%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP767-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 : Sat Jun 21 05:08:38 AM UTC 2025
% Result : Unsatisfiable 101.93s 102.14s
% Output : Proof 102.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 97
% Syntax : Number of formulae : 349 ( 268 unt; 0 typ; 0 def)
% Number of atoms : 460 ( 444 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 150 ( 54 ~; 50 |; 0 &)
% ( 46 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 365 ( 335 !; 0 ?; 365 :)
% Comments :
%------------------------------------------------------------------------------
tff(j_type,type,
j: $i > $i ).
tff(x1_type,type,
x1: $i ).
tff(product_type,type,
product: ( $i * $i ) > $i ).
tff(x0_type,type,
x0: $i ).
tff(quotient_type,type,
quotient: ( $i * $i ) > $i ).
tff(one_type,type,
one: $i ).
tff(difference_type,type,
difference: ( $i * $i ) > $i ).
tff(t_type,type,
t: ( $i * $i ) > $i ).
tff(eta_type,type,
eta: $i > $i ).
tff(i_type,type,
i: $i > $i ).
tff(1,plain,
^ [A: $i] :
refl(( ( j(A) = quotient(one,A) )
<=> ( j(A) = quotient(one,A) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: $i] : ( j(A) = quotient(one,A) )
<=> ! [A: $i] : ( j(A) = quotient(one,A) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( j(A) = quotient(one,A) )
<=> ! [A: $i] : ( j(A) = quotient(one,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [A: $i] : ( j(A) = quotient(one,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
tff(5,plain,
! [A: $i] : ( j(A) = quotient(one,A) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( j(A) = quotient(one,A) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( j(A) = quotient(one,A) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
| ( j(x1) = quotient(one,x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
j(x1) = quotient(one,x1),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
quotient(one,x1) = j(x1),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i] :
refl(( ( difference(A,product(A,B)) = B )
<=> ( difference(A,product(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
<=> ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
<=> ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
tff(15,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(x0,j(x0)),product(product(x0,j(x0)),quotient(one,x1))) = quotient(one,x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
difference(product(x0,j(x0)),product(product(x0,j(x0)),quotient(one,x1))) = quotient(one,x1),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
^ [B: $i,A: $i] :
refl(( ( product(quotient(A,B),B) = A )
<=> ( product(quotient(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
tff(24,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))),quotient(one,x1)),quotient(one,x1)) = product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
product(quotient(product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))),quotient(one,x1)),quotient(one,x1)) = product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
^ [B: $i,A: $i] :
refl(( ( product(A,difference(A,B)) = B )
<=> ( product(A,difference(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
<=> ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
<=> ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
tff(33,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(x0,difference(x0,product(product(x0,j(product(x1,x0))),x1))) = product(product(x0,j(product(x1,x0))),x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
product(x0,difference(x0,product(product(x0,j(product(x1,x0))),x1))) = product(product(x0,j(product(x1,x0))),x1),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
| ( j(x0) = quotient(one,x0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
j(x0) = quotient(one,x0),
inference(unit_resolution,[status(thm)],[38,7]) ).
tff(40,plain,
quotient(one,x0) = j(x0),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(one,product(x1,x0)),product(x1,x0)) = one ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
product(quotient(one,product(x1,x0)),product(x1,x0)) = one,
inference(unit_resolution,[status(thm)],[41,26]) ).
tff(43,plain,
( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
| ( j(product(x1,x0)) = quotient(one,product(x1,x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
j(product(x1,x0)) = quotient(one,product(x1,x0)),
inference(unit_resolution,[status(thm)],[43,7]) ).
tff(45,plain,
product(j(product(x1,x0)),product(x1,x0)) = product(quotient(one,product(x1,x0)),product(x1,x0)),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
product(j(product(x1,x0)),product(x1,x0)) = one,
inference(transitivity,[status(thm)],[45,42]) ).
tff(47,plain,
quotient(product(j(product(x1,x0)),product(x1,x0)),x0) = quotient(one,x0),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
<=> ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) )),
inference(bind,[status(th)],[]) ).
tff(49,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
tff(52,plain,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,j(product(x1,x0))),x1)) = quotient(product(j(product(x1,x0)),product(x1,x0)),x0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
difference(x0,product(product(x0,j(product(x1,x0))),x1)) = quotient(product(j(product(x1,x0)),product(x1,x0)),x0),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
difference(x0,product(product(x0,j(product(x1,x0))),x1)) = j(x0),
inference(transitivity,[status(thm)],[56,47,40]) ).
tff(58,plain,
product(x0,difference(x0,product(product(x0,j(product(x1,x0))),x1))) = product(x0,j(x0)),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
product(x0,j(x0)) = product(x0,difference(x0,product(product(x0,j(product(x1,x0))),x1))),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
^ [A: $i] :
refl(( ( product(i(A),A) = product(A,j(A)) )
<=> ( product(i(A),A) = product(A,j(A)) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
<=> ! [A: $i] : ( product(i(A),A) = product(A,j(A)) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
<=> ! [A: $i] : ( product(i(A),A) = product(A,j(A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).
tff(64,plain,
! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( ~ ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
| ( product(i(x0),x0) = product(x0,j(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
product(i(x0),x0) = product(x0,j(x0)),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(quotient(one,x0),product(quotient(one,x0),x0)) = x0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
difference(quotient(one,x0),product(quotient(one,x0),x0)) = x0,
inference(unit_resolution,[status(thm)],[69,17]) ).
tff(71,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(one,x0),x0) = one ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
product(quotient(one,x0),x0) = one,
inference(unit_resolution,[status(thm)],[71,26]) ).
tff(73,plain,
one = product(quotient(one,x0),x0),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
difference(quotient(one,x0),one) = difference(quotient(one,x0),product(quotient(one,x0),x0)),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
^ [A: $i] :
refl(( ( i(A) = difference(A,one) )
<=> ( i(A) = difference(A,one) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [A: $i] : ( i(A) = difference(A,one) )
<=> ! [A: $i] : ( i(A) = difference(A,one) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [A: $i] : ( i(A) = difference(A,one) )
<=> ! [A: $i] : ( i(A) = difference(A,one) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
! [A: $i] : ( i(A) = difference(A,one) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
tff(79,plain,
! [A: $i] : ( i(A) = difference(A,one) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [A: $i] : ( i(A) = difference(A,one) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [A: $i] : ( i(A) = difference(A,one) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
( ~ ! [A: $i] : ( i(A) = difference(A,one) )
| ( i(quotient(one,x0)) = difference(quotient(one,x0),one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
i(quotient(one,x0)) = difference(quotient(one,x0),one),
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
i(quotient(one,x0)) = x0,
inference(transitivity,[status(thm)],[83,74,70]) ).
tff(85,plain,
i(i(quotient(one,x0))) = i(x0),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
product(i(i(quotient(one,x0))),x0) = product(i(x0),x0),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
^ [B: $i,A: $i] :
refl(( ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
<=> ( product(i(i(A)),B) = product(eta(A),product(A,B)) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
<=> ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
<=> ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos13) ).
tff(91,plain,
! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
( ~ ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
| ( product(i(i(quotient(one,x0))),x0) = product(eta(quotient(one,x0)),product(quotient(one,x0),x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
product(i(i(quotient(one,x0))),x0) = product(eta(quotient(one,x0)),product(quotient(one,x0),x0)),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
product(eta(quotient(one,x0)),product(quotient(one,x0),x0)) = product(i(i(quotient(one,x0))),x0),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
^ [A: $i] :
refl(( ( eta(A) = product(i(A),A) )
<=> ( eta(A) = product(i(A),A) ) )),
inference(bind,[status(th)],[]) ).
tff(98,plain,
( ! [A: $i] : ( eta(A) = product(i(A),A) )
<=> ! [A: $i] : ( eta(A) = product(i(A),A) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [A: $i] : ( eta(A) = product(i(A),A) )
<=> ! [A: $i] : ( eta(A) = product(i(A),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,axiom,
! [A: $i] : ( eta(A) = product(i(A),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).
tff(101,plain,
! [A: $i] : ( eta(A) = product(i(A),A) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
! [A: $i] : ( eta(A) = product(i(A),A) ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [A: $i] : ( eta(A) = product(i(A),A) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
( ~ ! [A: $i] : ( eta(A) = product(i(A),A) )
| ( eta(quotient(one,x0)) = product(i(quotient(one,x0)),quotient(one,x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
eta(quotient(one,x0)) = product(i(quotient(one,x0)),quotient(one,x0)),
inference(unit_resolution,[status(thm)],[104,103]) ).
tff(106,plain,
product(i(quotient(one,x0)),quotient(one,x0)) = eta(quotient(one,x0)),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
i(j(x0)) = i(quotient(one,x0)),
inference(monotonicity,[status(thm)],[39]) ).
tff(108,plain,
i(quotient(one,x0)) = i(j(x0)),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
product(i(quotient(one,x0)),quotient(one,x0)) = product(i(j(x0)),j(x0)),
inference(monotonicity,[status(thm)],[108,40]) ).
tff(110,plain,
product(i(j(x0)),j(x0)) = product(i(quotient(one,x0)),quotient(one,x0)),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
i(j(x0)) = x0,
inference(transitivity,[status(thm)],[107,83,74,70]) ).
tff(112,plain,
product(i(j(x0)),j(x0)) = product(x0,j(x0)),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
product(x0,j(x0)) = product(i(j(x0)),j(x0)),
inference(symmetry,[status(thm)],[112]) ).
tff(114,plain,
product(x0,j(x0)) = eta(quotient(one,x0)),
inference(transitivity,[status(thm)],[113,110,106]) ).
tff(115,plain,
product(product(x0,j(x0)),product(quotient(one,x0),x0)) = product(eta(quotient(one,x0)),product(quotient(one,x0),x0)),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(one,x1),x1) = one ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
product(quotient(one,x1),x1) = one,
inference(unit_resolution,[status(thm)],[116,26]) ).
tff(118,plain,
product(quotient(one,x1),x1) = product(quotient(one,x0),x0),
inference(transitivity,[status(thm)],[117,73]) ).
tff(119,plain,
^ [B: $i,A: $i] :
refl(( ( quotient(product(A,B),B) = A )
<=> ( quotient(product(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(120,plain,
( ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
( ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,axiom,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
tff(123,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[124,120]) ).
tff(126,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(x0,j(x0)),product(x0,j(x0))),product(x0,j(x0))) = product(x0,j(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
quotient(product(product(x0,j(x0)),product(x0,j(x0))),product(x0,j(x0))) = product(x0,j(x0)),
inference(unit_resolution,[status(thm)],[126,125]) ).
tff(128,plain,
^ [B: $i,A: $i] :
refl(( ( t(A,B) = quotient(product(A,B),A) )
<=> ( t(A,B) = quotient(product(A,B),A) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) )
<=> ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
( ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) )
<=> ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(131,axiom,
! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos19) ).
tff(132,plain,
! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ),
inference(modus_ponens,[status(thm)],[133,129]) ).
tff(135,plain,
( ~ ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) )
| ( t(product(x0,j(x0)),product(x0,j(x0))) = quotient(product(product(x0,j(x0)),product(x0,j(x0))),product(x0,j(x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
t(product(x0,j(x0)),product(x0,j(x0))) = quotient(product(product(x0,j(x0)),product(x0,j(x0))),product(x0,j(x0))),
inference(unit_resolution,[status(thm)],[135,134]) ).
tff(137,plain,
( ~ ! [A: $i] : ( eta(A) = product(i(A),A) )
| ( eta(x0) = product(i(x0),x0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
eta(x0) = product(i(x0),x0),
inference(unit_resolution,[status(thm)],[137,103]) ).
tff(139,plain,
product(i(x0),x0) = eta(x0),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
product(x0,j(x0)) = product(i(x0),x0),
inference(symmetry,[status(thm)],[68]) ).
tff(141,plain,
product(x0,j(x0)) = eta(x0),
inference(transitivity,[status(thm)],[140,139]) ).
tff(142,plain,
t(product(x0,j(x0)),product(x0,j(x0))) = t(eta(x0),eta(x0)),
inference(monotonicity,[status(thm)],[141,141]) ).
tff(143,plain,
t(eta(x0),eta(x0)) = t(product(x0,j(x0)),product(x0,j(x0))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
t(eta(x0),eta(x0)) = t(eta(x0),product(i(x0),x0)),
inference(monotonicity,[status(thm)],[138]) ).
tff(145,plain,
t(eta(x0),product(i(x0),x0)) = t(eta(x0),eta(x0)),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( t(eta(A),product(B,C)) = product(t(eta(A),B),t(eta(A),C)) )
<=> ( t(eta(A),product(B,C)) = product(t(eta(A),B),t(eta(A),C)) ) )),
inference(bind,[status(th)],[]) ).
tff(147,plain,
( ! [B: $i,A: $i,C: $i] : ( t(eta(A),product(B,C)) = product(t(eta(A),B),t(eta(A),C)) )
<=> ! [B: $i,A: $i,C: $i] : ( t(eta(A),product(B,C)) = product(t(eta(A),B),t(eta(A),C)) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,plain,
( ! [B: $i,A: $i,C: $i] : ( t(eta(A),product(B,C)) = product(t(eta(A),B),t(eta(A),C)) )
<=> ! [B: $i,A: $i,C: $i] : ( t(eta(A),product(B,C)) = product(t(eta(A),B),t(eta(A),C)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(149,axiom,
! [B: $i,A: $i,C: $i] : ( t(eta(A),product(B,C)) = product(t(eta(A),B),t(eta(A),C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos20) ).
tff(150,plain,
! [B: $i,A: $i,C: $i] : ( t(eta(A),product(B,C)) = product(t(eta(A),B),t(eta(A),C)) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [B: $i,A: $i,C: $i] : ( t(eta(A),product(B,C)) = product(t(eta(A),B),t(eta(A),C)) ),
inference(skolemize,[status(sab)],[150]) ).
tff(152,plain,
! [B: $i,A: $i,C: $i] : ( t(eta(A),product(B,C)) = product(t(eta(A),B),t(eta(A),C)) ),
inference(modus_ponens,[status(thm)],[151,147]) ).
tff(153,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( t(eta(A),product(B,C)) = product(t(eta(A),B),t(eta(A),C)) )
| ( t(eta(x0),product(i(x0),x0)) = product(t(eta(x0),i(x0)),t(eta(x0),x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
t(eta(x0),product(i(x0),x0)) = product(t(eta(x0),i(x0)),t(eta(x0),x0)),
inference(unit_resolution,[status(thm)],[153,152]) ).
tff(155,plain,
product(t(eta(x0),i(x0)),t(eta(x0),x0)) = t(eta(x0),product(i(x0),x0)),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
product(t(eta(x0),i(x0)),t(eta(x0),x0)) = product(x0,j(x0)),
inference(transitivity,[status(thm)],[155,145,143,136,127]) ).
tff(157,plain,
product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),product(quotient(one,x1),x1)) = product(product(x0,j(x0)),product(quotient(one,x0),x0)),
inference(monotonicity,[status(thm)],[156,118]) ).
tff(158,plain,
product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),product(quotient(one,x1),x1)) = product(product(x0,j(product(x1,x0))),x1),
inference(transitivity,[status(thm)],[157,115,96,86,68,59,37]) ).
tff(159,plain,
quotient(product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),product(quotient(one,x1),x1)),x1) = quotient(product(product(x0,j(product(x1,x0))),x1),x1),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
quotient(product(product(x0,j(product(x1,x0))),x1),x1) = quotient(product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),product(quotient(one,x1),x1)),x1),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(x0,j(product(x1,x0))),x1),x1) = product(x0,j(product(x1,x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,plain,
quotient(product(product(x0,j(product(x1,x0))),x1),x1) = product(x0,j(product(x1,x0))),
inference(unit_resolution,[status(thm)],[161,125]) ).
tff(163,plain,
product(x0,j(product(x1,x0))) = quotient(product(product(x0,j(product(x1,x0))),x1),x1),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(j(j(x0)),product(j(j(x0)),quotient(one,x0))) = quotient(one,x0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
difference(j(j(x0)),product(j(j(x0)),quotient(one,x0))) = quotient(one,x0),
inference(unit_resolution,[status(thm)],[164,17]) ).
tff(166,plain,
quotient(one,quotient(one,x0)) = quotient(one,j(x0)),
inference(monotonicity,[status(thm)],[40]) ).
tff(167,plain,
quotient(one,j(x0)) = quotient(one,quotient(one,x0)),
inference(symmetry,[status(thm)],[166]) ).
tff(168,plain,
( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
| ( j(j(x0)) = quotient(one,j(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(169,plain,
j(j(x0)) = quotient(one,j(x0)),
inference(unit_resolution,[status(thm)],[168,7]) ).
tff(170,plain,
j(j(x0)) = quotient(one,quotient(one,x0)),
inference(transitivity,[status(thm)],[169,167]) ).
tff(171,plain,
product(j(j(x0)),quotient(one,x0)) = product(quotient(one,quotient(one,x0)),quotient(one,x0)),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
product(quotient(one,quotient(one,x0)),quotient(one,x0)) = product(j(j(x0)),quotient(one,x0)),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(one,quotient(one,x0)),quotient(one,x0)) = one ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
product(quotient(one,quotient(one,x0)),quotient(one,x0)) = one,
inference(unit_resolution,[status(thm)],[173,26]) ).
tff(175,plain,
one = product(quotient(one,quotient(one,x0)),quotient(one,x0)),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
one = product(j(j(x0)),quotient(one,x0)),
inference(transitivity,[status(thm)],[175,172]) ).
tff(177,plain,
difference(j(j(x0)),one) = difference(j(j(x0)),product(j(j(x0)),quotient(one,x0))),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ~ ! [A: $i] : ( i(A) = difference(A,one) )
| ( i(j(j(x0))) = difference(j(j(x0)),one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
i(j(j(x0))) = difference(j(j(x0)),one),
inference(unit_resolution,[status(thm)],[178,81]) ).
tff(180,plain,
i(j(j(x0))) = j(x0),
inference(transitivity,[status(thm)],[179,177,165,40]) ).
tff(181,plain,
i(i(j(j(x0)))) = i(j(x0)),
inference(monotonicity,[status(thm)],[180]) ).
tff(182,plain,
i(j(x0)) = i(i(j(j(x0)))),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
difference(quotient(one,x0),one) = i(quotient(one,x0)),
inference(symmetry,[status(thm)],[83]) ).
tff(184,plain,
difference(quotient(one,x0),product(quotient(one,x0),x0)) = difference(quotient(one,x0),one),
inference(symmetry,[status(thm)],[74]) ).
tff(185,plain,
x0 = difference(quotient(one,x0),product(quotient(one,x0),x0)),
inference(symmetry,[status(thm)],[70]) ).
tff(186,plain,
x0 = i(i(j(j(x0)))),
inference(transitivity,[status(thm)],[185,184,183,108,182]) ).
tff(187,plain,
product(x0,j(product(x1,x0))) = product(i(i(j(j(x0)))),j(product(x1,x0))),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
product(i(i(j(j(x0)))),j(product(x1,x0))) = product(x0,j(product(x1,x0))),
inference(symmetry,[status(thm)],[187]) ).
tff(189,plain,
( ~ ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
| ( product(i(i(j(j(x0)))),j(product(x1,x0))) = product(eta(j(j(x0))),product(j(j(x0)),j(product(x1,x0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(190,plain,
product(i(i(j(j(x0)))),j(product(x1,x0))) = product(eta(j(j(x0))),product(j(j(x0)),j(product(x1,x0)))),
inference(unit_resolution,[status(thm)],[189,93]) ).
tff(191,plain,
product(eta(j(j(x0))),product(j(j(x0)),j(product(x1,x0)))) = product(i(i(j(j(x0)))),j(product(x1,x0))),
inference(symmetry,[status(thm)],[190]) ).
tff(192,plain,
( ~ ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
| ( product(i(j(x0)),j(x0)) = product(j(x0),j(j(x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(193,plain,
product(i(j(x0)),j(x0)) = product(j(x0),j(j(x0))),
inference(unit_resolution,[status(thm)],[192,66]) ).
tff(194,plain,
product(j(x0),j(j(x0))) = product(i(j(x0)),j(x0)),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
product(i(j(j(x0))),j(j(x0))) = product(j(x0),j(j(x0))),
inference(monotonicity,[status(thm)],[180]) ).
tff(196,plain,
( ~ ! [A: $i] : ( eta(A) = product(i(A),A) )
| ( eta(j(j(x0))) = product(i(j(j(x0))),j(j(x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(197,plain,
eta(j(j(x0))) = product(i(j(j(x0))),j(j(x0))),
inference(unit_resolution,[status(thm)],[196,103]) ).
tff(198,plain,
eta(j(j(x0))) = product(x0,j(x0)),
inference(transitivity,[status(thm)],[197,195,194,112]) ).
tff(199,plain,
product(eta(j(j(x0))),product(j(j(x0)),j(product(x1,x0)))) = product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))) = product(eta(j(j(x0))),product(j(j(x0)),j(product(x1,x0)))),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))) = quotient(product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),product(quotient(one,x1),x1)),x1),
inference(transitivity,[status(thm)],[200,191,188,163,160]) ).
tff(202,plain,
quotient(product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))),quotient(one,x1)) = quotient(quotient(product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),product(quotient(one,x1),x1)),x1),quotient(one,x1)),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
quotient(quotient(product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),product(quotient(one,x1),x1)),x1),quotient(one,x1)) = quotient(product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))),quotient(one,x1)),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
<=> ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) )),
inference(bind,[status(th)],[]) ).
tff(205,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) ),
inference(quant_intro,[status(thm)],[204]) ).
tff(206,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,axiom,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
tff(208,plain,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
inference(modus_ponens,[status(thm)],[207,206]) ).
tff(209,plain,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
inference(skolemize,[status(sab)],[208]) ).
tff(210,plain,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
inference(modus_ponens,[status(thm)],[209,205]) ).
tff(211,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(quotient(one,x1),x1),product(quotient(one,x1),product(x1,product(t(eta(x0),i(x0)),t(eta(x0),x0))))) = quotient(quotient(product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),product(quotient(one,x1),x1)),x1),quotient(one,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(212,plain,
difference(product(quotient(one,x1),x1),product(quotient(one,x1),product(x1,product(t(eta(x0),i(x0)),t(eta(x0),x0))))) = quotient(quotient(product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),product(quotient(one,x1),x1)),x1),quotient(one,x1)),
inference(unit_resolution,[status(thm)],[211,210]) ).
tff(213,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(j(j(x0)),product(x0,j(x0))),product(x0,j(x0))) = j(j(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(214,plain,
product(quotient(j(j(x0)),product(x0,j(x0))),product(x0,j(x0))) = j(j(x0)),
inference(unit_resolution,[status(thm)],[213,26]) ).
tff(215,plain,
^ [B: $i,A: $i] :
refl(( ( product(A,product(eta(A),B)) = product(j(j(A)),B) )
<=> ( product(A,product(eta(A),B)) = product(j(j(A)),B) ) )),
inference(bind,[status(th)],[]) ).
tff(216,plain,
( ! [B: $i,A: $i] : ( product(A,product(eta(A),B)) = product(j(j(A)),B) )
<=> ! [B: $i,A: $i] : ( product(A,product(eta(A),B)) = product(j(j(A)),B) ) ),
inference(quant_intro,[status(thm)],[215]) ).
tff(217,plain,
( ! [B: $i,A: $i] : ( product(A,product(eta(A),B)) = product(j(j(A)),B) )
<=> ! [B: $i,A: $i] : ( product(A,product(eta(A),B)) = product(j(j(A)),B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(218,axiom,
! [B: $i,A: $i] : ( product(A,product(eta(A),B)) = product(j(j(A)),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos14) ).
tff(219,plain,
! [B: $i,A: $i] : ( product(A,product(eta(A),B)) = product(j(j(A)),B) ),
inference(modus_ponens,[status(thm)],[218,217]) ).
tff(220,plain,
! [B: $i,A: $i] : ( product(A,product(eta(A),B)) = product(j(j(A)),B) ),
inference(skolemize,[status(sab)],[219]) ).
tff(221,plain,
! [B: $i,A: $i] : ( product(A,product(eta(A),B)) = product(j(j(A)),B) ),
inference(modus_ponens,[status(thm)],[220,216]) ).
tff(222,plain,
( ~ ! [B: $i,A: $i] : ( product(A,product(eta(A),B)) = product(j(j(A)),B) )
| ( product(x0,product(eta(x0),j(product(x1,x0)))) = product(j(j(x0)),j(product(x1,x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(223,plain,
product(x0,product(eta(x0),j(product(x1,x0)))) = product(j(j(x0)),j(product(x1,x0))),
inference(unit_resolution,[status(thm)],[222,221]) ).
tff(224,plain,
quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))) = quotient(product(j(j(x0)),j(product(x1,x0))),j(product(x1,x0))),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
quotient(product(j(j(x0)),j(product(x1,x0))),j(product(x1,x0))) = quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(j(j(x0)),j(product(x1,x0))),j(product(x1,x0))) = j(j(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(227,plain,
quotient(product(j(j(x0)),j(product(x1,x0))),j(product(x1,x0))) = j(j(x0)),
inference(unit_resolution,[status(thm)],[226,125]) ).
tff(228,plain,
j(j(x0)) = quotient(product(j(j(x0)),j(product(x1,x0))),j(product(x1,x0))),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
j(j(x0)) = quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),
inference(transitivity,[status(thm)],[228,225]) ).
tff(230,plain,
quotient(j(j(x0)),product(x0,j(x0))) = quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),
inference(monotonicity,[status(thm)],[229,141]) ).
tff(231,plain,
quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)) = quotient(j(j(x0)),product(x0,j(x0))),
inference(symmetry,[status(thm)],[230]) ).
tff(232,plain,
product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0))) = product(quotient(j(j(x0)),product(x0,j(x0))),product(x0,j(x0))),
inference(monotonicity,[status(thm)],[231]) ).
tff(233,plain,
product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0))) = j(j(x0)),
inference(transitivity,[status(thm)],[232,214]) ).
tff(234,plain,
product(quotient(one,x0),product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0)))) = product(j(x0),j(j(x0))),
inference(monotonicity,[status(thm)],[40,233]) ).
tff(235,plain,
product(j(x0),j(j(x0))) = product(quotient(one,x0),product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0)))),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(x0,j(x0)),i(x1)),i(x1)) = product(x0,j(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(237,plain,
quotient(product(product(x0,j(x0)),i(x1)),i(x1)) = product(x0,j(x0)),
inference(unit_resolution,[status(thm)],[236,125]) ).
tff(238,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(product(x0,j(x0)),i(x1)),x1),x1) = product(product(x0,j(x0)),i(x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(239,plain,
quotient(product(product(product(x0,j(x0)),i(x1)),x1),x1) = product(product(x0,j(x0)),i(x1)),
inference(unit_resolution,[status(thm)],[238,125]) ).
tff(240,plain,
product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),i(x1)) = product(product(x0,j(x0)),i(x1)),
inference(monotonicity,[status(thm)],[156]) ).
tff(241,plain,
product(product(x0,j(x0)),i(x1)) = product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),i(x1)),
inference(symmetry,[status(thm)],[240]) ).
tff(242,plain,
product(product(product(x0,j(x0)),i(x1)),x1) = product(product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),i(x1)),x1),
inference(monotonicity,[status(thm)],[241]) ).
tff(243,plain,
product(product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),i(x1)),x1) = product(product(product(x0,j(x0)),i(x1)),x1),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
eta(quotient(one,x0)) = product(x0,j(x0)),
inference(transitivity,[status(thm)],[105,109,112]) ).
tff(245,plain,
product(eta(quotient(one,x0)),i(x1)) = product(product(x0,j(x0)),i(x1)),
inference(monotonicity,[status(thm)],[244]) ).
tff(246,plain,
product(product(x0,j(x0)),i(x1)) = product(eta(quotient(one,x0)),i(x1)),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),i(x1)) = product(eta(quotient(one,x0)),i(x1)),
inference(transitivity,[status(thm)],[240,246]) ).
tff(248,plain,
product(product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),i(x1)),x1) = product(product(eta(quotient(one,x0)),i(x1)),x1),
inference(monotonicity,[status(thm)],[247]) ).
tff(249,plain,
product(product(eta(quotient(one,x0)),i(x1)),x1) = product(product(product(t(eta(x0),i(x0)),t(eta(x0),x0)),i(x1)),x1),
inference(symmetry,[status(thm)],[248]) ).
tff(250,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
<=> ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ) )),
inference(bind,[status(th)],[]) ).
tff(251,plain,
( ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ) ),
inference(quant_intro,[status(thm)],[250]) ).
tff(252,plain,
( ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(253,axiom,
! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos16) ).
tff(254,plain,
! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
inference(modus_ponens,[status(thm)],[253,252]) ).
tff(255,plain,
! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
inference(skolemize,[status(sab)],[254]) ).
tff(256,plain,
! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
inference(modus_ponens,[status(thm)],[255,251]) ).
tff(257,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
| ( product(eta(quotient(one,x0)),product(i(x1),x1)) = product(product(eta(quotient(one,x0)),i(x1)),x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(258,plain,
product(eta(quotient(one,x0)),product(i(x1),x1)) = product(product(eta(quotient(one,x0)),i(x1)),x1),
inference(unit_resolution,[status(thm)],[257,256]) ).
tff(259,plain,
( ~ ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
| ( product(i(x1),x1) = product(x1,j(x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(260,plain,
product(i(x1),x1) = product(x1,j(x1)),
inference(unit_resolution,[status(thm)],[259,66]) ).
tff(261,plain,
product(eta(quotient(one,x0)),product(i(x1),x1)) = product(product(x0,j(x0)),product(x1,j(x1))),
inference(monotonicity,[status(thm)],[244,260]) ).
tff(262,plain,
product(product(x0,j(x0)),product(x1,j(x1))) = product(eta(quotient(one,x0)),product(i(x1),x1)),
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
product(product(x0,j(x0)),product(i(x1),x1)) = product(product(x0,j(x0)),product(x1,j(x1))),
inference(monotonicity,[status(thm)],[260]) ).
tff(264,plain,
product(product(x0,j(x0)),product(i(x1),x1)) = product(product(product(x0,j(x0)),i(x1)),x1),
inference(transitivity,[status(thm)],[263,262,258,249,243]) ).
tff(265,plain,
quotient(product(product(x0,j(x0)),product(i(x1),x1)),x1) = quotient(product(product(product(x0,j(x0)),i(x1)),x1),x1),
inference(monotonicity,[status(thm)],[264]) ).
tff(266,plain,
quotient(product(product(x0,j(x0)),product(i(x1),x1)),x1) = product(product(x0,j(x0)),i(x1)),
inference(transitivity,[status(thm)],[265,239]) ).
tff(267,plain,
quotient(quotient(product(product(x0,j(x0)),product(i(x1),x1)),x1),i(x1)) = quotient(product(product(x0,j(x0)),i(x1)),i(x1)),
inference(monotonicity,[status(thm)],[266]) ).
tff(268,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(i(x1),x1),product(i(x1),product(x1,product(x0,j(x0))))) = quotient(quotient(product(product(x0,j(x0)),product(i(x1),x1)),x1),i(x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(269,plain,
difference(product(i(x1),x1),product(i(x1),product(x1,product(x0,j(x0))))) = quotient(quotient(product(product(x0,j(x0)),product(i(x1),x1)),x1),i(x1)),
inference(unit_resolution,[status(thm)],[268,210]) ).
tff(270,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(quotient(one,x1),product(quotient(one,x1),x1)) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(271,plain,
difference(quotient(one,x1),product(quotient(one,x1),x1)) = x1,
inference(unit_resolution,[status(thm)],[270,17]) ).
tff(272,plain,
one = product(quotient(one,x1),x1),
inference(symmetry,[status(thm)],[117]) ).
tff(273,plain,
difference(quotient(one,x1),one) = difference(quotient(one,x1),product(quotient(one,x1),x1)),
inference(monotonicity,[status(thm)],[272]) ).
tff(274,plain,
( ~ ! [A: $i] : ( i(A) = difference(A,one) )
| ( i(quotient(one,x1)) = difference(quotient(one,x1),one) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(275,plain,
i(quotient(one,x1)) = difference(quotient(one,x1),one),
inference(unit_resolution,[status(thm)],[274,81]) ).
tff(276,plain,
i(quotient(one,x1)) = x1,
inference(transitivity,[status(thm)],[275,273,271]) ).
tff(277,plain,
i(i(quotient(one,x1))) = i(x1),
inference(monotonicity,[status(thm)],[276]) ).
tff(278,plain,
product(i(i(quotient(one,x1))),product(x1,product(x0,j(x0)))) = product(i(x1),product(x1,product(x0,j(x0)))),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
( ~ ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
| ( product(i(i(quotient(one,x1))),product(x1,product(x0,j(x0)))) = product(eta(quotient(one,x1)),product(quotient(one,x1),product(x1,product(x0,j(x0))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(280,plain,
product(i(i(quotient(one,x1))),product(x1,product(x0,j(x0)))) = product(eta(quotient(one,x1)),product(quotient(one,x1),product(x1,product(x0,j(x0))))),
inference(unit_resolution,[status(thm)],[279,93]) ).
tff(281,plain,
product(eta(quotient(one,x1)),product(quotient(one,x1),product(x1,product(x0,j(x0))))) = product(i(i(quotient(one,x1))),product(x1,product(x0,j(x0)))),
inference(symmetry,[status(thm)],[280]) ).
tff(282,plain,
( ~ ! [A: $i] : ( eta(A) = product(i(A),A) )
| ( eta(quotient(one,x1)) = product(i(quotient(one,x1)),quotient(one,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(283,plain,
eta(quotient(one,x1)) = product(i(quotient(one,x1)),quotient(one,x1)),
inference(unit_resolution,[status(thm)],[282,103]) ).
tff(284,plain,
product(i(quotient(one,x1)),quotient(one,x1)) = eta(quotient(one,x1)),
inference(symmetry,[status(thm)],[283]) ).
tff(285,plain,
product(i(quotient(one,x1)),quotient(one,x1)) = product(x1,j(x1)),
inference(monotonicity,[status(thm)],[276,10]) ).
tff(286,plain,
product(x1,j(x1)) = product(i(quotient(one,x1)),quotient(one,x1)),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
product(x1,j(x1)) = eta(quotient(one,x1)),
inference(transitivity,[status(thm)],[286,284]) ).
tff(288,plain,
product(product(x1,j(x1)),product(quotient(one,x1),product(x1,product(x0,j(x0))))) = product(eta(quotient(one,x1)),product(quotient(one,x1),product(x1,product(x0,j(x0))))),
inference(monotonicity,[status(thm)],[287]) ).
tff(289,plain,
product(product(x1,j(x1)),product(quotient(one,x1),product(x1,product(x0,j(x0))))) = product(i(x1),product(x1,product(x0,j(x0)))),
inference(transitivity,[status(thm)],[288,281,278]) ).
tff(290,plain,
product(x1,j(x1)) = product(i(x1),x1),
inference(symmetry,[status(thm)],[260]) ).
tff(291,plain,
difference(product(x1,j(x1)),product(product(x1,j(x1)),product(quotient(one,x1),product(x1,product(x0,j(x0)))))) = difference(product(i(x1),x1),product(i(x1),product(x1,product(x0,j(x0))))),
inference(monotonicity,[status(thm)],[290,289]) ).
tff(292,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(x1,j(x1)),product(product(x1,j(x1)),product(quotient(one,x1),product(x1,product(x0,j(x0)))))) = product(quotient(one,x1),product(x1,product(x0,j(x0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(293,plain,
difference(product(x1,j(x1)),product(product(x1,j(x1)),product(quotient(one,x1),product(x1,product(x0,j(x0)))))) = product(quotient(one,x1),product(x1,product(x0,j(x0)))),
inference(unit_resolution,[status(thm)],[292,17]) ).
tff(294,plain,
product(quotient(one,x1),product(x1,product(x0,j(x0)))) = difference(product(x1,j(x1)),product(product(x1,j(x1)),product(quotient(one,x1),product(x1,product(x0,j(x0)))))),
inference(symmetry,[status(thm)],[293]) ).
tff(295,plain,
product(x1,product(t(eta(x0),i(x0)),t(eta(x0),x0))) = product(x1,product(x0,j(x0))),
inference(monotonicity,[status(thm)],[156]) ).
tff(296,plain,
product(quotient(one,x1),product(x1,product(t(eta(x0),i(x0)),t(eta(x0),x0)))) = product(quotient(one,x1),product(x1,product(x0,j(x0)))),
inference(monotonicity,[status(thm)],[295]) ).
tff(297,plain,
product(quotient(one,x1),product(x1,product(t(eta(x0),i(x0)),t(eta(x0),x0)))) = product(quotient(one,x0),product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0)))),
inference(transitivity,[status(thm)],[296,294,291,269,267,237,113,193,235]) ).
tff(298,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(eta(x0),j(product(x1,x0))),product(product(eta(x0),j(product(x1,x0))),x0)) = x0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(299,plain,
difference(product(eta(x0),j(product(x1,x0))),product(product(eta(x0),j(product(x1,x0))),x0)) = x0,
inference(unit_resolution,[status(thm)],[298,17]) ).
tff(300,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
| ( product(eta(x0),product(j(product(x1,x0)),x0)) = product(product(eta(x0),j(product(x1,x0))),x0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(301,plain,
product(eta(x0),product(j(product(x1,x0)),x0)) = product(product(eta(x0),j(product(x1,x0))),x0),
inference(unit_resolution,[status(thm)],[300,256]) ).
tff(302,plain,
difference(product(eta(x0),j(product(x1,x0))),product(eta(x0),product(j(product(x1,x0)),x0))) = difference(product(eta(x0),j(product(x1,x0))),product(product(eta(x0),j(product(x1,x0))),x0)),
inference(monotonicity,[status(thm)],[301]) ).
tff(303,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(eta(x0),j(product(x1,x0))),product(eta(x0),product(j(product(x1,x0)),x0))) = quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(304,plain,
difference(product(eta(x0),j(product(x1,x0))),product(eta(x0),product(j(product(x1,x0)),x0))) = quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),
inference(unit_resolution,[status(thm)],[303,210]) ).
tff(305,plain,
quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)) = difference(product(eta(x0),j(product(x1,x0))),product(eta(x0),product(j(product(x1,x0)),x0))),
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)) = x0,
inference(transitivity,[status(thm)],[305,302,299]) ).
tff(307,plain,
product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))) = product(quotient(one,x0),x0),
inference(monotonicity,[status(thm)],[306]) ).
tff(308,plain,
product(quotient(one,x0),x0) = product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))),
inference(symmetry,[status(thm)],[307]) ).
tff(309,plain,
product(quotient(one,x1),x1) = product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))),
inference(transitivity,[status(thm)],[117,73,308]) ).
tff(310,plain,
difference(product(quotient(one,x1),x1),product(quotient(one,x1),product(x1,product(t(eta(x0),i(x0)),t(eta(x0),x0))))) = difference(product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))),product(quotient(one,x0),product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0))))),
inference(monotonicity,[status(thm)],[309,297]) ).
tff(311,plain,
difference(product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))),product(quotient(one,x0),product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0))))) = difference(product(quotient(one,x1),x1),product(quotient(one,x1),product(x1,product(t(eta(x0),i(x0)),t(eta(x0),x0))))),
inference(symmetry,[status(thm)],[310]) ).
tff(312,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))),product(quotient(one,x0),product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0))))) = quotient(quotient(product(product(x0,j(x0)),product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)))),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))),quotient(one,x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(313,plain,
difference(product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))),product(quotient(one,x0),product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0))))) = quotient(quotient(product(product(x0,j(x0)),product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)))),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))),quotient(one,x0)),
inference(unit_resolution,[status(thm)],[312,210]) ).
tff(314,plain,
quotient(quotient(product(product(x0,j(x0)),product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)))),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))),quotient(one,x0)) = difference(product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))),product(quotient(one,x0),product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0))))),
inference(symmetry,[status(thm)],[313]) ).
tff(315,plain,
product(product(x0,j(x0)),quotient(one,x0)) = product(eta(x0),quotient(one,x0)),
inference(monotonicity,[status(thm)],[141]) ).
tff(316,plain,
product(eta(x0),quotient(one,x0)) = product(product(x0,j(x0)),quotient(one,x0)),
inference(symmetry,[status(thm)],[315]) ).
tff(317,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(x0,product(x0,product(eta(x0),quotient(one,x0)))) = product(eta(x0),quotient(one,x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(318,plain,
difference(x0,product(x0,product(eta(x0),quotient(one,x0)))) = product(eta(x0),quotient(one,x0)),
inference(unit_resolution,[status(thm)],[317,17]) ).
tff(319,plain,
( ~ ! [B: $i,A: $i] : ( product(A,product(eta(A),B)) = product(j(j(A)),B) )
| ( product(x0,product(eta(x0),quotient(one,x0))) = product(j(j(x0)),quotient(one,x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(320,plain,
product(x0,product(eta(x0),quotient(one,x0))) = product(j(j(x0)),quotient(one,x0)),
inference(unit_resolution,[status(thm)],[319,221]) ).
tff(321,plain,
product(x0,product(eta(x0),quotient(one,x0))) = one,
inference(transitivity,[status(thm)],[320,171,174]) ).
tff(322,plain,
difference(x0,product(x0,product(eta(x0),quotient(one,x0)))) = difference(x0,one),
inference(monotonicity,[status(thm)],[321]) ).
tff(323,plain,
difference(x0,one) = difference(x0,product(x0,product(eta(x0),quotient(one,x0)))),
inference(symmetry,[status(thm)],[322]) ).
tff(324,plain,
product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0))) = quotient(one,quotient(one,x0)),
inference(transitivity,[status(thm)],[232,214,169,167]) ).
tff(325,plain,
product(product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0))),quotient(one,x0)) = product(quotient(one,quotient(one,x0)),quotient(one,x0)),
inference(monotonicity,[status(thm)],[324]) ).
tff(326,plain,
product(product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0))),quotient(one,x0)) = one,
inference(transitivity,[status(thm)],[325,174]) ).
tff(327,plain,
difference(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0))),quotient(one,x0))) = difference(x0,one),
inference(monotonicity,[status(thm)],[306,326]) ).
tff(328,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0))),quotient(one,x0))) = quotient(product(product(x0,j(x0)),product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)))),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(329,plain,
difference(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0))),quotient(one,x0))) = quotient(product(product(x0,j(x0)),product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)))),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))),
inference(unit_resolution,[status(thm)],[328,54]) ).
tff(330,plain,
quotient(product(product(x0,j(x0)),product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)))),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))) = difference(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(product(quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)),product(x0,j(x0))),quotient(one,x0))),
inference(symmetry,[status(thm)],[329]) ).
tff(331,plain,
quotient(product(product(x0,j(x0)),product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)))),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))) = product(product(x0,j(x0)),quotient(one,x0)),
inference(transitivity,[status(thm)],[330,327,323,318,316]) ).
tff(332,plain,
quotient(quotient(product(product(x0,j(x0)),product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)))),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))),quotient(one,x0)) = quotient(product(product(x0,j(x0)),quotient(one,x0)),quotient(one,x0)),
inference(monotonicity,[status(thm)],[331]) ).
tff(333,plain,
quotient(product(product(x0,j(x0)),quotient(one,x0)),quotient(one,x0)) = quotient(quotient(product(product(x0,j(x0)),product(quotient(one,x0),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0)))),quotient(quotient(product(x0,product(eta(x0),j(product(x1,x0)))),j(product(x1,x0))),eta(x0))),quotient(one,x0)),
inference(symmetry,[status(thm)],[332]) ).
tff(334,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(x0,j(x0)),quotient(one,x0)),quotient(one,x0)) = product(x0,j(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(335,plain,
quotient(product(product(x0,j(x0)),quotient(one,x0)),quotient(one,x0)) = product(x0,j(x0)),
inference(unit_resolution,[status(thm)],[334,125]) ).
tff(336,plain,
product(x0,j(x0)) = quotient(product(product(x0,j(x0)),quotient(one,x0)),quotient(one,x0)),
inference(symmetry,[status(thm)],[335]) ).
tff(337,plain,
product(x0,j(x0)) = quotient(product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))),quotient(one,x1)),
inference(transitivity,[status(thm)],[336,333,314,311,212,203]) ).
tff(338,plain,
product(product(x0,j(x0)),quotient(one,x1)) = product(quotient(product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))),quotient(one,x1)),quotient(one,x1)),
inference(monotonicity,[status(thm)],[337]) ).
tff(339,plain,
product(product(x0,j(x0)),quotient(one,x1)) = product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))),
inference(transitivity,[status(thm)],[338,28]) ).
tff(340,plain,
difference(product(x0,j(x0)),product(product(x0,j(x0)),quotient(one,x1))) = difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))),
inference(monotonicity,[status(thm)],[339]) ).
tff(341,plain,
difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))) = difference(product(x0,j(x0)),product(product(x0,j(x0)),quotient(one,x1))),
inference(symmetry,[status(thm)],[340]) ).
tff(342,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))) = product(j(j(x0)),j(product(x1,x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(343,plain,
difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))) = product(j(j(x0)),j(product(x1,x0))),
inference(unit_resolution,[status(thm)],[342,17]) ).
tff(344,plain,
product(j(j(x0)),j(product(x1,x0))) = difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))),
inference(symmetry,[status(thm)],[343]) ).
tff(345,plain,
product(j(j(x0)),j(product(x1,x0))) = j(x1),
inference(transitivity,[status(thm)],[344,341,19,10]) ).
tff(346,plain,
( ( product(j(j(x0)),j(product(x1,x0))) != j(x1) )
<=> ( product(j(j(x0)),j(product(x1,x0))) != j(x1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(347,axiom,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(348,plain,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
inference(modus_ponens,[status(thm)],[347,346]) ).
tff(349,plain,
$false,
inference(unit_resolution,[status(thm)],[348,345]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP767-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 17:06:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 101.93/102.14 % SZS status Unsatisfiable
% 101.93/102.14 % SZS output start Proof
% See solution above
% 102.05/102.23 % E exiting
%------------------------------------------------------------------------------