
cnf(c_0_42,negated_conjecture,
product(esk1_0,product(esk3_0,product(esk4_0,product(esk2_0,product(esk1_0,esk3_0))))) = product(esk1_0,esk3_0),
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_21,c_0_39]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_36]),c_0_9]) ).
cnf(c_0_43,plain,
( d(X1,product(X2,X3))
| product(X2,product(X3,product(X1,product(X2,X3)))) != product(X2,X3)
| product(X1,product(X2,product(X3,X1))) != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_9]),c_0_9]) ).
cnf(c_0_44,plain,
product(X1,product(X2,product(X3,product(X4,product(X1,product(X2,product(X3,product(X4,X5)))))))) = product(X1,product(X2,product(X3,product(X4,X5)))),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_40]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_9]) ).
cnf(c_0_45,negated_conjecture,
product(esk2_0,product(esk4_0,product(esk1_0,product(esk3_0,product(esk1_0,product(esk2_0,esk4_0)))))) = product(esk2_0,esk4_0),
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_21,c_0_41]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_12]),c_0_9]) ).
cnf(c_0_46,negated_conjecture,
d(product(esk1_0,esk3_0),product(esk2_0,product(esk4_0,product(esk2_0,product(esk1_0,esk3_0))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_42]),c_0_9]),c_0_12])]) ).
cnf(c_0_47,plain,
( d(product(X1,product(X2,product(X3,product(X1,X2)))),product(X4,X3))
| product(X1,product(X2,product(X3,product(X1,product(X2,product(X4,product(X3,product(X1,X2)))))))) != product(X1,product(X2,product(X3,product(X1,X2))))
| product(X4,product(X3,product(X1,product(X2,product(X4,X3))))) != product(X4,X3) ),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_19]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_25]) ).
cnf(c_0_48,negated_conjecture,
product(esk2_0,product(esk4_0,product(esk1_0,product(esk3_0,product(esk2_0,esk4_0))))) = product(esk2_0,esk4_0),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,negated_conjecture,
~ d(product(esk1_0,esk3_0),product(esk2_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_50,negated_conjecture,
product(esk1_0,product(esk3_0,product(esk2_0,product(esk4_0,product(esk2_0,product(esk1_0,esk3_0)))))) = product(esk1_0,esk3_0),
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_21,c_0_46]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_12]),c_0_9]) ).
cnf(c_0_51,negated_conjecture,
product(esk1_0,product(esk3_0,product(esk4_0,product(esk1_0,product(esk3_0,product(esk2_0,product(esk4_0,product(esk1_0,esk3_0)))))))) != product(esk1_0,esk3_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_36]),c_0_36]),c_0_49]) ).
cnf(c_0_52,negated_conjecture,
product(esk1_0,product(esk3_0,product(esk2_0,product(esk4_0,product(esk1_0,esk3_0))))) = product(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_44,c_0_50]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP774+1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 14:05:26 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 42.71/29.05 % Version : CSE_E---1.7
% 42.71/29.05 % Problem : theBenchmark.p
% 42.71/29.05 % SZS status Theorem for theBenchmark.p
% 42.71/29.05 % SZS output start CNFRefutation
% See solution above
% 42.99/29.30 % Total time : 19.378s
%------------------------------------------------------------------------------