%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP766-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 1.23s 1.41s
% Output : Proof 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 65
% Syntax : Number of formulae : 261 ( 205 unt; 0 typ; 0 def)
% Number of atoms : 333 ( 324 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 107 ( 43 ~; 39 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 8 ( 8 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 266 ( 247 !; 0 ?; 266 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i ) > $i ).
tff(x2_type,type,
x2: $i ).
tff(x1_type,type,
x1: $i ).
tff(eta_type,type,
eta: $i > $i ).
tff(x0_type,type,
x0: $i ).
tff(quotient_type,type,
quotient: ( $i * $i ) > $i ).
tff(t_type,type,
t: ( $i * $i ) > $i ).
tff(difference_type,type,
difference: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( product(quotient(A,B),B) = A )
<=> ( product(quotient(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(2,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)],[1]) ).
tff(3,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(4,axiom,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
tff(5,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(product(eta(x0),x1),x2),eta(x0)),eta(x0)) = product(product(eta(x0),x1),x2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
product(quotient(product(product(eta(x0),x1),x2),eta(x0)),eta(x0)) = product(product(eta(x0),x1),x2),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,axiom,
! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos18) ).
tff(14,plain,
! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) )
| ( t(eta(x0),eta(x0)) = quotient(product(eta(x0),eta(x0)),eta(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
t(eta(x0),eta(x0)) = quotient(product(eta(x0),eta(x0)),eta(x0)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
quotient(product(eta(x0),eta(x0)),eta(x0)) = t(eta(x0),eta(x0)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [B: $i,A: $i] :
refl(( ( quotient(product(A,B),B) = A )
<=> ( quotient(product(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(21,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)],[20]) ).
tff(22,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(23,axiom,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
tff(24,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(eta(x0),eta(x0)),eta(x0)) = eta(x0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
quotient(product(eta(x0),eta(x0)),eta(x0)) = eta(x0),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
eta(x0) = quotient(product(eta(x0),eta(x0)),eta(x0)),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
eta(x0) = t(eta(x0),eta(x0)),
inference(transitivity,[status(thm)],[29,19]) ).
tff(31,plain,
( ~ ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) )
| ( t(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))) = quotient(product(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))),eta(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
t(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))) = quotient(product(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))),eta(x0)),
inference(unit_resolution,[status(thm)],[31,16]) ).
tff(33,plain,
quotient(product(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))),eta(x0)) = t(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(eta(x0),x1),eta(x0)),eta(x0)) = product(eta(x0),x1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
product(quotient(product(eta(x0),x1),eta(x0)),eta(x0)) = product(eta(x0),x1),
inference(unit_resolution,[status(thm)],[34,7]) ).
tff(36,plain,
product(quotient(product(product(eta(x0),x1),x2),product(eta(x0),x1)),product(quotient(product(eta(x0),x1),eta(x0)),eta(x0))) = product(quotient(product(product(eta(x0),x1),x2),product(eta(x0),x1)),product(eta(x0),x1)),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
product(quotient(product(product(eta(x0),x1),x2),product(eta(x0),x1)),product(eta(x0),x1)) = product(quotient(product(product(eta(x0),x1),x2),product(eta(x0),x1)),product(quotient(product(eta(x0),x1),eta(x0)),eta(x0))),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(product(eta(x0),x1),x2),product(eta(x0),x1)),product(eta(x0),x1)) = product(product(eta(x0),x1),x2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
product(quotient(product(product(eta(x0),x1),x2),product(eta(x0),x1)),product(eta(x0),x1)) = product(product(eta(x0),x1),x2),
inference(unit_resolution,[status(thm)],[38,7]) ).
tff(40,plain,
product(product(eta(x0),x1),x2) = product(quotient(product(product(eta(x0),x1),x2),product(eta(x0),x1)),product(eta(x0),x1)),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
^ [B: $i,A: $i] :
refl(( ( product(A,difference(A,B)) = B )
<=> ( product(A,difference(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(42,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)],[41]) ).
tff(43,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(44,axiom,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
tff(45,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(eta(x0),difference(eta(x0),product(product(eta(x0),x1),x2))) = product(product(eta(x0),x1),x2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
product(eta(x0),difference(eta(x0),product(product(eta(x0),x1),x2))) = product(product(eta(x0),x1),x2),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,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(51,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)],[50]) ).
tff(52,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(53,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(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)],[53,52]) ).
tff(55,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)],[54]) ).
tff(56,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)],[55,51]) ).
tff(57,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(eta(x0),product(product(eta(x0),x1),x2)) = quotient(product(x1,product(x2,eta(x0))),eta(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
difference(eta(x0),product(product(eta(x0),x1),x2)) = quotient(product(x1,product(x2,eta(x0))),eta(x0)),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
quotient(product(x1,product(x2,eta(x0))),eta(x0)) = difference(eta(x0),product(product(eta(x0),x1),x2)),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
product(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))) = product(eta(x0),difference(eta(x0),product(product(eta(x0),x1),x2))),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
product(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))) = product(quotient(product(product(eta(x0),x1),x2),product(eta(x0),x1)),product(quotient(product(eta(x0),x1),eta(x0)),eta(x0))),
inference(transitivity,[status(thm)],[60,49,40,37]) ).
tff(62,plain,
quotient(product(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))),eta(x0)) = quotient(product(quotient(product(product(eta(x0),x1),x2),product(eta(x0),x1)),product(quotient(product(eta(x0),x1),eta(x0)),eta(x0))),eta(x0)),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
quotient(product(quotient(product(product(eta(x0),x1),x2),product(eta(x0),x1)),product(quotient(product(eta(x0),x1),eta(x0)),eta(x0))),eta(x0)) = quotient(product(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))),eta(x0)),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
product(product(eta(x0),x1),x2) = product(quotient(product(product(eta(x0),x1),x2),product(eta(x0),x1)),product(quotient(product(eta(x0),x1),eta(x0)),eta(x0))),
inference(transitivity,[status(thm)],[40,37]) ).
tff(65,plain,
quotient(product(product(eta(x0),x1),x2),eta(x0)) = quotient(product(quotient(product(product(eta(x0),x1),x2),product(eta(x0),x1)),product(quotient(product(eta(x0),x1),eta(x0)),eta(x0))),eta(x0)),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
quotient(product(product(eta(x0),x1),x2),eta(x0)) = t(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))),
inference(transitivity,[status(thm)],[65,63,33]) ).
tff(67,plain,
product(quotient(product(product(eta(x0),x1),x2),eta(x0)),eta(x0)) = product(t(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))),t(eta(x0),eta(x0))),
inference(monotonicity,[status(thm)],[66,30]) ).
tff(68,plain,
product(t(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))),t(eta(x0),eta(x0))) = product(quotient(product(product(eta(x0),x1),x2),eta(x0)),eta(x0)),
inference(symmetry,[status(thm)],[67]) ).
tff(69,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(70,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)],[69]) ).
tff(71,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(72,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',sos19) ).
tff(73,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)],[72,71]) ).
tff(74,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)],[73]) ).
tff(75,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)],[74,70]) ).
tff(76,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(quotient(product(x1,product(x2,eta(x0))),eta(x0)),eta(x0))) = product(t(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))),t(eta(x0),eta(x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
t(eta(x0),product(quotient(product(x1,product(x2,eta(x0))),eta(x0)),eta(x0))) = product(t(eta(x0),quotient(product(x1,product(x2,eta(x0))),eta(x0))),t(eta(x0),eta(x0))),
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(x1,product(x2,eta(x0))),eta(x0)),eta(x0)) = product(x1,product(x2,eta(x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
product(quotient(product(x1,product(x2,eta(x0))),eta(x0)),eta(x0)) = product(x1,product(x2,eta(x0))),
inference(unit_resolution,[status(thm)],[78,7]) ).
tff(80,plain,
t(eta(x0),product(quotient(product(x1,product(x2,eta(x0))),eta(x0)),eta(x0))) = t(eta(x0),product(x1,product(x2,eta(x0)))),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
t(eta(x0),product(x1,product(x2,eta(x0)))) = t(eta(x0),product(quotient(product(x1,product(x2,eta(x0))),eta(x0)),eta(x0))),
inference(symmetry,[status(thm)],[80]) ).
tff(82,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(x1,product(x2,eta(x0)))) = product(t(eta(x0),x1),t(eta(x0),product(x2,eta(x0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
t(eta(x0),product(x1,product(x2,eta(x0)))) = product(t(eta(x0),x1),t(eta(x0),product(x2,eta(x0)))),
inference(unit_resolution,[status(thm)],[82,75]) ).
tff(84,plain,
product(t(eta(x0),x1),t(eta(x0),product(x2,eta(x0)))) = t(eta(x0),product(x1,product(x2,eta(x0)))),
inference(symmetry,[status(thm)],[83]) ).
tff(85,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(x2,eta(x0))) = product(t(eta(x0),x2),t(eta(x0),eta(x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
t(eta(x0),product(x2,eta(x0))) = product(t(eta(x0),x2),t(eta(x0),eta(x0))),
inference(unit_resolution,[status(thm)],[85,75]) ).
tff(87,plain,
( ~ ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) )
| ( t(eta(x0),x1) = quotient(product(eta(x0),x1),eta(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
t(eta(x0),x1) = quotient(product(eta(x0),x1),eta(x0)),
inference(unit_resolution,[status(thm)],[87,16]) ).
tff(89,plain,
product(t(eta(x0),x1),t(eta(x0),product(x2,eta(x0)))) = product(quotient(product(eta(x0),x1),eta(x0)),product(t(eta(x0),x2),t(eta(x0),eta(x0)))),
inference(monotonicity,[status(thm)],[88,86]) ).
tff(90,plain,
product(quotient(product(eta(x0),x1),eta(x0)),product(t(eta(x0),x2),t(eta(x0),eta(x0)))) = product(t(eta(x0),x1),t(eta(x0),product(x2,eta(x0)))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))) = quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),t(eta(x0),eta(x0))),
inference(monotonicity,[status(thm)],[19]) ).
tff(92,plain,
quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),t(eta(x0),eta(x0))) = quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,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(94,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)],[93]) ).
tff(95,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(96,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(97,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)],[96,95]) ).
tff(98,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)],[97]) ).
tff(99,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)],[98,94]) ).
tff(100,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(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))) = quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),t(eta(x0),eta(x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))) = quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),t(eta(x0),eta(x0))),
inference(unit_resolution,[status(thm)],[100,99]) ).
tff(102,plain,
difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))) = quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))),
inference(transitivity,[status(thm)],[101,92]) ).
tff(103,plain,
product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),eta(x0)) = product(quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))),
inference(monotonicity,[status(thm)],[102,29]) ).
tff(104,plain,
product(quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))) = product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),eta(x0)),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) )
| ( t(eta(x0),x2) = quotient(product(eta(x0),x2),eta(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
t(eta(x0),x2) = quotient(product(eta(x0),x2),eta(x0)),
inference(unit_resolution,[status(thm)],[105,16]) ).
tff(107,plain,
^ [B: $i,A: $i] :
refl(( ( difference(A,product(A,B)) = B )
<=> ( difference(A,product(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(108,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)],[107]) ).
tff(109,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(110,axiom,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
tff(111,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),product(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),t(eta(x0),x2))) = t(eta(x0),x2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
difference(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),product(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),t(eta(x0),x2))) = t(eta(x0),x2),
inference(unit_resolution,[status(thm)],[114,113]) ).
tff(116,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(eta(x0),x1)) = product(t(eta(x0),eta(x0)),t(eta(x0),x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
t(eta(x0),product(eta(x0),x1)) = product(t(eta(x0),eta(x0)),t(eta(x0),x1)),
inference(unit_resolution,[status(thm)],[116,75]) ).
tff(118,plain,
product(t(eta(x0),eta(x0)),t(eta(x0),x1)) = t(eta(x0),product(eta(x0),x1)),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
product(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),t(eta(x0),x2)) = product(t(eta(x0),product(eta(x0),x1)),t(eta(x0),x2)),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
product(t(eta(x0),product(eta(x0),x1)),t(eta(x0),x2)) = product(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),t(eta(x0),x2)),
inference(symmetry,[status(thm)],[119]) ).
tff(121,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(product(eta(x0),x1),x2)) = product(t(eta(x0),product(eta(x0),x1)),t(eta(x0),x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
t(eta(x0),product(product(eta(x0),x1),x2)) = product(t(eta(x0),product(eta(x0),x1)),t(eta(x0),x2)),
inference(unit_resolution,[status(thm)],[121,75]) ).
tff(123,plain,
product(quotient(product(eta(x0),x1),eta(x0)),product(t(eta(x0),x2),t(eta(x0),eta(x0)))) = product(product(eta(x0),x1),x2),
inference(transitivity,[status(thm)],[90,84,81,77,68,9]) ).
tff(124,plain,
t(eta(x0),product(quotient(product(eta(x0),x1),eta(x0)),product(t(eta(x0),x2),t(eta(x0),eta(x0))))) = t(eta(x0),product(product(eta(x0),x1),x2)),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,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(quotient(product(eta(x0),x1),eta(x0)),product(t(eta(x0),x2),t(eta(x0),eta(x0))))) = product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),t(eta(x0),product(t(eta(x0),x2),t(eta(x0),eta(x0))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
t(eta(x0),product(quotient(product(eta(x0),x1),eta(x0)),product(t(eta(x0),x2),t(eta(x0),eta(x0))))) = product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),t(eta(x0),product(t(eta(x0),x2),t(eta(x0),eta(x0))))),
inference(unit_resolution,[status(thm)],[125,75]) ).
tff(127,plain,
product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),t(eta(x0),product(t(eta(x0),x2),t(eta(x0),eta(x0))))) = t(eta(x0),product(quotient(product(eta(x0),x1),eta(x0)),product(t(eta(x0),x2),t(eta(x0),eta(x0))))),
inference(symmetry,[status(thm)],[126]) ).
tff(128,plain,
quotient(product(eta(x0),x2),eta(x0)) = t(eta(x0),x2),
inference(symmetry,[status(thm)],[106]) ).
tff(129,plain,
product(quotient(product(eta(x0),x2),eta(x0)),eta(x0)) = product(t(eta(x0),x2),t(eta(x0),eta(x0))),
inference(monotonicity,[status(thm)],[128,30]) ).
tff(130,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(eta(x0),x2),eta(x0)),eta(x0)) = product(eta(x0),x2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
product(quotient(product(eta(x0),x2),eta(x0)),eta(x0)) = product(eta(x0),x2),
inference(unit_resolution,[status(thm)],[130,7]) ).
tff(132,plain,
product(eta(x0),x2) = product(quotient(product(eta(x0),x2),eta(x0)),eta(x0)),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
product(eta(x0),x2) = product(t(eta(x0),x2),t(eta(x0),eta(x0))),
inference(transitivity,[status(thm)],[132,129]) ).
tff(134,plain,
t(eta(x0),product(eta(x0),x2)) = t(eta(x0),product(t(eta(x0),x2),t(eta(x0),eta(x0)))),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,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(eta(x0),x2)) = product(t(eta(x0),eta(x0)),t(eta(x0),x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
t(eta(x0),product(eta(x0),x2)) = product(t(eta(x0),eta(x0)),t(eta(x0),x2)),
inference(unit_resolution,[status(thm)],[135,75]) ).
tff(137,plain,
product(t(eta(x0),eta(x0)),t(eta(x0),x2)) = t(eta(x0),product(eta(x0),x2)),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
product(eta(x0),quotient(product(eta(x0),x2),eta(x0))) = product(t(eta(x0),eta(x0)),t(eta(x0),x2)),
inference(monotonicity,[status(thm)],[30,128]) ).
tff(139,plain,
product(eta(x0),quotient(product(eta(x0),x2),eta(x0))) = t(eta(x0),product(t(eta(x0),x2),t(eta(x0),eta(x0)))),
inference(transitivity,[status(thm)],[138,137,134]) ).
tff(140,plain,
product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),product(eta(x0),quotient(product(eta(x0),x2),eta(x0)))) = product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),t(eta(x0),product(t(eta(x0),x2),t(eta(x0),eta(x0))))),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),product(eta(x0),quotient(product(eta(x0),x2),eta(x0)))) = product(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),t(eta(x0),x2)),
inference(transitivity,[status(thm)],[140,127,124,122,120]) ).
tff(142,plain,
t(eta(x0),product(quotient(product(eta(x0),x1),eta(x0)),eta(x0))) = t(eta(x0),product(eta(x0),x1)),
inference(monotonicity,[status(thm)],[35]) ).
tff(143,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(quotient(product(eta(x0),x1),eta(x0)),eta(x0))) = product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),t(eta(x0),eta(x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(144,plain,
t(eta(x0),product(quotient(product(eta(x0),x1),eta(x0)),eta(x0))) = product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),t(eta(x0),eta(x0))),
inference(unit_resolution,[status(thm)],[143,75]) ).
tff(145,plain,
product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),t(eta(x0),eta(x0))) = t(eta(x0),product(quotient(product(eta(x0),x1),eta(x0)),eta(x0))),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0)) = product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),t(eta(x0),eta(x0))),
inference(monotonicity,[status(thm)],[30]) ).
tff(147,plain,
product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0)) = product(t(eta(x0),eta(x0)),t(eta(x0),x1)),
inference(transitivity,[status(thm)],[146,145,142,117]) ).
tff(148,plain,
difference(product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0)),product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),product(eta(x0),quotient(product(eta(x0),x2),eta(x0))))) = difference(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),product(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),t(eta(x0),x2))),
inference(monotonicity,[status(thm)],[147,141]) ).
tff(149,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(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0)),product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),product(eta(x0),quotient(product(eta(x0),x2),eta(x0))))) = quotient(quotient(product(quotient(product(eta(x0),x2),eta(x0)),product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0))),eta(x0)),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
difference(product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0)),product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),product(eta(x0),quotient(product(eta(x0),x2),eta(x0))))) = quotient(quotient(product(quotient(product(eta(x0),x2),eta(x0)),product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0))),eta(x0)),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))),
inference(unit_resolution,[status(thm)],[149,99]) ).
tff(151,plain,
quotient(quotient(product(quotient(product(eta(x0),x2),eta(x0)),product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0))),eta(x0)),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))) = difference(product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0)),product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),product(eta(x0),quotient(product(eta(x0),x2),eta(x0))))),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),x1),eta(x0))) = product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
product(quotient(product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),x1),eta(x0))) = product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),
inference(unit_resolution,[status(thm)],[152,7]) ).
tff(154,plain,
quotient(product(eta(x0),x1),eta(x0)) = t(eta(x0),x1),
inference(symmetry,[status(thm)],[88]) ).
tff(155,plain,
product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))) = product(t(eta(x0),eta(x0)),t(eta(x0),x1)),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))) = t(eta(x0),product(eta(x0),x1)),
inference(transitivity,[status(thm)],[155,118]) ).
tff(157,plain,
product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))) = product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))) = product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
quotient(product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))),quotient(product(eta(x0),x1),eta(x0))) = quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))) = quotient(product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))),quotient(product(eta(x0),x1),eta(x0))),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
product(quotient(product(eta(x0),eta(x0)),eta(x0)),quotient(product(eta(x0),x1),eta(x0))) = product(t(eta(x0),eta(x0)),t(eta(x0),x1)),
inference(monotonicity,[status(thm)],[19,154]) ).
tff(162,plain,
product(quotient(product(eta(x0),eta(x0)),eta(x0)),quotient(product(eta(x0),x1),eta(x0))) = t(eta(x0),product(eta(x0),x1)),
inference(transitivity,[status(thm)],[161,118]) ).
tff(163,plain,
product(quotient(product(eta(x0),x2),eta(x0)),product(quotient(product(eta(x0),eta(x0)),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))) = product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))),
inference(monotonicity,[status(thm)],[128,162]) ).
tff(164,plain,
product(quotient(product(eta(x0),x2),eta(x0)),product(quotient(product(eta(x0),eta(x0)),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))) = product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),
inference(transitivity,[status(thm)],[163,158]) ).
tff(165,plain,
quotient(product(quotient(product(eta(x0),x2),eta(x0)),product(quotient(product(eta(x0),eta(x0)),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))) = quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0)))) = quotient(product(quotient(product(eta(x0),x2),eta(x0)),product(quotient(product(eta(x0),eta(x0)),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0)))) = quotient(product(quotient(product(eta(x0),x2),eta(x0)),product(quotient(product(eta(x0),eta(x0)),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),
inference(unit_resolution,[status(thm)],[166,56]) ).
tff(168,plain,
product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))) = product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),eta(x0)),
inference(monotonicity,[status(thm)],[28]) ).
tff(169,plain,
product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),eta(x0)) = product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),eta(x0))) = difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0)))),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
( ~ ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) )
| ( t(eta(x0),product(x1,x2)) = quotient(product(eta(x0),product(x1,x2)),eta(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
t(eta(x0),product(x1,x2)) = quotient(product(eta(x0),product(x1,x2)),eta(x0)),
inference(unit_resolution,[status(thm)],[171,16]) ).
tff(173,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(x1,x2)) = product(t(eta(x0),x1),t(eta(x0),x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
t(eta(x0),product(x1,x2)) = product(t(eta(x0),x1),t(eta(x0),x2)),
inference(unit_resolution,[status(thm)],[173,75]) ).
tff(175,plain,
product(t(eta(x0),x1),t(eta(x0),x2)) = t(eta(x0),product(x1,x2)),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))) = product(t(eta(x0),x1),t(eta(x0),x2)),
inference(monotonicity,[status(thm)],[154,128]) ).
tff(177,plain,
product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))) = quotient(product(eta(x0),product(x1,x2)),eta(x0)),
inference(transitivity,[status(thm)],[176,175,172]) ).
tff(178,plain,
product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),eta(x0)) = product(quotient(product(eta(x0),product(x1,x2)),eta(x0)),eta(x0)),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
product(quotient(product(eta(x0),product(x1,x2)),eta(x0)),eta(x0)) = product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),eta(x0)),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(eta(x0),product(x1,x2)),eta(x0)),eta(x0)) = product(eta(x0),product(x1,x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
product(quotient(product(eta(x0),product(x1,x2)),eta(x0)),eta(x0)) = product(eta(x0),product(x1,x2)),
inference(unit_resolution,[status(thm)],[180,7]) ).
tff(182,plain,
product(eta(x0),product(x1,x2)) = product(quotient(product(eta(x0),product(x1,x2)),eta(x0)),eta(x0)),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(product(eta(x0),x1),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))) = product(eta(x0),product(x1,x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(184,plain,
product(product(eta(x0),x1),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))) = product(eta(x0),product(x1,x2)),
inference(unit_resolution,[status(thm)],[183,47]) ).
tff(185,plain,
product(product(quotient(product(eta(x0),x1),eta(x0)),eta(x0)),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))) = product(product(eta(x0),x1),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))),
inference(monotonicity,[status(thm)],[35]) ).
tff(186,plain,
product(product(quotient(product(eta(x0),x1),eta(x0)),eta(x0)),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))) = product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),eta(x0)),
inference(transitivity,[status(thm)],[185,184,182,179]) ).
tff(187,plain,
difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),eta(x0)),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))) = difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),eta(x0))),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),eta(x0)),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))) = quotient(product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),eta(x0)),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))) = quotient(product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),
inference(unit_resolution,[status(thm)],[188,56]) ).
tff(190,plain,
quotient(product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))) = difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),eta(x0)),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
quotient(product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))) = quotient(product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))),quotient(product(eta(x0),x1),eta(x0))),
inference(transitivity,[status(thm)],[190,187,170,167,165,160]) ).
tff(192,plain,
product(quotient(product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),x1),eta(x0))) = product(quotient(product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),x1),eta(x0))),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
product(quotient(product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),x1),eta(x0))) = product(quotient(product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),x1),eta(x0))),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),x1),eta(x0))) = product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(195,plain,
product(quotient(product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),x1),eta(x0))) = product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))),
inference(unit_resolution,[status(thm)],[194,7]) ).
tff(196,plain,
product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))) = product(quotient(product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),x1),eta(x0))),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0)) = t(eta(x0),product(eta(x0),x1)),
inference(transitivity,[status(thm)],[146,145,142]) ).
tff(198,plain,
product(quotient(product(eta(x0),x2),eta(x0)),product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0))) = product(t(eta(x0),x2),t(eta(x0),product(eta(x0),x1))),
inference(monotonicity,[status(thm)],[128,197]) ).
tff(199,plain,
product(quotient(product(eta(x0),x2),eta(x0)),product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0))) = product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),
inference(transitivity,[status(thm)],[198,196,193,153]) ).
tff(200,plain,
quotient(product(quotient(product(eta(x0),x2),eta(x0)),product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0))),eta(x0)) = quotient(product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),eta(x0)),
inference(monotonicity,[status(thm)],[199]) ).
tff(201,plain,
quotient(product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),eta(x0)) = quotient(product(quotient(product(eta(x0),x2),eta(x0)),product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0))),eta(x0)),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
( ~ ! [B: $i,A: $i] : ( t(A,B) = quotient(product(A,B),A) )
| ( t(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))) = quotient(product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),eta(x0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(203,plain,
t(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))) = quotient(product(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),eta(x0)),
inference(unit_resolution,[status(thm)],[202,16]) ).
tff(204,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(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))) = product(t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(205,plain,
t(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))) = product(t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))),
inference(unit_resolution,[status(thm)],[204,75]) ).
tff(206,plain,
product(t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))) = t(eta(x0),product(difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))),quotient(product(eta(x0),x1),eta(x0)))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)) = product(t(eta(x0),x1),t(eta(x0),x2)),
inference(monotonicity,[status(thm)],[154]) ).
tff(208,plain,
product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)) = t(eta(x0),product(x1,x2)),
inference(transitivity,[status(thm)],[207,175]) ).
tff(209,plain,
product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2))) = product(t(eta(x0),eta(x0)),t(eta(x0),product(x1,x2))),
inference(monotonicity,[status(thm)],[208]) ).
tff(210,plain,
product(t(eta(x0),eta(x0)),t(eta(x0),product(x1,x2))) = product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2))),
inference(symmetry,[status(thm)],[209]) ).
tff(211,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(eta(x0),product(x1,x2))) = product(t(eta(x0),eta(x0)),t(eta(x0),product(x1,x2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(212,plain,
t(eta(x0),product(eta(x0),product(x1,x2))) = product(t(eta(x0),eta(x0)),t(eta(x0),product(x1,x2))),
inference(unit_resolution,[status(thm)],[211,75]) ).
tff(213,plain,
t(eta(x0),product(product(eta(x0),x1),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))) = t(eta(x0),product(eta(x0),product(x1,x2))),
inference(monotonicity,[status(thm)],[184]) ).
tff(214,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(product(eta(x0),x1),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))) = product(t(eta(x0),product(eta(x0),x1)),t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(215,plain,
t(eta(x0),product(product(eta(x0),x1),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))) = product(t(eta(x0),product(eta(x0),x1)),t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))),
inference(unit_resolution,[status(thm)],[214,75]) ).
tff(216,plain,
product(t(eta(x0),product(eta(x0),x1)),t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))) = t(eta(x0),product(product(eta(x0),x1),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))),
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
product(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))) = product(t(eta(x0),product(eta(x0),x1)),t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))),
inference(monotonicity,[status(thm)],[118]) ).
tff(218,plain,
product(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))) = product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2))),
inference(transitivity,[status(thm)],[217,216,213,212,210]) ).
tff(219,plain,
product(t(eta(x0),eta(x0)),t(eta(x0),x1)) = product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),
inference(symmetry,[status(thm)],[155]) ).
tff(220,plain,
difference(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),product(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))))) = difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),
inference(monotonicity,[status(thm)],[219,218]) ).
tff(221,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),product(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))))) = t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(222,plain,
difference(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),product(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))))) = t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))),
inference(unit_resolution,[status(thm)],[221,113]) ).
tff(223,plain,
t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))) = difference(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),product(product(t(eta(x0),eta(x0)),t(eta(x0),x1)),t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))))),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))) = difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),
inference(transitivity,[status(thm)],[223,220]) ).
tff(225,plain,
product(t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))) = product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))),
inference(monotonicity,[status(thm)],[224]) ).
tff(226,plain,
product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))) = product(t(eta(x0),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))) = quotient(product(quotient(product(eta(x0),x2),eta(x0)),product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0))),eta(x0)),
inference(transitivity,[status(thm)],[226,206,203,201]) ).
tff(228,plain,
quotient(product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))) = quotient(quotient(product(quotient(product(eta(x0),x2),eta(x0)),product(t(eta(x0),quotient(product(eta(x0),x1),eta(x0))),eta(x0))),eta(x0)),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))),
inference(monotonicity,[status(thm)],[227]) ).
tff(229,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))) = difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(230,plain,
quotient(product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))) = difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),
inference(unit_resolution,[status(thm)],[229,26]) ).
tff(231,plain,
difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))) = quotient(product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))),t(eta(x0),quotient(product(eta(x0),x1),eta(x0)))),
inference(symmetry,[status(thm)],[230]) ).
tff(232,plain,
quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),t(eta(x0),eta(x0))) = difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),
inference(symmetry,[status(thm)],[101]) ).
tff(233,plain,
quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))) = quotient(product(eta(x0),x2),eta(x0)),
inference(transitivity,[status(thm)],[91,232,231,228,151,148,115,106]) ).
tff(234,plain,
product(quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))) = product(quotient(product(eta(x0),x2),eta(x0)),eta(x0)),
inference(monotonicity,[status(thm)],[233,28]) ).
tff(235,plain,
product(quotient(product(eta(x0),x2),eta(x0)),eta(x0)) = product(quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
product(t(eta(x0),x2),t(eta(x0),eta(x0))) = product(quotient(product(eta(x0),x2),eta(x0)),eta(x0)),
inference(symmetry,[status(thm)],[129]) ).
tff(237,plain,
product(t(eta(x0),x2),t(eta(x0),eta(x0))) = product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),eta(x0)),
inference(transitivity,[status(thm)],[236,235,104]) ).
tff(238,plain,
product(quotient(product(eta(x0),x1),eta(x0)),product(t(eta(x0),x2),t(eta(x0),eta(x0)))) = product(quotient(product(eta(x0),x1),eta(x0)),product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),eta(x0))),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
product(quotient(product(eta(x0),x1),eta(x0)),product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),eta(x0))) = product(quotient(product(eta(x0),x1),eta(x0)),product(t(eta(x0),x2),t(eta(x0),eta(x0)))),
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
product(product(eta(x0),x1),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))) = product(product(quotient(product(eta(x0),x1),eta(x0)),eta(x0)),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))),
inference(symmetry,[status(thm)],[185]) ).
tff(241,plain,
product(eta(x0),product(x1,x2)) = product(product(eta(x0),x1),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))),
inference(symmetry,[status(thm)],[184]) ).
tff(242,plain,
product(eta(x0),product(x1,x2)) = product(product(quotient(product(eta(x0),x1),eta(x0)),eta(x0)),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2)))),
inference(transitivity,[status(thm)],[241,240]) ).
tff(243,plain,
difference(quotient(product(eta(x0),x1),eta(x0)),product(eta(x0),product(x1,x2))) = difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),eta(x0)),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))),
inference(monotonicity,[status(thm)],[242]) ).
tff(244,plain,
difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),eta(x0)),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))) = difference(quotient(product(eta(x0),x1),eta(x0)),product(eta(x0),product(x1,x2))),
inference(symmetry,[status(thm)],[243]) ).
tff(245,plain,
difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),eta(x0))) = difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),eta(x0)),difference(product(eta(x0),x1),product(eta(x0),product(x1,x2))))),
inference(symmetry,[status(thm)],[187]) ).
tff(246,plain,
difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0)))) = difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),eta(x0))),
inference(symmetry,[status(thm)],[170]) ).
tff(247,plain,
quotient(product(quotient(product(eta(x0),x2),eta(x0)),product(quotient(product(eta(x0),eta(x0)),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))) = difference(quotient(product(eta(x0),x1),eta(x0)),product(product(quotient(product(eta(x0),x1),eta(x0)),quotient(product(eta(x0),x2),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0)))),
inference(symmetry,[status(thm)],[167]) ).
tff(248,plain,
quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))) = quotient(product(quotient(product(eta(x0),x2),eta(x0)),product(quotient(product(eta(x0),eta(x0)),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),
inference(symmetry,[status(thm)],[165]) ).
tff(249,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))) = quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(250,plain,
product(quotient(quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))),quotient(product(eta(x0),eta(x0)),eta(x0))) = quotient(product(t(eta(x0),x2),product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0)))),quotient(product(eta(x0),x1),eta(x0))),
inference(unit_resolution,[status(thm)],[249,7]) ).
tff(251,plain,
product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),eta(x0)) = difference(quotient(product(eta(x0),x1),eta(x0)),product(eta(x0),product(x1,x2))),
inference(transitivity,[status(thm)],[103,250,248,247,246,245,244]) ).
tff(252,plain,
product(quotient(product(eta(x0),x1),eta(x0)),product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),eta(x0))) = product(quotient(product(eta(x0),x1),eta(x0)),difference(quotient(product(eta(x0),x1),eta(x0)),product(eta(x0),product(x1,x2)))),
inference(monotonicity,[status(thm)],[251]) ).
tff(253,plain,
product(quotient(product(eta(x0),x1),eta(x0)),difference(quotient(product(eta(x0),x1),eta(x0)),product(eta(x0),product(x1,x2)))) = product(quotient(product(eta(x0),x1),eta(x0)),product(difference(product(t(eta(x0),eta(x0)),quotient(product(eta(x0),x1),eta(x0))),product(t(eta(x0),eta(x0)),product(quotient(product(eta(x0),x1),eta(x0)),t(eta(x0),x2)))),eta(x0))),
inference(symmetry,[status(thm)],[252]) ).
tff(254,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(quotient(product(eta(x0),x1),eta(x0)),difference(quotient(product(eta(x0),x1),eta(x0)),product(eta(x0),product(x1,x2)))) = product(eta(x0),product(x1,x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(255,plain,
product(quotient(product(eta(x0),x1),eta(x0)),difference(quotient(product(eta(x0),x1),eta(x0)),product(eta(x0),product(x1,x2)))) = product(eta(x0),product(x1,x2)),
inference(unit_resolution,[status(thm)],[254,47]) ).
tff(256,plain,
product(eta(x0),product(x1,x2)) = product(quotient(product(eta(x0),x1),eta(x0)),difference(quotient(product(eta(x0),x1),eta(x0)),product(eta(x0),product(x1,x2)))),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
product(eta(x0),product(x1,x2)) = product(product(eta(x0),x1),x2),
inference(transitivity,[status(thm)],[256,253,239,90,84,81,77,68,9]) ).
tff(258,plain,
( ( product(eta(x0),product(x1,x2)) != product(product(eta(x0),x1),x2) )
<=> ( product(eta(x0),product(x1,x2)) != product(product(eta(x0),x1),x2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(259,axiom,
product(eta(x0),product(x1,x2)) != product(product(eta(x0),x1),x2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(260,plain,
product(eta(x0),product(x1,x2)) != product(product(eta(x0),x1),x2),
inference(modus_ponens,[status(thm)],[259,258]) ).
tff(261,plain,
$false,
inference(unit_resolution,[status(thm)],[260,257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP766-1 : TPTP v9.0.0. Released v4.1.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 17:05:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.23/1.41 % SZS status Unsatisfiable
% 1.23/1.41 % SZS output start Proof
% See solution above
% 1.23/1.45 % E exiting
%------------------------------------------------------------------------------