%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP775+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 : Sun Sep 27 07:31:25 AM UTC 2026
% Result : Theorem 4.78s 1.02s
% Output : CNFRefutation 4.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 6
% Syntax : Number of formulae : 79 ( 35 unt; 0 def)
% Number of atoms : 167 ( 80 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 150 ( 62 ~; 66 |; 17 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos01,axiom,
! [C,B,A] : product(product(A,B),C) = product(A,product(B,C)),
file('theBenchmark.p',sos01) ).
fof(sos02,axiom,
! [A] : product(A,A) = A,
file('theBenchmark.p',sos02) ).
fof(sos03,axiom,
! [X0,X1] :
( l(X0,X1)
<=> ( product(X1,X0) = X1
& product(X0,X1) = X0 ) ),
file('theBenchmark.p',sos03) ).
fof(sos04,axiom,
! [X2,X3] :
( r(X2,X3)
<=> ( product(X3,X2) = X2
& product(X2,X3) = X3 ) ),
file('theBenchmark.p',sos04) ).
fof(sos05,axiom,
! [X4,X5] :
( d(X4,X5)
<=> ? [X6] :
( l(X6,X5)
& r(X4,X6) ) ),
file('theBenchmark.p',sos05) ).
fof(goals,conjecture,
! [X7,X8] :
( d(X7,X8)
<=> ( product(X8,product(X7,X8)) = X8
& product(X7,product(X8,X7)) = X7 ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X7,X8] :
( d(X7,X8)
<=> ( product(X8,product(X7,X8)) = X8
& product(X7,product(X8,X7)) = X7 ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_7,plain,
( product(B,A) != B
| product(A,B) != A
| l(A,B) ),
inference(clausify,[status(thm)],[sos03]) ).
cnf(c_8,plain,
( product(B,A) = B
| ~ l(A,B) ),
inference(clausify,[status(thm)],[sos03]) ).
cnf(c_9,plain,
( product(A,B) = A
| ~ l(A,B) ),
inference(clausify,[status(thm)],[sos03]) ).
fof(nnf_5,plain,
! [X4,X5] :
( ( ! [X6] :
( ~ l(X6,X5)
| ~ r(X4,X6) )
| d(X4,X5) )
& ( ? [X9] :
( l(X9,X5)
& r(X4,X9) )
| ~ d(X4,X5) ) ),
inference(fof_nnf,[status(thm)],[sos05]) ).
fof(sk_sos05_sk,plain,
! [X4,X5] :
( ( ! [X6] :
( ~ l(X6,X5)
| ~ r(X4,X6) )
| d(X4,X5) )
& ( ( l(sK0(X4,X5),X5)
& r(X4,sK0(X4,X5)) )
| ~ d(X4,X5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X9,sK0(X4,X5))],[nnf_5]) ).
fof(sk_sos05,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ l(VAR_2,VAR_1)
| ~ r(VAR_0,VAR_2)
| d(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( l(sK0(VAR_0,VAR_1),VAR_1)
| ~ d(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( r(VAR_0,sK0(VAR_0,VAR_1))
| ~ d(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_sos05_sk]) ).
cnf(c_10,plain,
( l(sK0(A,B),B)
| ~ d(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos05]) ).
cnf(c_11,plain,
( ~ l(C,B)
| ~ r(A,C)
| d(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos05]) ).
cnf(c_12,plain,
( product(B,C) != B
| product(C,B) != C
| ~ r(A,C)
| d(A,B) ),
inference(resolve,[status(thm)],[c_11,c_7]) ).
cnf(c_14,plain,
( product(sK0(A,B),B) = sK0(A,B)
| ~ d(A,B) ),
inference(resolve,[status(thm)],[c_10,c_9]) ).
cnf(c_15,plain,
( product(B,sK0(A,B)) = B
| ~ d(A,B) ),
inference(resolve,[status(thm)],[c_10,c_8]) ).
fof(nnf_6,plain,
? [X7,X8] :
( ( product(X8,product(X7,X8)) != X8
| product(X7,product(X8,X7)) != X7
| ~ d(X7,X8) )
& ( ( product(X8,product(X7,X8)) = X8
& product(X7,product(X8,X7)) = X7 )
| d(X7,X8) ) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ( product(sK2,product(sK1,sK2)) != sK2
| product(sK1,product(sK2,sK1)) != sK1
| ~ d(sK1,sK2) )
& ( ( product(sK2,product(sK1,sK2)) = sK2
& product(sK1,product(sK2,sK1)) = sK1 )
| d(sK1,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X7,sK1),skolemize(X8,sK2)],[nnf_6]) ).
fof(sk_goals_neg,plain,
( ( product(sK2,product(sK1,sK2)) != sK2
| product(sK1,product(sK2,sK1)) != sK1
| ~ d(sK1,sK2) )
& ( product(sK2,product(sK1,sK2)) = sK2
| d(sK1,sK2) )
& ( product(sK1,product(sK2,sK1)) = sK1
| d(sK1,sK2) ) ),
inference(cnf_transformation,[status(thm)],[sk_goals_neg_sk]) ).
cnf(c_16,negated_conjecture,
( product(sK2,product(sK1,sK2)) != sK2
| product(sK1,product(sK2,sK1)) != sK1
| ~ d(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_17,negated_conjecture,
( product(sK2,product(sK1,sK2)) = sK2
| d(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_18,negated_conjecture,
( product(sK1,product(sK2,sK1)) = sK1
| d(sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_19,plain,
( r(A,sK0(A,B))
| ~ d(A,B) ),
inference(split_conjunct,[status(thm)],[sk_sos05]) ).
cnf(c_20,plain,
( product(B,A) != A
| product(A,B) != B
| r(A,B) ),
inference(clausify,[status(thm)],[sos04]) ).
cnf(c_21,plain,
( product(B,A) = A
| ~ r(A,B) ),
inference(clausify,[status(thm)],[sos04]) ).
cnf(c_22,plain,
( product(A,B) = B
| ~ r(A,B) ),
inference(clausify,[status(thm)],[sos04]) ).
cnf(c_23,plain,
product(A,A) = A,
inference(clausify,[status(thm)],[sos02]) ).
cnf(c_24,plain,
product(product(A,B),C) = product(A,product(B,C)),
inference(clausify,[status(thm)],[sos01]) ).
cnf(c_1572,negated_conjecture,
( product(product(sK1,sK2),sK2) != product(sK1,sK2)
| ~ r(A,product(sK1,sK2))
| d(A,sK2)
| d(sK1,sK2) ),
inference(resolve,[status(thm)],[c_17,c_12]) ).
cnf(c_1573,negated_conjecture,
( product(sK1,product(sK2,sK2)) != product(sK1,sK2)
| ~ r(A,product(sK1,sK2))
| d(A,sK2)
| d(sK1,sK2) ),
inference(paramod,[status(thm)],[c_24,c_1572]) ).
cnf(c_1574,negated_conjecture,
( product(sK1,sK2) != product(sK1,sK2)
| ~ r(A,product(sK1,sK2))
| d(A,sK2)
| d(sK1,sK2) ),
inference(paramod,[status(thm)],[c_23,c_1573]) ).
cnf(c_30,negated_conjecture,
( ~ r(A,product(sK1,sK2))
| d(A,sK2)
| d(sK1,sK2) ),
inference(copy,[status(thm)],[c_1574]) ).
cnf(c_32,plain,
( ~ r(sK1,product(sK1,sK2))
| d(sK1,sK2) ),
inference(factor,[status(thm)],[c_30]) ).
cnf(c_48,plain,
product(A,product(B,product(A,B))) = product(A,B),
inference(paramod,[status(thm)],[c_24,c_23]) ).
cnf(c_1575,plain,
product(A,B) = product(A,product(A,B)),
inference(paramod,[status(thm)],[c_23,c_24]) ).
cnf(c_49,plain,
product(A,product(A,B)) = product(A,B),
inference(copy,[status(thm)],[c_1575]) ).
cnf(c_1576,plain,
( product(product(A,B),A) != A
| r(product(A,B),A) ),
inference(resolve,[status(thm)],[c_49,c_20]) ).
cnf(c_315,plain,
( product(A,product(B,A)) != A
| r(product(A,B),A) ),
inference(paramod,[status(thm)],[c_24,c_1576]) ).
cnf(c_1577,plain,
( product(product(A,B),product(A,B)) != product(A,B)
| r(product(product(A,B),A),product(A,B)) ),
inference(paramod,[status(thm)],[c_49,c_315]) ).
cnf(c_1578,plain,
( product(product(A,B),product(A,B)) != product(A,B)
| r(product(A,product(B,A)),product(A,B)) ),
inference(paramod,[status(thm)],[c_24,c_1577]) ).
cnf(c_1579,plain,
( product(A,B) != product(A,B)
| r(product(A,product(B,A)),product(A,B)) ),
inference(paramod,[status(thm)],[c_23,c_1578]) ).
cnf(c_858,plain,
r(product(A,product(B,A)),product(A,B)),
inference(copy,[status(thm)],[c_1579]) ).
cnf(c_1119,plain,
( r(sK1,product(sK1,sK2))
| d(sK1,sK2) ),
inference(paramod,[status(thm)],[c_18,c_858]) ).
cnf(c_1580,plain,
( d(sK1,sK2)
| d(sK1,sK2) ),
inference(resolve,[status(thm)],[c_1119,c_32]) ).
cnf(c_1224,plain,
d(sK1,sK2),
inference(copy,[status(thm)],[c_1580]) ).
cnf(c_1227,negated_conjecture,
( product(sK2,product(sK1,sK2)) != sK2
| product(sK1,product(sK2,sK1)) != sK1 ),
inference(resolve,[status(thm)],[c_1224,c_16]) ).
cnf(c_1229,plain,
r(sK1,sK0(sK1,sK2)),
inference(resolve,[status(thm)],[c_1224,c_19]) ).
cnf(c_1230,plain,
product(sK2,sK0(sK1,sK2)) = sK2,
inference(resolve,[status(thm)],[c_1224,c_15]) ).
cnf(c_1231,plain,
product(sK0(sK1,sK2),sK2) = sK0(sK1,sK2),
inference(resolve,[status(thm)],[c_1224,c_14]) ).
cnf(c_1293,plain,
product(sK1,sK0(sK1,sK2)) = sK0(sK1,sK2),
inference(resolve,[status(thm)],[c_1229,c_22]) ).
cnf(c_1294,plain,
product(sK0(sK1,sK2),sK1) = sK1,
inference(resolve,[status(thm)],[c_1229,c_21]) ).
cnf(c_1581,plain,
product(sK2,A) = product(sK2,product(sK0(sK1,sK2),A)),
inference(paramod,[status(thm)],[c_1230,c_24]) ).
cnf(c_1313,plain,
product(sK2,product(sK0(sK1,sK2),A)) = product(sK2,A),
inference(copy,[status(thm)],[c_1581]) ).
cnf(c_1582,plain,
product(sK1,A) = product(sK0(sK1,sK2),product(sK1,A)),
inference(paramod,[status(thm)],[c_1294,c_24]) ).
cnf(c_1323,plain,
product(sK0(sK1,sK2),product(sK1,A)) = product(sK1,A),
inference(copy,[status(thm)],[c_1582]) ).
cnf(c_1583,plain,
product(sK0(sK1,sK2),A) = product(sK0(sK1,sK2),product(sK2,A)),
inference(paramod,[status(thm)],[c_1231,c_24]) ).
cnf(c_1338,plain,
product(sK0(sK1,sK2),product(sK2,A)) = product(sK0(sK1,sK2),A),
inference(copy,[status(thm)],[c_1583]) ).
cnf(c_1584,plain,
product(sK2,product(sK0(sK1,sK2),A)) = product(sK2,product(A,product(sK0(sK1,sK2),A))),
inference(paramod,[status(thm)],[c_48,c_1313]) ).
cnf(c_1585,plain,
product(sK2,A) = product(sK2,product(A,product(sK0(sK1,sK2),A))),
inference(paramod,[status(thm)],[c_1313,c_1584]) ).
cnf(c_1448,plain,
product(sK2,product(A,product(sK0(sK1,sK2),A))) = product(sK2,A),
inference(copy,[status(thm)],[c_1585]) ).
cnf(c_1586,plain,
( product(product(sK2,A),product(sK0(sK1,sK2),A)) != product(sK2,A)
| r(product(product(sK2,A),sK0(sK1,sK2)),product(sK2,A)) ),
inference(paramod,[status(thm)],[c_1338,c_315]) ).
cnf(c_1587,plain,
( product(product(sK2,A),product(sK0(sK1,sK2),A)) != product(sK2,A)
| r(product(sK2,product(A,sK0(sK1,sK2))),product(sK2,A)) ),
inference(paramod,[status(thm)],[c_24,c_1586]) ).
cnf(c_1588,plain,
( product(sK2,product(A,product(sK0(sK1,sK2),A))) != product(sK2,A)
| r(product(sK2,product(A,sK0(sK1,sK2))),product(sK2,A)) ),
inference(paramod,[status(thm)],[c_24,c_1587]) ).
cnf(c_1589,plain,
( product(sK2,A) != product(sK2,A)
| r(product(sK2,product(A,sK0(sK1,sK2))),product(sK2,A)) ),
inference(paramod,[status(thm)],[c_1448,c_1588]) ).
cnf(c_1468,plain,
r(product(sK2,product(A,sK0(sK1,sK2))),product(sK2,A)),
inference(copy,[status(thm)],[c_1589]) ).
cnf(c_1590,plain,
r(product(sK2,sK0(sK1,sK2)),product(sK2,sK1)),
inference(paramod,[status(thm)],[c_1293,c_1468]) ).
cnf(c_1490,plain,
r(sK2,product(sK2,sK1)),
inference(paramod,[status(thm)],[c_1230,c_1590]) ).
cnf(c_1591,plain,
product(product(sK2,sK1),sK2) = sK2,
inference(resolve,[status(thm)],[c_1490,c_21]) ).
cnf(c_1492,plain,
product(sK2,product(sK1,sK2)) = sK2,
inference(paramod,[status(thm)],[c_24,c_1591]) ).
cnf(c_1592,negated_conjecture,
( sK2 != sK2
| product(sK1,product(sK2,sK1)) != sK1 ),
inference(paramod,[status(thm)],[c_1492,c_1227]) ).
cnf(c_1494,negated_conjecture,
product(sK1,product(sK2,sK1)) != sK1,
inference(copy,[status(thm)],[c_1592]) ).
cnf(c_1593,plain,
product(sK0(sK1,sK2),sK2) = product(sK0(sK1,sK2),product(sK1,sK2)),
inference(paramod,[status(thm)],[c_1492,c_1338]) ).
cnf(c_1594,plain,
sK0(sK1,sK2) = product(sK0(sK1,sK2),product(sK1,sK2)),
inference(paramod,[status(thm)],[c_1231,c_1593]) ).
cnf(c_1517,plain,
sK0(sK1,sK2) = product(sK1,sK2),
inference(paramod,[status(thm)],[c_1323,c_1594]) ).
cnf(c_1595,plain,
product(product(sK1,sK2),sK1) = sK1,
inference(paramod,[status(thm)],[c_1517,c_1294]) ).
cnf(c_1596,plain,
product(sK1,product(sK2,sK1)) = sK1,
inference(paramod,[status(thm)],[c_24,c_1595]) ).
cnf(c_1571,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1494,c_1596]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP775+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 15:41:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2674643 was started by sandbox2 on n017,
% 0.10/0.37 % Fri Sep 25 15:41:33 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 4.78/1.02
% 4.78/1.02 % SZS status Theorem for theBenchmark
% 4.78/1.02
% 4.78/1.02 % Proof 1 at 0.44 (+ 0.16) seconds.
% 4.78/1.02 % Length of proof is 47.
% 4.78/1.02 % Level of proof is 14.
% 4.78/1.02 % Maximum clause weight is 27.000.
% 4.78/1.02 % Given clauses 351.
% 4.78/1.02
% 4.78/1.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------