%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP777-10 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:08:39 AM UTC 2025
% Result : Unsatisfiable 228.49s 228.75s
% Output : Proof 228.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 102
% Syntax : Number of formulae : 523 ( 429 unt; 0 typ; 0 def)
% Number of atoms : 629 ( 622 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 184 ( 84 ~; 80 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 6 ( 6 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; 4 con; 0-3 aty)
% Number of variables : 416 ( 402 !; 0 ?; 416 :)
% Comments :
%------------------------------------------------------------------------------
tff(bigC_type,type,
bigC: ( $i * $i * $i ) > $i ).
tff(x0_type,type,
x0: $i ).
tff(c_type,type,
c: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(product_type,type,
product: ( $i * $i ) > $i ).
tff(quotient_type,type,
quotient: ( $i * $i ) > $i ).
tff(difference_type,type,
difference: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( bigC(A,B,C) = product(product(A,B),product(C,A)) )
<=> ( bigC(A,B,C) = product(product(A,B),product(C,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( bigC(A,B,C) = product(product(A,B),product(C,A)) )
<=> ! [B: $i,A: $i,C: $i] : ( bigC(A,B,C) = product(product(A,B),product(C,A)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( bigC(A,B,C) = product(product(A,B),product(C,A)) )
<=> ! [B: $i,A: $i,C: $i] : ( bigC(A,B,C) = product(product(A,B),product(C,A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( bigC(A,B,C) = product(product(A,B),product(C,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( bigC(A,B,C) = product(product(A,B),product(C,A)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( bigC(A,B,C) = product(product(A,B),product(C,A)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( bigC(A,B,C) = product(product(A,B),product(C,A)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( bigC(A,B,C) = product(product(A,B),product(C,A)) )
| ( bigC(c,c,x0) = product(product(c,c),product(x0,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
bigC(c,c,x0) = product(product(c,c),product(x0,c)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
product(product(c,c),product(x0,c)) = bigC(c,c,x0),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i] :
refl(( ( quotient(product(A,B),B) = A )
<=> ( quotient(product(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(12,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)],[11]) ).
tff(13,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(14,axiom,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
tff(15,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(product(c,c),product(x0,c)),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))) = product(product(c,c),product(x0,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
quotient(product(product(product(c,c),product(x0,c)),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))) = product(product(c,c),product(x0,c)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
^ [B: $i,A: $i] :
refl(( ( difference(A,product(A,B)) = B )
<=> ( difference(A,product(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(21,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)],[20]) ).
tff(22,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(23,axiom,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
tff(24,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(a,c),product(product(a,c),product(product(c,product(c,c)),product(c,product(b,b))))) = product(product(c,product(c,c)),product(c,product(b,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
difference(product(a,c),product(product(a,c),product(product(c,product(c,c)),product(c,product(b,b))))) = product(product(c,product(c,c)),product(c,product(b,b))),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
^ [A: $i] :
refl(( ( product(A,A) = A )
<=> ( product(A,A) = A ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [A: $i] : ( product(A,A) = A )
<=> ! [A: $i] : ( product(A,A) = A ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [A: $i] : ( product(A,A) = A )
<=> ! [A: $i] : ( product(A,A) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [A: $i] : ( product(A,A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
tff(33,plain,
! [A: $i] : ( product(A,A) = A ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [A: $i] : ( product(A,A) = A ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [A: $i] : ( product(A,A) = A ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [A: $i] : ( product(A,A) = A )
| ( product(c,c) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
product(c,c) = c,
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
product(product(c,c),product(product(c,c),product(b,b))) = product(c,product(product(c,c),product(b,b))),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
<=> ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
<=> ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
<=> ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
tff(43,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(c,c),product(product(c,c),product(b,b))) = product(product(c,product(c,c)),product(c,product(b,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
product(product(c,c),product(product(c,c),product(b,b))) = product(product(c,product(c,c)),product(c,product(b,b))),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
product(product(c,product(c,c)),product(c,product(b,b))) = product(product(c,c),product(product(c,c),product(b,b))),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
product(product(c,product(c,c)),product(c,product(b,b))) = product(c,product(product(c,c),product(b,b))),
inference(transitivity,[status(thm)],[48,38]) ).
tff(50,plain,
( ~ ! [A: $i] : ( product(A,A) = A )
| ( product(product(a,c),product(a,c)) = product(a,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
product(product(a,c),product(a,c)) = product(a,c),
inference(unit_resolution,[status(thm)],[50,35]) ).
tff(52,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(a,c),product(a,c)) = product(product(a,a),product(c,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
product(product(a,c),product(a,c)) = product(product(a,a),product(c,c)),
inference(unit_resolution,[status(thm)],[52,45]) ).
tff(54,plain,
product(product(a,a),product(c,c)) = product(product(a,c),product(a,c)),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
product(product(a,a),product(c,c)) = product(a,c),
inference(transitivity,[status(thm)],[54,51]) ).
tff(56,plain,
product(product(a,c),product(product(a,a),product(c,c))) = product(product(a,c),product(a,c)),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
product(product(a,c),product(a,c)) = product(product(a,c),product(product(a,a),product(c,c))),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
product(a,c) = product(product(a,c),product(a,c)),
inference(symmetry,[status(thm)],[51]) ).
tff(59,plain,
product(a,c) = product(product(a,c),product(product(a,a),product(c,c))),
inference(transitivity,[status(thm)],[58,57]) ).
tff(60,plain,
product(product(a,c),product(product(c,product(c,c)),product(c,product(b,b)))) = product(product(product(a,c),product(product(a,a),product(c,c))),product(c,product(product(c,c),product(b,b)))),
inference(monotonicity,[status(thm)],[59,49]) ).
tff(61,plain,
product(product(product(a,c),product(product(a,a),product(c,c))),product(c,product(product(c,c),product(b,b)))) = product(product(a,c),product(product(c,product(c,c)),product(c,product(b,b)))),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),c),product(product(product(a,a),product(c,c)),product(product(c,c),product(b,b)))) = product(product(product(a,c),product(product(a,a),product(c,c))),product(c,product(product(c,c),product(b,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
product(product(product(a,c),c),product(product(product(a,a),product(c,c)),product(product(c,c),product(b,b)))) = product(product(product(a,c),product(product(a,a),product(c,c))),product(c,product(product(c,c),product(b,b)))),
inference(unit_resolution,[status(thm)],[62,45]) ).
tff(64,plain,
( ( product(product(a,c),product(c,b)) = product(a,b) )
<=> ( product(product(a,c),product(c,b)) = product(a,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
product(product(a,c),product(c,b)) = product(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
tff(66,plain,
product(product(a,c),product(c,b)) = product(a,b),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
product(a,b) = product(product(a,c),product(c,b)),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
product(product(a,b),product(a,b)) = product(product(product(a,c),product(c,b)),product(product(a,c),product(c,b))),
inference(monotonicity,[status(thm)],[67,67]) ).
tff(69,plain,
product(product(product(a,c),product(c,b)),product(product(a,c),product(c,b))) = product(product(a,b),product(a,b)),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),product(c,b)),product(product(a,c),product(c,b))) = product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
product(product(product(a,c),product(c,b)),product(product(a,c),product(c,b))) = product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b))),
inference(unit_resolution,[status(thm)],[70,45]) ).
tff(72,plain,
product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b))) = product(product(product(a,c),product(c,b)),product(product(a,c),product(c,b))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(c,b),product(c,b)) = product(product(c,c),product(b,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
product(product(c,b),product(c,b)) = product(product(c,c),product(b,b)),
inference(unit_resolution,[status(thm)],[73,45]) ).
tff(75,plain,
product(product(c,c),product(b,b)) = product(product(c,b),product(c,b)),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
product(product(product(a,a),product(c,c)),product(product(c,c),product(b,b))) = product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b))),
inference(monotonicity,[status(thm)],[54,75]) ).
tff(77,plain,
product(product(product(a,a),product(c,c)),product(product(c,c),product(b,b))) = product(product(a,b),product(a,b)),
inference(transitivity,[status(thm)],[76,72,69]) ).
tff(78,plain,
product(product(product(a,c),c),product(product(product(a,a),product(c,c)),product(product(c,c),product(b,b)))) = product(product(product(a,c),c),product(product(a,b),product(a,b))),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
product(product(product(a,c),c),product(product(a,b),product(a,b))) = product(product(product(a,c),c),product(product(product(a,a),product(c,c)),product(product(c,c),product(b,b)))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(a,b),product(a,b)) = product(product(a,a),product(b,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
product(product(a,b),product(a,b)) = product(product(a,a),product(b,b)),
inference(unit_resolution,[status(thm)],[80,45]) ).
tff(82,plain,
product(product(product(a,c),c),product(product(a,b),product(a,b))) = product(product(product(a,c),c),product(product(a,a),product(b,b))),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
product(product(product(a,c),c),product(product(a,a),product(b,b))) = product(product(product(a,c),c),product(product(a,b),product(a,b))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),c),product(product(a,a),product(b,b))) = product(product(product(a,c),product(a,a)),product(c,product(b,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
product(product(product(a,c),c),product(product(a,a),product(b,b))) = product(product(product(a,c),product(a,a)),product(c,product(b,b))),
inference(unit_resolution,[status(thm)],[84,45]) ).
tff(86,plain,
product(product(product(a,c),product(a,a)),product(c,product(b,b))) = product(product(product(a,c),c),product(product(a,a),product(b,b))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
c = product(c,c),
inference(symmetry,[status(thm)],[37]) ).
tff(88,plain,
product(c,product(b,b)) = product(product(c,c),product(b,b)),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(a,c),product(a,a)) = product(product(a,a),product(c,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
product(product(a,c),product(a,a)) = product(product(a,a),product(c,a)),
inference(unit_resolution,[status(thm)],[89,45]) ).
tff(91,plain,
product(product(product(a,c),product(a,a)),product(c,product(b,b))) = product(product(product(a,a),product(c,a)),product(product(c,c),product(b,b))),
inference(monotonicity,[status(thm)],[90,88]) ).
tff(92,plain,
product(product(product(a,a),product(c,a)),product(product(c,c),product(b,b))) = product(product(product(a,c),product(a,a)),product(c,product(b,b))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,a),product(c,c)),product(product(c,a),product(b,b))) = product(product(product(a,a),product(c,a)),product(product(c,c),product(b,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
product(product(product(a,a),product(c,c)),product(product(c,a),product(b,b))) = product(product(product(a,a),product(c,a)),product(product(c,c),product(b,b))),
inference(unit_resolution,[status(thm)],[93,45]) ).
tff(95,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(c,b),product(a,b)) = product(product(c,a),product(b,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
product(product(c,b),product(a,b)) = product(product(c,a),product(b,b)),
inference(unit_resolution,[status(thm)],[95,45]) ).
tff(97,plain,
product(product(c,a),product(b,b)) = product(product(c,b),product(a,b)),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
product(product(product(a,a),product(c,c)),product(product(c,a),product(b,b))) = product(product(product(a,a),product(c,c)),product(product(c,b),product(a,b))),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
product(product(product(a,a),product(c,c)),product(product(c,b),product(a,b))) = product(product(product(a,a),product(c,c)),product(product(c,a),product(b,b))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
product(product(product(a,a),product(c,c)),product(product(c,b),product(a,b))) = product(product(product(a,c),product(a,c)),product(product(c,b),product(a,b))),
inference(monotonicity,[status(thm)],[54]) ).
tff(101,plain,
product(product(product(a,c),product(a,c)),product(product(c,b),product(a,b))) = product(product(product(a,a),product(c,c)),product(product(c,b),product(a,b))),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),product(a,c)),product(product(c,b),product(a,b))) = product(product(product(a,c),product(c,b)),product(product(a,c),product(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,plain,
product(product(product(a,c),product(a,c)),product(product(c,b),product(a,b))) = product(product(product(a,c),product(c,b)),product(product(a,c),product(a,b))),
inference(unit_resolution,[status(thm)],[102,45]) ).
tff(104,plain,
product(product(product(a,c),product(c,b)),product(product(a,c),product(a,b))) = product(product(product(a,c),product(a,c)),product(product(c,b),product(a,b))),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(a,c),product(product(a,c),product(c,b))) = product(product(a,product(a,c)),product(c,product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
product(product(a,c),product(product(a,c),product(c,b))) = product(product(a,product(a,c)),product(c,product(c,b))),
inference(unit_resolution,[status(thm)],[105,45]) ).
tff(107,plain,
product(product(a,c),product(a,b)) = product(product(a,c),product(product(a,c),product(c,b))),
inference(monotonicity,[status(thm)],[67]) ).
tff(108,plain,
product(product(a,c),product(a,b)) = product(product(a,product(a,c)),product(c,product(c,b))),
inference(transitivity,[status(thm)],[107,106]) ).
tff(109,plain,
( ~ ! [A: $i] : ( product(A,A) = A )
| ( product(product(a,b),product(a,b)) = product(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
product(product(a,b),product(a,b)) = product(a,b),
inference(unit_resolution,[status(thm)],[109,35]) ).
tff(111,plain,
product(a,b) = product(product(a,b),product(a,b)),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
product(product(a,c),product(c,b)) = product(product(a,b),product(a,b)),
inference(transitivity,[status(thm)],[66,111]) ).
tff(113,plain,
product(product(product(a,c),product(c,b)),product(product(a,c),product(a,b))) = product(product(product(a,b),product(a,b)),product(product(a,product(a,c)),product(c,product(c,b)))),
inference(monotonicity,[status(thm)],[112,108]) ).
tff(114,plain,
product(product(product(a,b),product(a,b)),product(product(a,product(a,c)),product(c,product(c,b)))) = product(product(product(a,c),product(c,b)),product(product(a,c),product(a,b))),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
product(product(product(product(a,a),product(c,c)),product(product(c,c),product(b,b))),product(product(a,product(a,c)),product(c,product(c,b)))) = product(product(product(a,b),product(a,b)),product(product(a,product(a,c)),product(c,product(c,b)))),
inference(monotonicity,[status(thm)],[77]) ).
tff(116,plain,
product(product(product(product(a,a),product(c,c)),product(product(c,c),product(b,b))),product(product(a,c),product(a,b))) = product(product(product(product(a,a),product(c,c)),product(product(c,c),product(b,b))),product(product(a,product(a,c)),product(c,product(c,b)))),
inference(monotonicity,[status(thm)],[108]) ).
tff(117,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(product(a,a),product(c,c)),product(product(c,c),product(b,b))),product(product(a,c),product(a,b))) = product(product(product(product(a,a),product(c,c)),product(a,c)),product(product(product(c,c),product(b,b)),product(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
product(product(product(product(a,a),product(c,c)),product(product(c,c),product(b,b))),product(product(a,c),product(a,b))) = product(product(product(product(a,a),product(c,c)),product(a,c)),product(product(product(c,c),product(b,b)),product(a,b))),
inference(unit_resolution,[status(thm)],[117,45]) ).
tff(119,plain,
product(product(product(product(a,a),product(c,c)),product(a,c)),product(product(product(c,c),product(b,b)),product(a,b))) = product(product(product(product(a,a),product(c,c)),product(product(c,c),product(b,b))),product(product(a,c),product(a,b))),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
( ~ ! [A: $i] : ( product(A,A) = A )
| ( product(product(c,b),product(c,b)) = product(c,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
product(product(c,b),product(c,b)) = product(c,b),
inference(unit_resolution,[status(thm)],[120,35]) ).
tff(122,plain,
product(product(c,c),product(b,b)) = product(c,b),
inference(transitivity,[status(thm)],[75,121]) ).
tff(123,plain,
product(product(product(c,c),product(b,b)),product(a,b)) = product(product(c,b),product(product(a,c),product(c,b))),
inference(monotonicity,[status(thm)],[122,67]) ).
tff(124,plain,
product(product(c,b),product(product(a,c),product(c,b))) = product(product(product(c,c),product(b,b)),product(a,b)),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
product(product(c,b),product(product(a,c),product(c,b))) = product(product(c,b),product(product(a,b),product(a,b))),
inference(monotonicity,[status(thm)],[112]) ).
tff(126,plain,
product(product(c,b),product(product(a,b),product(a,b))) = product(product(c,b),product(product(a,c),product(c,b))),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
product(c,b) = product(product(c,b),product(c,b)),
inference(symmetry,[status(thm)],[121]) ).
tff(128,plain,
product(c,b) = product(product(c,c),product(b,b)),
inference(transitivity,[status(thm)],[127,74]) ).
tff(129,plain,
product(product(c,b),product(product(a,b),product(a,b))) = product(product(product(c,c),product(b,b)),product(product(a,b),product(a,b))),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
product(product(product(c,c),product(b,b)),product(product(a,b),product(a,b))) = product(product(c,b),product(product(a,b),product(a,b))),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(c,c),product(b,b)),product(product(a,b),product(a,b))) = product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(132,plain,
product(product(product(c,c),product(b,b)),product(product(a,b),product(a,b))) = product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))),
inference(unit_resolution,[status(thm)],[131,45]) ).
tff(133,plain,
product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))) = product(product(product(c,c),product(b,b)),product(product(a,b),product(a,b))),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))) = product(product(product(c,c),product(b,b)),product(a,b)),
inference(transitivity,[status(thm)],[133,130,126,124]) ).
tff(135,plain,
product(product(product(a,a),product(c,c)),product(a,c)) = product(product(a,c),product(a,c)),
inference(monotonicity,[status(thm)],[55]) ).
tff(136,plain,
product(product(a,c),product(a,c)) = product(product(product(a,a),product(c,c)),product(a,c)),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
product(a,c) = product(product(product(a,a),product(c,c)),product(a,c)),
inference(transitivity,[status(thm)],[58,136]) ).
tff(138,plain,
product(product(a,c),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))) = product(product(product(product(a,a),product(c,c)),product(a,c)),product(product(product(c,c),product(b,b)),product(a,b))),
inference(monotonicity,[status(thm)],[137,134]) ).
tff(139,plain,
product(product(a,c),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))) = product(product(a,c),product(product(c,product(c,c)),product(c,product(b,b)))),
inference(transitivity,[status(thm)],[138,119,116,115,114,104,101,99,94,92,86,83,79,63,61]) ).
tff(140,plain,
difference(product(a,c),product(product(a,c),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))) = difference(product(a,c),product(product(a,c),product(product(c,product(c,c)),product(c,product(b,b))))),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(a,c),product(product(a,c),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))) = product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
difference(product(a,c),product(product(a,c),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))) = product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))),
inference(unit_resolution,[status(thm)],[141,26]) ).
tff(143,plain,
product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))) = difference(product(a,c),product(product(a,c),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))) = product(product(c,product(c,c)),product(c,product(b,b))),
inference(transitivity,[status(thm)],[143,140,28]) ).
tff(145,plain,
product(c,product(product(c,c),product(b,b))) = product(c,product(c,b)),
inference(monotonicity,[status(thm)],[122]) ).
tff(146,plain,
product(product(c,product(c,c)),product(c,product(b,b))) = product(c,product(c,b)),
inference(transitivity,[status(thm)],[48,38,145]) ).
tff(147,plain,
product(product(a,b),product(x0,a)) = product(product(product(a,b),product(a,b)),product(x0,a)),
inference(monotonicity,[status(thm)],[111]) ).
tff(148,plain,
product(product(product(a,b),product(a,b)),product(x0,a)) = product(product(a,b),product(x0,a)),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,b),product(a,b)),product(x0,a)) = product(product(product(a,b),x0),product(product(a,b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
product(product(product(a,b),product(a,b)),product(x0,a)) = product(product(product(a,b),x0),product(product(a,b),a)),
inference(unit_resolution,[status(thm)],[149,45]) ).
tff(151,plain,
product(product(product(a,b),x0),product(product(a,b),a)) = product(product(product(a,b),product(a,b)),product(x0,a)),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
product(product(product(a,b),x0),product(product(a,b),a)) = product(product(a,b),product(x0,a)),
inference(transitivity,[status(thm)],[151,148]) ).
tff(153,plain,
product(product(product(product(a,b),x0),product(product(a,b),a)),product(product(c,product(c,c)),product(c,product(b,b)))) = product(product(product(a,b),product(x0,a)),product(c,product(c,b))),
inference(monotonicity,[status(thm)],[152,146]) ).
tff(154,plain,
product(product(product(a,b),product(x0,a)),product(c,product(c,b))) = product(product(product(product(a,b),x0),product(product(a,b),a)),product(product(c,product(c,c)),product(c,product(b,b)))),
inference(symmetry,[status(thm)],[153]) ).
tff(155,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,b),product(x0,a)),product(c,product(c,b))) = product(product(product(a,b),c),product(product(x0,a),product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
product(product(product(a,b),product(x0,a)),product(c,product(c,b))) = product(product(product(a,b),c),product(product(x0,a),product(c,b))),
inference(unit_resolution,[status(thm)],[155,45]) ).
tff(157,plain,
product(product(product(a,b),c),product(product(x0,a),product(c,b))) = product(product(product(a,b),product(x0,a)),product(c,product(c,b))),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(a,b),product(c,c)) = product(product(a,c),product(b,c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
product(product(a,b),product(c,c)) = product(product(a,c),product(b,c)),
inference(unit_resolution,[status(thm)],[158,45]) ).
tff(160,plain,
product(product(a,b),product(c,c)) = product(product(a,b),c),
inference(monotonicity,[status(thm)],[37]) ).
tff(161,plain,
product(product(a,b),c) = product(product(a,b),product(c,c)),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
product(product(a,b),c) = product(product(a,c),product(b,c)),
inference(transitivity,[status(thm)],[161,159]) ).
tff(163,plain,
product(product(product(a,b),c),product(product(x0,a),product(c,b))) = product(product(product(a,c),product(b,c)),product(product(x0,a),product(c,b))),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
product(product(product(a,c),product(b,c)),product(product(x0,a),product(c,b))) = product(product(product(a,b),c),product(product(x0,a),product(c,b))),
inference(symmetry,[status(thm)],[163]) ).
tff(165,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),product(b,c)),product(product(x0,a),product(c,b))) = product(product(product(a,c),product(x0,a)),product(product(b,c),product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(166,plain,
product(product(product(a,c),product(b,c)),product(product(x0,a),product(c,b))) = product(product(product(a,c),product(x0,a)),product(product(b,c),product(c,b))),
inference(unit_resolution,[status(thm)],[165,45]) ).
tff(167,plain,
product(product(product(a,c),product(x0,a)),product(product(b,c),product(c,b))) = product(product(product(a,c),product(b,c)),product(product(x0,a),product(c,b))),
inference(symmetry,[status(thm)],[166]) ).
tff(168,plain,
( ~ ! [A: $i] : ( product(A,A) = A )
| ( product(a,a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(169,plain,
product(a,a) = a,
inference(unit_resolution,[status(thm)],[168,35]) ).
tff(170,plain,
a = product(a,a),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
product(product(a,c),a) = product(product(a,c),product(a,a)),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
product(product(a,c),product(a,a)) = product(product(a,c),a),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
product(a,c) = product(product(a,a),product(c,c)),
inference(transitivity,[status(thm)],[58,53]) ).
tff(174,plain,
product(product(a,c),product(a,a)) = product(product(product(a,a),product(c,c)),product(a,a)),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
product(product(product(a,a),product(c,c)),product(a,a)) = product(product(a,c),product(a,a)),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,a),product(c,c)),product(a,a)) = product(product(product(a,a),a),product(product(c,c),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
product(product(product(a,a),product(c,c)),product(a,a)) = product(product(product(a,a),a),product(product(c,c),a)),
inference(unit_resolution,[status(thm)],[176,45]) ).
tff(178,plain,
product(product(product(a,a),a),product(product(c,c),a)) = product(product(product(a,a),product(c,c)),product(a,a)),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
product(product(product(a,a),a),product(product(c,c),a)) = product(product(a,c),a),
inference(transitivity,[status(thm)],[178,175,172]) ).
tff(180,plain,
product(product(product(a,c),x0),product(product(product(a,a),a),product(product(c,c),a))) = product(product(product(a,c),x0),product(product(a,c),a)),
inference(monotonicity,[status(thm)],[179]) ).
tff(181,plain,
product(product(product(a,c),x0),product(product(a,c),a)) = product(product(product(a,c),x0),product(product(product(a,a),a),product(product(c,c),a))),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),product(a,c)),product(x0,a)) = product(product(product(a,c),x0),product(product(a,c),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(183,plain,
product(product(product(a,c),product(a,c)),product(x0,a)) = product(product(product(a,c),x0),product(product(a,c),a)),
inference(unit_resolution,[status(thm)],[182,45]) ).
tff(184,plain,
product(product(product(a,c),product(a,c)),product(x0,a)) = product(product(product(a,a),product(c,c)),product(x0,a)),
inference(monotonicity,[status(thm)],[53]) ).
tff(185,plain,
product(product(product(a,a),product(c,c)),product(x0,a)) = product(product(product(a,c),product(a,c)),product(x0,a)),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
product(product(product(a,a),product(c,c)),product(x0,a)) = product(product(a,c),product(x0,a)),
inference(monotonicity,[status(thm)],[55]) ).
tff(187,plain,
product(product(a,c),product(x0,a)) = product(product(product(a,a),product(c,c)),product(x0,a)),
inference(symmetry,[status(thm)],[186]) ).
tff(188,plain,
product(product(a,c),product(x0,a)) = product(product(product(a,c),x0),product(product(product(a,a),a),product(product(c,c),a))),
inference(transitivity,[status(thm)],[187,185,183,181]) ).
tff(189,plain,
product(product(product(a,c),product(x0,a)),product(product(b,c),product(c,b))) = product(product(product(product(a,c),x0),product(product(product(a,a),a),product(product(c,c),a))),product(product(b,c),product(c,b))),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,plain,
product(product(product(product(a,c),x0),product(product(product(a,a),a),product(product(c,c),a))),product(product(b,c),product(c,b))) = product(product(product(a,c),product(x0,a)),product(product(b,c),product(c,b))),
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(product(a,c),x0),product(b,c)),product(product(product(product(a,a),a),product(product(c,c),a)),product(c,b))) = product(product(product(product(a,c),x0),product(product(product(a,a),a),product(product(c,c),a))),product(product(b,c),product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
product(product(product(product(a,c),x0),product(b,c)),product(product(product(product(a,a),a),product(product(c,c),a)),product(c,b))) = product(product(product(product(a,c),x0),product(product(product(a,a),a),product(product(c,c),a))),product(product(b,c),product(c,b))),
inference(unit_resolution,[status(thm)],[191,45]) ).
tff(193,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(product(a,c),a),product(product(c,b),c)),product(product(a,product(a,c)),product(b,product(c,b)))) = product(product(product(product(a,c),a),product(a,product(a,c))),product(product(product(c,b),c),product(b,product(c,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(194,plain,
product(product(product(product(a,c),a),product(product(c,b),c)),product(product(a,product(a,c)),product(b,product(c,b)))) = product(product(product(product(a,c),a),product(a,product(a,c))),product(product(product(c,b),c),product(b,product(c,b)))),
inference(unit_resolution,[status(thm)],[193,45]) ).
tff(195,plain,
product(product(a,b),product(product(a,c),product(c,b))) = product(product(product(a,c),product(c,b)),product(product(a,c),product(c,b))),
inference(monotonicity,[status(thm)],[67]) ).
tff(196,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(a,b),product(product(a,c),product(c,b))) = product(product(a,product(a,c)),product(b,product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(197,plain,
product(product(a,b),product(product(a,c),product(c,b))) = product(product(a,product(a,c)),product(b,product(c,b))),
inference(unit_resolution,[status(thm)],[196,45]) ).
tff(198,plain,
product(product(a,product(a,c)),product(b,product(c,b))) = product(product(a,b),product(product(a,c),product(c,b))),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
product(product(a,product(a,c)),product(b,product(c,b))) = product(product(a,b),product(a,b)),
inference(transitivity,[status(thm)],[198,195,69]) ).
tff(200,plain,
product(product(a,b),product(a,c)) = product(product(product(a,c),product(c,b)),product(a,c)),
inference(monotonicity,[status(thm)],[67]) ).
tff(201,plain,
product(product(product(a,c),product(c,b)),product(a,c)) = product(product(a,b),product(a,c)),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),product(c,b)),product(a,c)) = product(product(product(a,c),a),product(product(c,b),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(203,plain,
product(product(product(a,c),product(c,b)),product(a,c)) = product(product(product(a,c),a),product(product(c,b),c)),
inference(unit_resolution,[status(thm)],[202,45]) ).
tff(204,plain,
product(product(product(a,c),a),product(product(c,b),c)) = product(product(product(a,c),product(c,b)),product(a,c)),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
product(product(product(a,c),a),product(product(c,b),c)) = product(product(a,b),product(a,c)),
inference(transitivity,[status(thm)],[204,201]) ).
tff(206,plain,
product(product(product(product(a,c),a),product(product(c,b),c)),product(product(a,product(a,c)),product(b,product(c,b)))) = product(product(product(a,b),product(a,c)),product(product(a,b),product(a,b))),
inference(monotonicity,[status(thm)],[205,199]) ).
tff(207,plain,
product(product(product(a,b),product(a,c)),product(product(a,b),product(a,b))) = product(product(product(product(a,c),a),product(product(c,b),c)),product(product(a,product(a,c)),product(b,product(c,b)))),
inference(symmetry,[status(thm)],[206]) ).
tff(208,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,b),product(a,b)),product(product(a,c),product(a,b))) = product(product(product(a,b),product(a,c)),product(product(a,b),product(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(209,plain,
product(product(product(a,b),product(a,b)),product(product(a,c),product(a,b))) = product(product(product(a,b),product(a,c)),product(product(a,b),product(a,b))),
inference(unit_resolution,[status(thm)],[208,45]) ).
tff(210,plain,
product(product(product(a,b),product(a,b)),product(product(a,c),product(a,b))) = product(product(product(a,b),product(a,b)),product(product(a,product(a,c)),product(c,product(c,b)))),
inference(monotonicity,[status(thm)],[108]) ).
tff(211,plain,
product(product(product(a,b),product(a,b)),product(product(a,product(a,c)),product(c,product(c,b)))) = product(product(product(a,b),product(a,b)),product(product(a,c),product(a,b))),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
product(product(product(a,a),product(c,a)),product(product(c,c),product(b,b))) = product(product(product(a,a),product(c,c)),product(product(c,a),product(b,b))),
inference(symmetry,[status(thm)],[94]) ).
tff(213,plain,
product(product(product(a,a),a),product(product(c,c),a)) = product(product(a,a),product(c,a)),
inference(transitivity,[status(thm)],[178,175,90]) ).
tff(214,plain,
product(product(product(product(a,a),a),product(product(c,c),a)),product(c,b)) = product(product(product(a,a),product(c,a)),product(product(c,c),product(b,b))),
inference(monotonicity,[status(thm)],[213,128]) ).
tff(215,plain,
product(product(product(product(a,a),a),product(product(c,c),a)),product(c,b)) = product(product(product(product(a,c),a),product(a,product(a,c))),product(product(product(c,b),c),product(b,product(c,b)))),
inference(transitivity,[status(thm)],[214,212,98,100,103,113,211,209,207,194]) ).
tff(216,plain,
product(product(product(product(a,c),x0),product(b,c)),product(product(product(product(a,a),a),product(product(c,c),a)),product(c,b))) = product(product(product(product(a,c),x0),product(b,c)),product(product(product(product(a,c),a),product(a,product(a,c))),product(product(product(c,b),c),product(b,product(c,b))))),
inference(monotonicity,[status(thm)],[215]) ).
tff(217,plain,
product(product(product(product(a,c),x0),product(b,c)),product(product(product(product(a,c),a),product(a,product(a,c))),product(product(product(c,b),c),product(b,product(c,b))))) = product(product(product(product(a,c),x0),product(b,c)),product(product(product(product(a,a),a),product(product(c,c),a)),product(c,b))),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(a,c),product(a,b)) = product(product(a,a),product(c,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(219,plain,
product(product(a,c),product(a,b)) = product(product(a,a),product(c,b)),
inference(unit_resolution,[status(thm)],[218,45]) ).
tff(220,plain,
product(product(a,a),product(c,b)) = product(product(a,c),product(a,b)),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
product(product(a,a),product(c,b)) = product(product(a,product(a,c)),product(c,product(c,b))),
inference(transitivity,[status(thm)],[220,107,106]) ).
tff(222,plain,
product(product(a,a),product(b,b)) = product(product(a,b),product(a,b)),
inference(symmetry,[status(thm)],[81]) ).
tff(223,plain,
product(product(product(a,a),product(b,b)),product(product(a,a),product(c,b))) = product(product(product(a,b),product(a,b)),product(product(a,product(a,c)),product(c,product(c,b)))),
inference(monotonicity,[status(thm)],[222,221]) ).
tff(224,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,a),product(b,b)),product(product(a,a),product(c,b))) = product(product(product(a,a),product(a,a)),product(product(b,b),product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(225,plain,
product(product(product(a,a),product(b,b)),product(product(a,a),product(c,b))) = product(product(product(a,a),product(a,a)),product(product(b,b),product(c,b))),
inference(unit_resolution,[status(thm)],[224,45]) ).
tff(226,plain,
product(product(product(a,a),product(a,a)),product(product(b,b),product(c,b))) = product(product(product(a,a),product(b,b)),product(product(a,a),product(c,b))),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
product(product(b,b),product(c,b)) = product(product(b,b),product(product(c,c),product(b,b))),
inference(monotonicity,[status(thm)],[128]) ).
tff(228,plain,
product(product(b,b),product(product(c,c),product(b,b))) = product(product(b,b),product(c,b)),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(b,b),product(product(c,c),product(b,b))) = product(product(b,product(c,c)),product(b,product(b,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(230,plain,
product(product(b,b),product(product(c,c),product(b,b))) = product(product(b,product(c,c)),product(b,product(b,b))),
inference(unit_resolution,[status(thm)],[229,45]) ).
tff(231,plain,
product(product(b,product(c,c)),product(b,product(b,b))) = product(product(b,b),product(product(c,c),product(b,b))),
inference(symmetry,[status(thm)],[230]) ).
tff(232,plain,
product(product(b,product(c,c)),product(b,product(b,b))) = product(product(b,b),product(c,b)),
inference(transitivity,[status(thm)],[231,228]) ).
tff(233,plain,
product(product(a,a),product(a,a)) = product(a,a),
inference(monotonicity,[status(thm)],[169,169]) ).
tff(234,plain,
product(a,a) = product(product(a,a),product(a,a)),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
a = product(product(a,a),product(a,a)),
inference(transitivity,[status(thm)],[170,234]) ).
tff(236,plain,
product(a,product(product(b,product(c,c)),product(b,product(b,b)))) = product(product(product(a,a),product(a,a)),product(product(b,b),product(c,b))),
inference(monotonicity,[status(thm)],[235,232]) ).
tff(237,plain,
product(a,product(product(b,product(c,c)),product(b,product(b,b)))) = product(product(product(product(a,c),a),product(a,product(a,c))),product(product(product(c,b),c),product(b,product(c,b)))),
inference(transitivity,[status(thm)],[236,226,223,211,209,207,194]) ).
tff(238,plain,
product(product(product(product(a,c),x0),product(b,c)),product(a,product(product(b,product(c,c)),product(b,product(b,b))))) = product(product(product(product(a,c),x0),product(b,c)),product(product(product(product(a,c),a),product(a,product(a,c))),product(product(product(c,b),c),product(b,product(c,b))))),
inference(monotonicity,[status(thm)],[237]) ).
tff(239,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(product(a,c),x0),a),product(product(b,c),product(product(b,product(c,c)),product(b,product(b,b))))) = product(product(product(product(a,c),x0),product(b,c)),product(a,product(product(b,product(c,c)),product(b,product(b,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(240,plain,
product(product(product(product(a,c),x0),a),product(product(b,c),product(product(b,product(c,c)),product(b,product(b,b))))) = product(product(product(product(a,c),x0),product(b,c)),product(a,product(product(b,product(c,c)),product(b,product(b,b))))),
inference(unit_resolution,[status(thm)],[239,45]) ).
tff(241,plain,
( ~ ! [A: $i] : ( product(A,A) = A )
| ( product(b,b) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(242,plain,
product(b,b) = b,
inference(unit_resolution,[status(thm)],[241,35]) ).
tff(243,plain,
b = product(b,b),
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
product(b,product(c,b)) = product(product(b,b),product(c,b)),
inference(monotonicity,[status(thm)],[243]) ).
tff(245,plain,
product(product(b,b),product(c,b)) = product(b,product(c,b)),
inference(symmetry,[status(thm)],[244]) ).
tff(246,plain,
product(product(b,product(c,c)),product(b,product(b,b))) = product(b,product(c,b)),
inference(transitivity,[status(thm)],[231,228,245]) ).
tff(247,plain,
product(product(b,c),product(product(b,product(c,c)),product(b,product(b,b)))) = product(product(b,c),product(b,product(c,b))),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
product(product(b,c),product(b,product(c,b))) = product(product(b,c),product(product(b,product(c,c)),product(b,product(b,b)))),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(b,b),product(c,product(c,b))) = product(product(b,c),product(b,product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(250,plain,
product(product(b,b),product(c,product(c,b))) = product(product(b,c),product(b,product(c,b))),
inference(unit_resolution,[status(thm)],[249,45]) ).
tff(251,plain,
product(product(b,b),product(c,product(c,b))) = product(b,product(c,product(c,b))),
inference(monotonicity,[status(thm)],[242]) ).
tff(252,plain,
product(b,product(c,product(c,b))) = product(product(b,b),product(c,product(c,b))),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
product(b,product(product(c,product(c,c)),product(c,product(b,b)))) = product(b,product(c,product(c,b))),
inference(monotonicity,[status(thm)],[146]) ).
tff(254,plain,
product(b,product(product(c,product(c,c)),product(c,product(b,b)))) = product(product(b,c),product(product(b,product(c,c)),product(b,product(b,b)))),
inference(transitivity,[status(thm)],[253,252,250,248]) ).
tff(255,plain,
product(product(product(product(a,c),x0),a),product(b,product(product(c,product(c,c)),product(c,product(b,b))))) = product(product(product(product(a,c),x0),a),product(product(b,c),product(product(b,product(c,c)),product(b,product(b,b))))),
inference(monotonicity,[status(thm)],[254]) ).
tff(256,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(product(a,c),x0),a),product(b,product(product(c,product(c,c)),product(c,product(b,b))))) = product(product(product(product(a,c),x0),b),product(a,product(product(c,product(c,c)),product(c,product(b,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(257,plain,
product(product(product(product(a,c),x0),a),product(b,product(product(c,product(c,c)),product(c,product(b,b))))) = product(product(product(product(a,c),x0),b),product(a,product(product(c,product(c,c)),product(c,product(b,b))))),
inference(unit_resolution,[status(thm)],[256,45]) ).
tff(258,plain,
product(product(product(product(a,c),x0),b),product(a,product(product(c,product(c,c)),product(c,product(b,b))))) = product(product(product(product(a,c),x0),a),product(b,product(product(c,product(c,c)),product(c,product(b,b))))),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
product(a,product(product(c,product(c,c)),product(c,product(b,b)))) = product(a,product(c,product(c,b))),
inference(monotonicity,[status(thm)],[146]) ).
tff(260,plain,
product(a,product(c,product(c,b))) = product(a,product(product(c,product(c,c)),product(c,product(b,b)))),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
product(a,product(c,product(c,b))) = product(product(a,a),product(c,product(c,b))),
inference(monotonicity,[status(thm)],[170]) ).
tff(262,plain,
product(product(a,a),product(c,product(c,b))) = product(a,product(c,product(c,b))),
inference(symmetry,[status(thm)],[261]) ).
tff(263,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(a,a),product(c,product(c,b))) = product(product(a,c),product(a,product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(264,plain,
product(product(a,a),product(c,product(c,b))) = product(product(a,c),product(a,product(c,b))),
inference(unit_resolution,[status(thm)],[263,45]) ).
tff(265,plain,
product(product(a,c),product(a,product(c,b))) = product(product(a,a),product(c,product(c,b))),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
product(a,product(c,b)) = product(product(a,a),product(c,b)),
inference(monotonicity,[status(thm)],[170]) ).
tff(267,plain,
product(a,product(c,b)) = product(product(a,product(a,c)),product(c,product(c,b))),
inference(transitivity,[status(thm)],[266,220,107,106]) ).
tff(268,plain,
product(product(a,c),product(a,product(c,b))) = product(product(a,c),product(product(a,product(a,c)),product(c,product(c,b)))),
inference(monotonicity,[status(thm)],[267]) ).
tff(269,plain,
product(product(a,c),product(product(a,product(a,c)),product(c,product(c,b)))) = product(product(a,c),product(a,product(c,b))),
inference(symmetry,[status(thm)],[268]) ).
tff(270,plain,
product(product(a,c),product(product(a,c),product(c,b))) = product(product(a,c),product(product(a,b),product(a,b))),
inference(monotonicity,[status(thm)],[112]) ).
tff(271,plain,
product(product(a,c),product(product(a,b),product(a,b))) = product(product(a,c),product(product(a,c),product(c,b))),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
product(product(a,c),product(product(a,b),product(a,b))) = product(product(product(a,a),product(c,c)),product(product(a,b),product(a,b))),
inference(monotonicity,[status(thm)],[173]) ).
tff(273,plain,
product(product(product(a,a),product(c,c)),product(product(a,b),product(a,b))) = product(product(a,c),product(product(a,b),product(a,b))),
inference(symmetry,[status(thm)],[272]) ).
tff(274,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,a),product(c,c)),product(product(a,b),product(a,b))) = product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(275,plain,
product(product(product(a,a),product(c,c)),product(product(a,b),product(a,b))) = product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b))),
inference(unit_resolution,[status(thm)],[274,45]) ).
tff(276,plain,
product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b))) = product(product(product(a,a),product(c,c)),product(product(a,b),product(a,b))),
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b))) = product(product(a,product(a,c)),product(c,product(c,b))),
inference(transitivity,[status(thm)],[276,273,271,106]) ).
tff(278,plain,
product(product(a,c),product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b)))) = product(product(a,c),product(product(a,product(a,c)),product(c,product(c,b)))),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
product(product(a,c),product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b)))) = product(a,product(product(c,product(c,c)),product(c,product(b,b)))),
inference(transitivity,[status(thm)],[278,269,265,262,260]) ).
tff(280,plain,
product(product(product(product(a,c),x0),b),product(product(a,c),product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b))))) = product(product(product(product(a,c),x0),b),product(a,product(product(c,product(c,c)),product(c,product(b,b))))),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
product(product(a,c),product(product(a,product(a,c)),product(c,product(c,b)))) = product(product(a,c),product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b)))),
inference(symmetry,[status(thm)],[278]) ).
tff(282,plain,
product(product(a,c),product(product(a,c),product(c,b))) = product(product(a,c),product(a,b)),
inference(symmetry,[status(thm)],[107]) ).
tff(283,plain,
product(product(a,product(a,c)),product(c,product(c,b))) = product(product(a,c),product(product(a,c),product(c,b))),
inference(symmetry,[status(thm)],[106]) ).
tff(284,plain,
product(product(a,product(a,c)),product(c,product(c,b))) = product(product(a,c),product(a,b)),
inference(transitivity,[status(thm)],[283,282]) ).
tff(285,plain,
product(product(a,c),product(product(a,product(a,c)),product(c,product(c,b)))) = product(product(product(a,a),product(c,c)),product(product(a,c),product(a,b))),
inference(monotonicity,[status(thm)],[173,284]) ).
tff(286,plain,
product(product(product(a,a),product(c,c)),product(product(a,c),product(a,b))) = product(product(a,c),product(product(a,product(a,c)),product(c,product(c,b)))),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
product(product(product(a,c),product(a,c)),product(product(a,a),product(c,b))) = product(product(product(a,a),product(c,c)),product(product(a,c),product(a,b))),
inference(monotonicity,[status(thm)],[53,220]) ).
tff(288,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),product(a,c)),product(product(a,a),product(c,b))) = product(product(product(a,c),product(a,a)),product(product(a,c),product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(289,plain,
product(product(product(a,c),product(a,c)),product(product(a,a),product(c,b))) = product(product(product(a,c),product(a,a)),product(product(a,c),product(c,b))),
inference(unit_resolution,[status(thm)],[288,45]) ).
tff(290,plain,
product(product(product(a,c),product(a,a)),product(product(a,c),product(c,b))) = product(product(product(a,c),product(a,c)),product(product(a,a),product(c,b))),
inference(symmetry,[status(thm)],[289]) ).
tff(291,plain,
product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b))) = product(product(a,c),product(c,b)),
inference(transitivity,[status(thm)],[72,69,110,67]) ).
tff(292,plain,
product(product(product(a,a),a),product(product(c,c),a)) = product(product(a,c),product(a,a)),
inference(transitivity,[status(thm)],[178,175]) ).
tff(293,plain,
product(product(product(product(a,a),a),product(product(c,c),a)),product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b)))) = product(product(product(a,c),product(a,a)),product(product(a,c),product(c,b))),
inference(monotonicity,[status(thm)],[292,291]) ).
tff(294,plain,
product(product(product(product(a,a),a),product(product(c,c),a)),product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b)))) = product(product(a,c),product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b)))),
inference(transitivity,[status(thm)],[293,290,287,286,281]) ).
tff(295,plain,
product(product(product(product(a,c),x0),b),product(product(product(product(a,a),a),product(product(c,c),a)),product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b))))) = product(product(product(product(a,c),x0),b),product(product(a,c),product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b))))),
inference(monotonicity,[status(thm)],[294]) ).
tff(296,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(product(a,c),x0),product(product(product(a,a),a),product(product(c,c),a))),product(b,product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b))))) = product(product(product(product(a,c),x0),b),product(product(product(product(a,a),a),product(product(c,c),a)),product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(297,plain,
product(product(product(product(a,c),x0),product(product(product(a,a),a),product(product(c,c),a))),product(b,product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b))))) = product(product(product(product(a,c),x0),b),product(product(product(product(a,a),a),product(product(c,c),a)),product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b))))),
inference(unit_resolution,[status(thm)],[296,45]) ).
tff(298,plain,
product(product(product(a,c),product(x0,a)),product(b,product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b))))) = product(product(product(product(a,c),x0),product(product(product(a,a),a),product(product(c,c),a))),product(b,product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b))))),
inference(monotonicity,[status(thm)],[188]) ).
tff(299,plain,
product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b))) = product(product(a,b),product(a,b)),
inference(transitivity,[status(thm)],[72,69]) ).
tff(300,plain,
product(b,product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b)))) = product(product(b,b),product(product(a,b),product(a,b))),
inference(monotonicity,[status(thm)],[243,299]) ).
tff(301,plain,
product(product(b,b),product(product(a,b),product(a,b))) = product(b,product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b)))),
inference(symmetry,[status(thm)],[300]) ).
tff(302,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(b,b),product(product(a,b),product(a,b))) = product(product(b,product(a,b)),product(b,product(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(303,plain,
product(product(b,b),product(product(a,b),product(a,b))) = product(product(b,product(a,b)),product(b,product(a,b))),
inference(unit_resolution,[status(thm)],[302,45]) ).
tff(304,plain,
product(product(b,product(a,b)),product(b,product(a,b))) = product(product(b,b),product(product(a,b),product(a,b))),
inference(symmetry,[status(thm)],[303]) ).
tff(305,plain,
product(product(b,product(a,b)),product(b,product(a,b))) = product(b,product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b)))),
inference(transitivity,[status(thm)],[304,301]) ).
tff(306,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,a),product(c,c)),product(x0,a)) = product(product(product(a,a),x0),product(product(c,c),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(307,plain,
product(product(product(a,a),product(c,c)),product(x0,a)) = product(product(product(a,a),x0),product(product(c,c),a)),
inference(unit_resolution,[status(thm)],[306,45]) ).
tff(308,plain,
product(product(product(a,a),x0),product(product(c,c),a)) = product(product(product(a,a),product(c,c)),product(x0,a)),
inference(symmetry,[status(thm)],[307]) ).
tff(309,plain,
product(product(product(a,a),x0),product(product(c,c),a)) = product(product(a,c),product(x0,a)),
inference(transitivity,[status(thm)],[308,186]) ).
tff(310,plain,
product(product(product(product(a,a),x0),product(product(c,c),a)),product(product(b,product(a,b)),product(b,product(a,b)))) = product(product(product(a,c),product(x0,a)),product(b,product(product(product(a,c),product(a,c)),product(product(c,b),product(c,b))))),
inference(monotonicity,[status(thm)],[309,305]) ).
tff(311,plain,
product(product(b,b),product(product(a,b),product(a,b))) = product(b,product(a,b)),
inference(monotonicity,[status(thm)],[242,110]) ).
tff(312,plain,
product(product(b,product(a,b)),product(b,product(a,b))) = product(b,product(a,b)),
inference(transitivity,[status(thm)],[304,311]) ).
tff(313,plain,
product(product(product(b,product(a,b)),product(b,product(a,b))),product(product(b,product(a,b)),product(b,product(a,b)))) = product(product(b,product(a,b)),product(b,product(a,b))),
inference(monotonicity,[status(thm)],[312,312]) ).
tff(314,plain,
product(product(a,c),product(x0,a)) = product(product(product(a,a),x0),product(product(c,c),a)),
inference(transitivity,[status(thm)],[187,307]) ).
tff(315,plain,
product(product(product(a,c),product(x0,a)),product(product(product(b,product(a,b)),product(b,product(a,b))),product(product(b,product(a,b)),product(b,product(a,b))))) = product(product(product(product(a,a),x0),product(product(c,c),a)),product(product(b,product(a,b)),product(b,product(a,b)))),
inference(monotonicity,[status(thm)],[314,313]) ).
tff(316,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),product(x0,a)),product(product(product(b,product(a,b)),product(b,product(a,b))),product(product(b,product(a,b)),product(b,product(a,b))))) = product(product(product(a,c),product(product(b,product(a,b)),product(b,product(a,b)))),product(product(x0,a),product(product(b,product(a,b)),product(b,product(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(317,plain,
product(product(product(a,c),product(x0,a)),product(product(product(b,product(a,b)),product(b,product(a,b))),product(product(b,product(a,b)),product(b,product(a,b))))) = product(product(product(a,c),product(product(b,product(a,b)),product(b,product(a,b)))),product(product(x0,a),product(product(b,product(a,b)),product(b,product(a,b))))),
inference(unit_resolution,[status(thm)],[316,45]) ).
tff(318,plain,
product(product(product(a,c),product(product(b,product(a,b)),product(b,product(a,b)))),product(product(x0,a),product(product(b,product(a,b)),product(b,product(a,b))))) = product(product(product(a,c),product(x0,a)),product(product(product(b,product(a,b)),product(b,product(a,b))),product(product(b,product(a,b)),product(b,product(a,b))))),
inference(symmetry,[status(thm)],[317]) ).
tff(319,plain,
product(b,product(a,b)) = product(product(b,b),product(a,b)),
inference(monotonicity,[status(thm)],[243]) ).
tff(320,plain,
product(product(b,product(a,b)),product(b,product(a,b))) = product(product(b,b),product(a,b)),
inference(transitivity,[status(thm)],[304,311,319]) ).
tff(321,plain,
product(product(a,c),product(product(b,product(a,b)),product(b,product(a,b)))) = product(product(product(a,c),product(a,c)),product(product(b,b),product(a,b))),
inference(monotonicity,[status(thm)],[58,320]) ).
tff(322,plain,
product(product(product(a,c),product(a,c)),product(product(b,b),product(a,b))) = product(product(a,c),product(product(b,product(a,b)),product(b,product(a,b)))),
inference(symmetry,[status(thm)],[321]) ).
tff(323,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),product(b,b)),product(product(a,c),product(a,b))) = product(product(product(a,c),product(a,c)),product(product(b,b),product(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(324,plain,
product(product(product(a,c),product(b,b)),product(product(a,c),product(a,b))) = product(product(product(a,c),product(a,c)),product(product(b,b),product(a,b))),
inference(unit_resolution,[status(thm)],[323,45]) ).
tff(325,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(a,b),product(c,b)) = product(product(a,c),product(b,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(326,plain,
product(product(a,b),product(c,b)) = product(product(a,c),product(b,b)),
inference(unit_resolution,[status(thm)],[325,45]) ).
tff(327,plain,
product(product(a,c),product(b,b)) = product(product(a,b),product(c,b)),
inference(symmetry,[status(thm)],[326]) ).
tff(328,plain,
product(product(product(a,c),product(b,b)),product(product(a,c),product(a,b))) = product(product(product(a,b),product(c,b)),product(product(a,product(a,c)),product(c,product(c,b)))),
inference(monotonicity,[status(thm)],[327,108]) ).
tff(329,plain,
product(product(product(a,b),product(c,b)),product(product(a,product(a,c)),product(c,product(c,b)))) = product(product(product(a,c),product(b,b)),product(product(a,c),product(a,b))),
inference(symmetry,[status(thm)],[328]) ).
tff(330,plain,
product(product(a,b),product(c,b)) = product(product(product(a,c),product(c,b)),product(c,b)),
inference(monotonicity,[status(thm)],[67]) ).
tff(331,plain,
product(product(product(a,c),product(c,b)),product(c,b)) = product(product(a,b),product(c,b)),
inference(symmetry,[status(thm)],[330]) ).
tff(332,plain,
product(product(product(a,c),product(c,b)),product(c,b)) = product(product(product(a,b),product(a,b)),product(c,b)),
inference(monotonicity,[status(thm)],[112]) ).
tff(333,plain,
product(product(product(a,b),product(a,b)),product(c,b)) = product(product(product(a,c),product(c,b)),product(c,b)),
inference(symmetry,[status(thm)],[332]) ).
tff(334,plain,
product(product(product(a,b),product(a,b)),product(c,b)) = product(product(product(a,b),product(a,b)),product(product(c,c),product(b,b))),
inference(monotonicity,[status(thm)],[128]) ).
tff(335,plain,
product(product(product(a,b),product(a,b)),product(product(c,c),product(b,b))) = product(product(product(a,b),product(a,b)),product(c,b)),
inference(symmetry,[status(thm)],[334]) ).
tff(336,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,b),product(a,b)),product(product(c,c),product(b,b))) = product(product(product(a,b),product(c,c)),product(product(a,b),product(b,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(337,plain,
product(product(product(a,b),product(a,b)),product(product(c,c),product(b,b))) = product(product(product(a,b),product(c,c)),product(product(a,b),product(b,b))),
inference(unit_resolution,[status(thm)],[336,45]) ).
tff(338,plain,
product(product(product(a,b),product(c,c)),product(product(a,b),product(b,b))) = product(product(product(a,b),product(a,b)),product(product(c,c),product(b,b))),
inference(symmetry,[status(thm)],[337]) ).
tff(339,plain,
product(product(product(a,b),product(c,c)),product(product(a,b),product(b,b))) = product(product(a,b),product(c,b)),
inference(transitivity,[status(thm)],[338,335,333,331]) ).
tff(340,plain,
product(product(product(product(a,b),product(c,c)),product(product(a,b),product(b,b))),product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b)))) = product(product(product(a,b),product(c,b)),product(product(a,product(a,c)),product(c,product(c,b)))),
inference(monotonicity,[status(thm)],[339,277]) ).
tff(341,plain,
product(product(product(product(a,b),product(c,c)),product(product(a,b),product(b,b))),product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b)))) = product(product(a,c),product(product(b,product(a,b)),product(b,product(a,b)))),
inference(transitivity,[status(thm)],[340,329,324,322]) ).
tff(342,plain,
product(product(product(product(product(a,b),product(c,c)),product(product(a,b),product(b,b))),product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b)))),product(product(x0,a),product(product(b,product(a,b)),product(b,product(a,b))))) = product(product(product(a,c),product(product(b,product(a,b)),product(b,product(a,b)))),product(product(x0,a),product(product(b,product(a,b)),product(b,product(a,b))))),
inference(monotonicity,[status(thm)],[341]) ).
tff(343,plain,
product(product(product(a,b),product(c,b)),product(product(a,product(a,c)),product(c,product(c,b)))) = product(product(product(product(a,b),product(c,c)),product(product(a,b),product(b,b))),product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b)))),
inference(symmetry,[status(thm)],[340]) ).
tff(344,plain,
product(product(product(a,c),product(b,b)),product(product(a,a),product(c,b))) = product(product(product(a,b),product(c,b)),product(product(a,product(a,c)),product(c,product(c,b)))),
inference(monotonicity,[status(thm)],[327,221]) ).
tff(345,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),product(b,b)),product(product(a,a),product(c,b))) = product(product(product(a,c),product(a,a)),product(product(b,b),product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(346,plain,
product(product(product(a,c),product(b,b)),product(product(a,a),product(c,b))) = product(product(product(a,c),product(a,a)),product(product(b,b),product(c,b))),
inference(unit_resolution,[status(thm)],[345,45]) ).
tff(347,plain,
product(product(product(a,c),product(a,a)),product(product(b,b),product(c,b))) = product(product(product(a,c),product(b,b)),product(product(a,a),product(c,b))),
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
product(product(product(product(a,a),a),product(product(c,c),a)),product(product(b,product(c,c)),product(b,product(b,b)))) = product(product(product(a,c),product(a,a)),product(product(b,b),product(c,b))),
inference(monotonicity,[status(thm)],[292,232]) ).
tff(349,plain,
product(product(product(product(a,a),a),product(product(c,c),a)),product(product(b,product(c,c)),product(b,product(b,b)))) = product(product(product(product(a,b),product(c,c)),product(product(a,b),product(b,b))),product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b)))),
inference(transitivity,[status(thm)],[348,347,344,343]) ).
tff(350,plain,
product(product(product(product(product(a,a),a),product(product(c,c),a)),product(product(b,product(c,c)),product(b,product(b,b)))),product(product(x0,a),product(product(b,product(a,b)),product(b,product(a,b))))) = product(product(product(product(product(a,b),product(c,c)),product(product(a,b),product(b,b))),product(product(product(a,a),product(a,b)),product(product(c,c),product(a,b)))),product(product(x0,a),product(product(b,product(a,b)),product(b,product(a,b))))),
inference(monotonicity,[status(thm)],[349]) ).
tff(351,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(product(product(a,a),a),product(product(c,c),a)),product(x0,a)),product(product(product(b,product(c,c)),product(b,product(b,b))),product(product(b,product(a,b)),product(b,product(a,b))))) = product(product(product(product(product(a,a),a),product(product(c,c),a)),product(product(b,product(c,c)),product(b,product(b,b)))),product(product(x0,a),product(product(b,product(a,b)),product(b,product(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(352,plain,
product(product(product(product(product(a,a),a),product(product(c,c),a)),product(x0,a)),product(product(product(b,product(c,c)),product(b,product(b,b))),product(product(b,product(a,b)),product(b,product(a,b))))) = product(product(product(product(product(a,a),a),product(product(c,c),a)),product(product(b,product(c,c)),product(b,product(b,b)))),product(product(x0,a),product(product(b,product(a,b)),product(b,product(a,b))))),
inference(unit_resolution,[status(thm)],[351,45]) ).
tff(353,plain,
product(product(product(b,product(c,c)),product(b,product(b,b))),product(product(b,product(a,b)),product(b,product(a,b)))) = product(product(b,product(c,b)),product(b,product(a,b))),
inference(monotonicity,[status(thm)],[246,312]) ).
tff(354,plain,
product(product(b,product(c,b)),product(b,product(a,b))) = product(product(product(b,product(c,c)),product(b,product(b,b))),product(product(b,product(a,b)),product(b,product(a,b)))),
inference(symmetry,[status(thm)],[353]) ).
tff(355,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(b,b),product(product(c,b),product(a,b))) = product(product(b,product(c,b)),product(b,product(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(356,plain,
product(product(b,b),product(product(c,b),product(a,b))) = product(product(b,product(c,b)),product(b,product(a,b))),
inference(unit_resolution,[status(thm)],[355,45]) ).
tff(357,plain,
product(product(c,b),product(a,b)) = product(product(c,b),product(product(a,c),product(c,b))),
inference(monotonicity,[status(thm)],[67]) ).
tff(358,plain,
product(product(c,b),product(product(a,c),product(c,b))) = product(product(c,b),product(a,b)),
inference(symmetry,[status(thm)],[357]) ).
tff(359,plain,
product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))) = product(product(c,b),product(a,b)),
inference(transitivity,[status(thm)],[133,130,126,358]) ).
tff(360,plain,
product(b,product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))) = product(product(b,b),product(product(c,b),product(a,b))),
inference(monotonicity,[status(thm)],[243,359]) ).
tff(361,plain,
product(b,product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))) = product(product(product(b,product(c,c)),product(b,product(b,b))),product(product(b,product(a,b)),product(b,product(a,b)))),
inference(transitivity,[status(thm)],[360,356,354]) ).
tff(362,plain,
product(product(product(product(product(a,a),a),product(product(c,c),a)),product(x0,a)),product(b,product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))) = product(product(product(product(product(a,a),a),product(product(c,c),a)),product(x0,a)),product(product(product(b,product(c,c)),product(b,product(b,b))),product(product(b,product(a,b)),product(b,product(a,b))))),
inference(monotonicity,[status(thm)],[361]) ).
tff(363,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(product(product(a,a),a),product(product(c,c),a)),b),product(product(x0,a),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))) = product(product(product(product(product(a,a),a),product(product(c,c),a)),product(x0,a)),product(b,product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(364,plain,
product(product(product(product(product(a,a),a),product(product(c,c),a)),b),product(product(x0,a),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))) = product(product(product(product(product(a,a),a),product(product(c,c),a)),product(x0,a)),product(b,product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))),
inference(unit_resolution,[status(thm)],[363,45]) ).
tff(365,plain,
product(product(product(product(a,a),a),product(product(c,c),a)),b) = product(product(product(a,c),a),b),
inference(monotonicity,[status(thm)],[179]) ).
tff(366,plain,
product(product(product(a,c),a),b) = product(product(product(product(a,a),a),product(product(c,c),a)),b),
inference(symmetry,[status(thm)],[365]) ).
tff(367,plain,
product(product(product(a,c),a),b) = product(product(product(a,c),a),product(b,b)),
inference(monotonicity,[status(thm)],[243]) ).
tff(368,plain,
product(product(product(a,c),a),product(b,b)) = product(product(product(a,c),a),b),
inference(symmetry,[status(thm)],[367]) ).
tff(369,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),a),product(b,b)) = product(product(product(a,c),b),product(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(370,plain,
product(product(product(a,c),a),product(b,b)) = product(product(product(a,c),b),product(a,b)),
inference(unit_resolution,[status(thm)],[369,45]) ).
tff(371,plain,
product(product(product(a,c),b),product(a,b)) = product(product(product(a,c),a),product(b,b)),
inference(symmetry,[status(thm)],[370]) ).
tff(372,plain,
product(product(product(a,c),b),product(a,b)) = product(product(product(a,c),b),product(product(a,c),product(c,b))),
inference(monotonicity,[status(thm)],[67]) ).
tff(373,plain,
product(product(product(a,c),b),product(product(a,c),product(c,b))) = product(product(product(a,c),b),product(a,b)),
inference(symmetry,[status(thm)],[372]) ).
tff(374,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),product(a,c)),product(b,product(c,b))) = product(product(product(a,c),b),product(product(a,c),product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(375,plain,
product(product(product(a,c),product(a,c)),product(b,product(c,b))) = product(product(product(a,c),b),product(product(a,c),product(c,b))),
inference(unit_resolution,[status(thm)],[374,45]) ).
tff(376,plain,
product(product(product(a,c),product(a,c)),product(b,product(c,b))) = product(product(product(a,a),product(c,c)),product(b,product(c,b))),
inference(monotonicity,[status(thm)],[53]) ).
tff(377,plain,
product(product(product(a,a),product(c,c)),product(b,product(c,b))) = product(product(product(a,c),product(a,c)),product(b,product(c,b))),
inference(symmetry,[status(thm)],[376]) ).
tff(378,plain,
product(product(product(a,a),product(c,c)),product(b,product(c,b))) = product(product(a,c),product(b,product(c,b))),
inference(monotonicity,[status(thm)],[55]) ).
tff(379,plain,
product(product(a,c),product(b,product(c,b))) = product(product(product(a,a),product(c,c)),product(b,product(c,b))),
inference(symmetry,[status(thm)],[378]) ).
tff(380,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(a,b),product(c,product(c,b))) = product(product(a,c),product(b,product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(381,plain,
product(product(a,b),product(c,product(c,b))) = product(product(a,c),product(b,product(c,b))),
inference(unit_resolution,[status(thm)],[380,45]) ).
tff(382,plain,
product(product(a,b),product(c,product(c,b))) = product(product(product(a,b),product(a,b)),product(c,product(c,b))),
inference(monotonicity,[status(thm)],[111]) ).
tff(383,plain,
product(product(product(a,b),product(a,b)),product(c,product(c,b))) = product(product(a,b),product(c,product(c,b))),
inference(symmetry,[status(thm)],[382]) ).
tff(384,plain,
product(product(product(a,b),product(a,b)),product(c,product(c,b))) = product(product(product(a,a),product(b,b)),product(c,product(c,b))),
inference(monotonicity,[status(thm)],[81]) ).
tff(385,plain,
product(product(product(a,a),product(b,b)),product(c,product(c,b))) = product(product(product(a,b),product(a,b)),product(c,product(c,b))),
inference(symmetry,[status(thm)],[384]) ).
tff(386,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,a),product(b,b)),product(c,product(c,b))) = product(product(product(a,a),c),product(product(b,b),product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(387,plain,
product(product(product(a,a),product(b,b)),product(c,product(c,b))) = product(product(product(a,a),c),product(product(b,b),product(c,b))),
inference(unit_resolution,[status(thm)],[386,45]) ).
tff(388,plain,
product(product(product(a,a),c),product(product(b,b),product(c,b))) = product(product(product(a,a),product(b,b)),product(c,product(c,b))),
inference(symmetry,[status(thm)],[387]) ).
tff(389,plain,
product(product(a,a),c) = product(product(a,a),product(c,c)),
inference(monotonicity,[status(thm)],[87]) ).
tff(390,plain,
product(product(a,a),c) = product(product(a,c),product(a,c)),
inference(transitivity,[status(thm)],[389,54]) ).
tff(391,plain,
product(product(product(a,a),c),product(product(b,b),product(c,b))) = product(product(product(a,c),product(a,c)),product(product(b,b),product(c,b))),
inference(monotonicity,[status(thm)],[390]) ).
tff(392,plain,
product(product(product(a,c),product(a,c)),product(product(b,b),product(c,b))) = product(product(product(a,a),c),product(product(b,b),product(c,b))),
inference(symmetry,[status(thm)],[391]) ).
tff(393,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),product(b,b)),product(product(a,c),product(c,b))) = product(product(product(a,c),product(a,c)),product(product(b,b),product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(394,plain,
product(product(product(a,c),product(b,b)),product(product(a,c),product(c,b))) = product(product(product(a,c),product(a,c)),product(product(b,b),product(c,b))),
inference(unit_resolution,[status(thm)],[393,45]) ).
tff(395,plain,
product(product(product(a,c),product(b,b)),product(product(a,c),product(c,b))) = product(product(product(a,b),product(c,b)),product(product(a,c),product(c,b))),
inference(monotonicity,[status(thm)],[327]) ).
tff(396,plain,
product(product(product(a,b),product(c,b)),product(product(a,c),product(c,b))) = product(product(product(a,c),product(b,b)),product(product(a,c),product(c,b))),
inference(symmetry,[status(thm)],[395]) ).
tff(397,plain,
product(product(product(a,b),product(c,b)),product(product(a,c),product(c,b))) = product(product(product(a,b),product(c,b)),product(product(a,b),product(a,b))),
inference(monotonicity,[status(thm)],[112]) ).
tff(398,plain,
product(product(product(a,b),product(c,b)),product(product(a,b),product(a,b))) = product(product(product(a,b),product(c,b)),product(product(a,c),product(c,b))),
inference(symmetry,[status(thm)],[397]) ).
tff(399,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,b),product(a,b)),product(product(c,b),product(a,b))) = product(product(product(a,b),product(c,b)),product(product(a,b),product(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(400,plain,
product(product(product(a,b),product(a,b)),product(product(c,b),product(a,b))) = product(product(product(a,b),product(c,b)),product(product(a,b),product(a,b))),
inference(unit_resolution,[status(thm)],[399,45]) ).
tff(401,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(c,b),product(product(a,c),product(c,b))) = product(product(c,product(a,c)),product(b,product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(402,plain,
product(product(c,b),product(product(a,c),product(c,b))) = product(product(c,product(a,c)),product(b,product(c,b))),
inference(unit_resolution,[status(thm)],[401,45]) ).
tff(403,plain,
product(product(c,b),product(a,b)) = product(product(c,product(a,c)),product(b,product(c,b))),
inference(transitivity,[status(thm)],[357,402]) ).
tff(404,plain,
product(product(product(a,b),product(a,b)),product(product(c,b),product(a,b))) = product(product(product(a,b),product(a,b)),product(product(c,product(a,c)),product(b,product(c,b)))),
inference(monotonicity,[status(thm)],[403]) ).
tff(405,plain,
product(product(product(a,b),product(a,b)),product(product(c,product(a,c)),product(b,product(c,b)))) = product(product(product(a,b),product(a,b)),product(product(c,b),product(a,b))),
inference(symmetry,[status(thm)],[404]) ).
tff(406,plain,
product(product(product(a,c),product(c,b)),product(a,b)) = product(product(product(a,c),product(c,b)),product(product(a,c),product(c,b))),
inference(monotonicity,[status(thm)],[67]) ).
tff(407,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),product(c,b)),product(a,b)) = product(product(product(a,c),a),product(product(c,b),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(408,plain,
product(product(product(a,c),product(c,b)),product(a,b)) = product(product(product(a,c),a),product(product(c,b),b)),
inference(unit_resolution,[status(thm)],[407,45]) ).
tff(409,plain,
product(product(product(a,c),a),product(product(c,b),b)) = product(product(product(a,c),product(c,b)),product(a,b)),
inference(symmetry,[status(thm)],[408]) ).
tff(410,plain,
product(product(product(a,c),a),product(product(c,b),b)) = product(product(a,b),product(a,b)),
inference(transitivity,[status(thm)],[409,406,69]) ).
tff(411,plain,
product(product(product(product(a,c),a),product(product(c,b),b)),product(product(c,product(a,c)),product(b,product(c,b)))) = product(product(product(a,b),product(a,b)),product(product(c,product(a,c)),product(b,product(c,b)))),
inference(monotonicity,[status(thm)],[410]) ).
tff(412,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(product(a,c),a),product(product(c,b),b)),product(product(c,product(a,c)),product(b,product(c,b)))) = product(product(product(product(a,c),a),product(c,product(a,c))),product(product(product(c,b),b),product(b,product(c,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(413,plain,
product(product(product(product(a,c),a),product(product(c,b),b)),product(product(c,product(a,c)),product(b,product(c,b)))) = product(product(product(product(a,c),a),product(c,product(a,c))),product(product(product(c,b),b),product(b,product(c,b)))),
inference(unit_resolution,[status(thm)],[412,45]) ).
tff(414,plain,
product(product(product(product(a,c),a),product(c,product(a,c))),product(product(product(c,b),b),product(b,product(c,b)))) = product(product(product(product(a,c),a),product(product(c,b),b)),product(product(c,product(a,c)),product(b,product(c,b)))),
inference(symmetry,[status(thm)],[413]) ).
tff(415,plain,
product(product(product(product(a,c),a),product(c,product(a,c))),product(product(product(c,b),b),product(b,product(c,b)))) = product(product(product(product(a,a),a),product(product(c,c),a)),b),
inference(transitivity,[status(thm)],[414,411,405,400,398,396,394,392,388,385,383,381,379,377,375,373,371,368,366]) ).
tff(416,plain,
product(product(product(product(product(a,c),a),product(c,product(a,c))),product(product(product(c,b),b),product(b,product(c,b)))),product(product(x0,a),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))) = product(product(product(product(product(a,a),a),product(product(c,c),a)),b),product(product(x0,a),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))),
inference(monotonicity,[status(thm)],[415]) ).
tff(417,plain,
product(product(product(a,b),product(a,b)),product(product(c,product(a,c)),product(b,product(c,b)))) = product(product(product(product(a,c),a),product(product(c,b),b)),product(product(c,product(a,c)),product(b,product(c,b)))),
inference(symmetry,[status(thm)],[411]) ).
tff(418,plain,
product(product(product(a,b),product(c,b)),product(product(a,b),product(a,b))) = product(product(product(a,b),product(a,b)),product(product(c,b),product(a,b))),
inference(symmetry,[status(thm)],[400]) ).
tff(419,plain,
product(product(product(a,c),product(a,c)),product(product(b,b),product(c,b))) = product(product(product(a,c),product(b,b)),product(product(a,c),product(c,b))),
inference(symmetry,[status(thm)],[394]) ).
tff(420,plain,
product(product(product(a,c),product(c,b)),product(c,product(c,b))) = product(product(a,b),product(c,product(c,b))),
inference(monotonicity,[status(thm)],[66]) ).
tff(421,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),product(c,b)),product(c,product(c,b))) = product(product(product(a,c),c),product(product(c,b),product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(422,plain,
product(product(product(a,c),product(c,b)),product(c,product(c,b))) = product(product(product(a,c),c),product(product(c,b),product(c,b))),
inference(unit_resolution,[status(thm)],[421,45]) ).
tff(423,plain,
product(product(product(a,c),c),product(product(c,b),product(c,b))) = product(product(product(a,c),product(c,b)),product(c,product(c,b))),
inference(symmetry,[status(thm)],[422]) ).
tff(424,plain,
product(product(product(a,c),c),product(product(c,c),product(b,b))) = product(product(product(a,c),c),product(product(c,b),product(c,b))),
inference(monotonicity,[status(thm)],[75]) ).
tff(425,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,c),c),product(product(c,c),product(b,b))) = product(product(product(a,c),product(c,c)),product(c,product(b,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(426,plain,
product(product(product(a,c),c),product(product(c,c),product(b,b))) = product(product(product(a,c),product(c,c)),product(c,product(b,b))),
inference(unit_resolution,[status(thm)],[425,45]) ).
tff(427,plain,
product(product(product(a,c),product(c,c)),product(c,product(b,b))) = product(product(product(a,c),c),product(product(c,c),product(b,b))),
inference(symmetry,[status(thm)],[426]) ).
tff(428,plain,
product(product(c,c),product(b,b)) = product(c,product(b,b)),
inference(symmetry,[status(thm)],[88]) ).
tff(429,plain,
product(c,b) = product(c,product(b,b)),
inference(transitivity,[status(thm)],[127,74,428]) ).
tff(430,plain,
product(product(product(a,a),product(c,c)),product(c,c)) = product(product(a,c),product(c,c)),
inference(monotonicity,[status(thm)],[55]) ).
tff(431,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(a,a),product(c,c)),product(c,c)) = product(product(product(a,a),c),product(product(c,c),c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(432,plain,
product(product(product(a,a),product(c,c)),product(c,c)) = product(product(product(a,a),c),product(product(c,c),c)),
inference(unit_resolution,[status(thm)],[431,45]) ).
tff(433,plain,
product(product(product(a,a),c),product(product(c,c),c)) = product(product(product(a,a),product(c,c)),product(c,c)),
inference(symmetry,[status(thm)],[432]) ).
tff(434,plain,
product(product(product(a,a),c),product(product(c,c),c)) = product(product(a,c),product(c,c)),
inference(transitivity,[status(thm)],[433,430]) ).
tff(435,plain,
product(product(product(product(a,a),c),product(product(c,c),c)),product(c,b)) = product(product(product(a,c),product(c,c)),product(c,product(b,b))),
inference(monotonicity,[status(thm)],[434,429]) ).
tff(436,plain,
product(product(product(product(a,a),c),product(product(c,c),c)),product(c,b)) = product(product(product(product(a,c),a),product(c,product(a,c))),product(product(product(c,b),b),product(b,product(c,b)))),
inference(transitivity,[status(thm)],[435,427,424,423,420,382,384,387,391,419,395,397,418,404,417,413]) ).
tff(437,plain,
product(product(product(product(product(a,a),c),product(product(c,c),c)),product(c,b)),product(product(x0,a),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))) = product(product(product(product(product(a,c),a),product(c,product(a,c))),product(product(product(c,b),b),product(b,product(c,b)))),product(product(x0,a),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))),
inference(monotonicity,[status(thm)],[436]) ).
tff(438,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(product(product(a,a),c),product(product(c,c),c)),product(c,b)),product(product(x0,a),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))) = product(product(product(product(product(a,a),c),product(product(c,c),c)),product(x0,a)),product(product(c,b),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(439,plain,
product(product(product(product(product(a,a),c),product(product(c,c),c)),product(c,b)),product(product(x0,a),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))) = product(product(product(product(product(a,a),c),product(product(c,c),c)),product(x0,a)),product(product(c,b),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))),
inference(unit_resolution,[status(thm)],[438,45]) ).
tff(440,plain,
product(product(product(product(product(a,a),c),product(product(c,c),c)),product(x0,a)),product(product(c,b),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))) = product(product(product(product(product(a,a),c),product(product(c,c),c)),product(c,b)),product(product(x0,a),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))),
inference(symmetry,[status(thm)],[439]) ).
tff(441,plain,
product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))) = product(product(c,product(a,c)),product(b,product(c,b))),
inference(transitivity,[status(thm)],[133,130,126,402]) ).
tff(442,plain,
product(product(c,b),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))) = product(product(c,b),product(product(c,product(a,c)),product(b,product(c,b)))),
inference(monotonicity,[status(thm)],[441]) ).
tff(443,plain,
product(product(c,b),product(product(c,product(a,c)),product(b,product(c,b)))) = product(product(c,b),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))),
inference(symmetry,[status(thm)],[442]) ).
tff(444,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(c,b),product(product(c,product(a,c)),product(b,product(c,b)))) = product(product(c,product(c,product(a,c))),product(b,product(b,product(c,b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(445,plain,
product(product(c,b),product(product(c,product(a,c)),product(b,product(c,b)))) = product(product(c,product(c,product(a,c))),product(b,product(b,product(c,b)))),
inference(unit_resolution,[status(thm)],[444,45]) ).
tff(446,plain,
product(product(c,product(c,product(a,c))),product(b,product(b,product(c,b)))) = product(product(c,b),product(product(c,product(a,c)),product(b,product(c,b)))),
inference(symmetry,[status(thm)],[445]) ).
tff(447,plain,
product(product(c,product(c,product(a,c))),product(b,product(b,product(c,b)))) = product(product(c,b),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))),
inference(transitivity,[status(thm)],[446,443]) ).
tff(448,plain,
product(product(product(product(product(a,a),c),product(product(c,c),c)),product(x0,a)),product(product(c,product(c,product(a,c))),product(b,product(b,product(c,b))))) = product(product(product(product(product(a,a),c),product(product(c,c),c)),product(x0,a)),product(product(c,b),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b))))),
inference(monotonicity,[status(thm)],[447]) ).
tff(449,plain,
product(product(c,a),product(b,b)) = product(product(c,product(a,c)),product(b,product(c,b))),
inference(transitivity,[status(thm)],[97,357,402]) ).
tff(450,plain,
product(product(c,b),product(product(c,a),product(b,b))) = product(product(c,b),product(product(c,product(a,c)),product(b,product(c,b)))),
inference(monotonicity,[status(thm)],[449]) ).
tff(451,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(c,b),product(product(c,a),product(b,b))) = product(product(c,product(c,a)),product(b,product(b,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(452,plain,
product(product(c,b),product(product(c,a),product(b,b))) = product(product(c,product(c,a)),product(b,product(b,b))),
inference(unit_resolution,[status(thm)],[451,45]) ).
tff(453,plain,
product(product(c,product(c,a)),product(b,product(b,b))) = product(product(c,b),product(product(c,a),product(b,b))),
inference(symmetry,[status(thm)],[452]) ).
tff(454,plain,
product(b,product(b,b)) = product(b,b),
inference(monotonicity,[status(thm)],[242]) ).
tff(455,plain,
product(b,b) = product(b,product(b,b)),
inference(symmetry,[status(thm)],[454]) ).
tff(456,plain,
b = product(b,product(b,b)),
inference(transitivity,[status(thm)],[243,455]) ).
tff(457,plain,
product(product(c,product(c,a)),b) = product(product(c,product(c,a)),product(b,product(b,b))),
inference(monotonicity,[status(thm)],[456]) ).
tff(458,plain,
product(product(c,product(c,a)),b) = product(product(c,product(c,product(a,c))),product(b,product(b,product(c,b)))),
inference(transitivity,[status(thm)],[457,453,450,445]) ).
tff(459,plain,
product(product(product(product(product(a,a),c),product(product(c,c),c)),product(x0,a)),product(product(c,product(c,a)),b)) = product(product(product(product(product(a,a),c),product(product(c,c),c)),product(x0,a)),product(product(c,product(c,product(a,c))),product(b,product(b,product(c,b))))),
inference(monotonicity,[status(thm)],[458]) ).
tff(460,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(product(product(a,a),c),product(product(c,c),c)),product(c,product(c,a))),product(product(x0,a),b)) = product(product(product(product(product(a,a),c),product(product(c,c),c)),product(x0,a)),product(product(c,product(c,a)),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(461,plain,
product(product(product(product(product(a,a),c),product(product(c,c),c)),product(c,product(c,a))),product(product(x0,a),b)) = product(product(product(product(product(a,a),c),product(product(c,c),c)),product(x0,a)),product(product(c,product(c,a)),b)),
inference(unit_resolution,[status(thm)],[460,45]) ).
tff(462,plain,
product(product(x0,a),b) = product(product(x0,a),product(b,b)),
inference(monotonicity,[status(thm)],[243]) ).
tff(463,plain,
product(product(x0,a),product(b,b)) = product(product(x0,a),b),
inference(symmetry,[status(thm)],[462]) ).
tff(464,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(x0,a),product(b,b)) = product(product(x0,b),product(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(465,plain,
product(product(x0,a),product(b,b)) = product(product(x0,b),product(a,b)),
inference(unit_resolution,[status(thm)],[464,45]) ).
tff(466,plain,
product(product(x0,b),product(a,b)) = product(product(x0,a),product(b,b)),
inference(symmetry,[status(thm)],[465]) ).
tff(467,plain,
product(product(x0,b),product(a,b)) = product(product(x0,a),b),
inference(transitivity,[status(thm)],[466,463]) ).
tff(468,plain,
product(product(a,c),product(c,c)) = product(product(a,c),c),
inference(monotonicity,[status(thm)],[37]) ).
tff(469,plain,
product(product(product(a,a),c),product(product(c,c),c)) = product(product(a,c),c),
inference(transitivity,[status(thm)],[433,430,468]) ).
tff(470,plain,
product(product(product(product(a,a),c),product(product(c,c),c)),product(c,product(c,a))) = product(product(product(a,c),c),product(c,product(c,a))),
inference(monotonicity,[status(thm)],[469]) ).
tff(471,plain,
product(product(product(a,c),c),product(c,product(c,a))) = product(product(product(product(a,a),c),product(product(c,c),c)),product(c,product(c,a))),
inference(symmetry,[status(thm)],[470]) ).
tff(472,plain,
^ [B: $i,A: $i] :
refl(( ( product(product(product(A,B),B),product(B,product(B,A))) = B )
<=> ( product(product(product(A,B),B),product(B,product(B,A))) = B ) )),
inference(bind,[status(th)],[]) ).
tff(473,plain,
( ! [B: $i,A: $i] : ( product(product(product(A,B),B),product(B,product(B,A))) = B )
<=> ! [B: $i,A: $i] : ( product(product(product(A,B),B),product(B,product(B,A))) = B ) ),
inference(quant_intro,[status(thm)],[472]) ).
tff(474,plain,
( ! [B: $i,A: $i] : ( product(product(product(A,B),B),product(B,product(B,A))) = B )
<=> ! [B: $i,A: $i] : ( product(product(product(A,B),B),product(B,product(B,A))) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(475,axiom,
! [B: $i,A: $i] : ( product(product(product(A,B),B),product(B,product(B,A))) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
tff(476,plain,
! [B: $i,A: $i] : ( product(product(product(A,B),B),product(B,product(B,A))) = B ),
inference(modus_ponens,[status(thm)],[475,474]) ).
tff(477,plain,
! [B: $i,A: $i] : ( product(product(product(A,B),B),product(B,product(B,A))) = B ),
inference(skolemize,[status(sab)],[476]) ).
tff(478,plain,
! [B: $i,A: $i] : ( product(product(product(A,B),B),product(B,product(B,A))) = B ),
inference(modus_ponens,[status(thm)],[477,473]) ).
tff(479,plain,
( ~ ! [B: $i,A: $i] : ( product(product(product(A,B),B),product(B,product(B,A))) = B )
| ( product(product(product(a,c),c),product(c,product(c,a))) = c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(480,plain,
product(product(product(a,c),c),product(c,product(c,a))) = c,
inference(unit_resolution,[status(thm)],[479,478]) ).
tff(481,plain,
c = product(product(product(a,c),c),product(c,product(c,a))),
inference(symmetry,[status(thm)],[480]) ).
tff(482,plain,
c = product(product(product(product(a,a),c),product(product(c,c),c)),product(c,product(c,a))),
inference(transitivity,[status(thm)],[481,471]) ).
tff(483,plain,
product(c,product(product(x0,b),product(a,b))) = product(product(product(product(product(a,a),c),product(product(c,c),c)),product(c,product(c,a))),product(product(x0,a),b)),
inference(monotonicity,[status(thm)],[482,467]) ).
tff(484,plain,
product(product(x0,a),b) = product(product(x0,b),product(a,b)),
inference(transitivity,[status(thm)],[462,465]) ).
tff(485,plain,
product(product(c,c),product(product(x0,a),b)) = product(c,product(product(x0,b),product(a,b))),
inference(monotonicity,[status(thm)],[37,484]) ).
tff(486,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(c,product(x0,a)),product(c,b)) = product(product(c,c),product(product(x0,a),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(487,plain,
product(product(c,product(x0,a)),product(c,b)) = product(product(c,c),product(product(x0,a),b)),
inference(unit_resolution,[status(thm)],[486,45]) ).
tff(488,plain,
product(product(c,c),product(x0,a)) = product(c,product(x0,a)),
inference(monotonicity,[status(thm)],[37]) ).
tff(489,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(c,c),product(x0,a)) = product(product(c,x0),product(c,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(490,plain,
product(product(c,c),product(x0,a)) = product(product(c,x0),product(c,a)),
inference(unit_resolution,[status(thm)],[489,45]) ).
tff(491,plain,
product(product(c,x0),product(c,a)) = product(product(c,c),product(x0,a)),
inference(symmetry,[status(thm)],[490]) ).
tff(492,plain,
product(product(c,x0),product(c,a)) = product(c,product(x0,a)),
inference(transitivity,[status(thm)],[491,488]) ).
tff(493,plain,
product(product(product(c,x0),product(c,a)),product(c,b)) = product(product(c,product(x0,a)),product(c,b)),
inference(monotonicity,[status(thm)],[492]) ).
tff(494,plain,
product(c,product(x0,a)) = product(product(c,c),product(x0,a)),
inference(symmetry,[status(thm)],[488]) ).
tff(495,plain,
product(c,product(x0,a)) = product(product(c,x0),product(c,a)),
inference(transitivity,[status(thm)],[494,490]) ).
tff(496,plain,
product(product(c,product(x0,a)),product(product(c,b),product(c,b))) = product(product(product(c,x0),product(c,a)),product(c,b)),
inference(monotonicity,[status(thm)],[495,121]) ).
tff(497,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(c,product(x0,a)),product(product(c,b),product(c,b))) = product(product(c,product(c,b)),product(product(x0,a),product(c,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(498,plain,
product(product(c,product(x0,a)),product(product(c,b),product(c,b))) = product(product(c,product(c,b)),product(product(x0,a),product(c,b))),
inference(unit_resolution,[status(thm)],[497,45]) ).
tff(499,plain,
product(product(c,product(c,b)),product(product(x0,a),product(c,b))) = product(product(c,product(x0,a)),product(product(c,b),product(c,b))),
inference(symmetry,[status(thm)],[498]) ).
tff(500,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(x0,a),product(c,b)) = product(product(x0,c),product(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(501,plain,
product(product(x0,a),product(c,b)) = product(product(x0,c),product(a,b)),
inference(unit_resolution,[status(thm)],[500,45]) ).
tff(502,plain,
product(product(x0,c),product(a,b)) = product(product(x0,a),product(c,b)),
inference(symmetry,[status(thm)],[501]) ).
tff(503,plain,
product(product(c,c),product(c,b)) = product(c,product(c,b)),
inference(monotonicity,[status(thm)],[37]) ).
tff(504,plain,
product(product(product(c,c),product(c,b)),product(product(x0,c),product(a,b))) = product(product(c,product(c,b)),product(product(x0,a),product(c,b))),
inference(monotonicity,[status(thm)],[503,502]) ).
tff(505,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) )
| ( product(product(product(c,c),product(x0,c)),product(product(c,b),product(a,b))) = product(product(product(c,c),product(c,b)),product(product(x0,c),product(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(506,plain,
product(product(product(c,c),product(x0,c)),product(product(c,b),product(a,b))) = product(product(product(c,c),product(c,b)),product(product(x0,c),product(a,b))),
inference(unit_resolution,[status(thm)],[505,45]) ).
tff(507,plain,
product(product(c,product(a,c)),product(b,product(c,b))) = product(product(c,b),product(product(a,c),product(c,b))),
inference(symmetry,[status(thm)],[402]) ).
tff(508,plain,
product(product(c,product(a,c)),product(b,product(c,b))) = product(product(c,b),product(a,b)),
inference(transitivity,[status(thm)],[507,358]) ).
tff(509,plain,
product(product(product(c,c),product(x0,c)),product(product(c,product(a,c)),product(b,product(c,b)))) = product(product(product(c,c),product(x0,c)),product(product(c,b),product(a,b))),
inference(monotonicity,[status(thm)],[508]) ).
tff(510,plain,
product(product(product(c,c),product(x0,c)),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))) = product(product(product(c,c),product(x0,c)),product(product(c,product(a,c)),product(b,product(c,b)))),
inference(monotonicity,[status(thm)],[441]) ).
tff(511,plain,
product(product(product(c,c),product(x0,c)),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))) = product(product(product(product(a,b),x0),product(product(a,b),a)),product(product(c,product(c,c)),product(c,product(b,b)))),
inference(transitivity,[status(thm)],[510,509,506,504,499,496,493,487,485,483,461,459,448,440,437,416,364,362,352,350,342,318,315,310,298,297,295,280,258,255,240,238,217,192,190,167,164,157,154]) ).
tff(512,plain,
quotient(product(product(product(c,c),product(x0,c)),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))) = quotient(product(product(product(product(a,b),x0),product(product(a,b),a)),product(product(c,product(c,c)),product(c,product(b,b)))),product(product(c,product(c,c)),product(c,product(b,b)))),
inference(monotonicity,[status(thm)],[511,144]) ).
tff(513,plain,
quotient(product(product(product(product(a,b),x0),product(product(a,b),a)),product(product(c,product(c,c)),product(c,product(b,b)))),product(product(c,product(c,c)),product(c,product(b,b)))) = quotient(product(product(product(c,c),product(x0,c)),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))),product(product(product(c,c),product(a,b)),product(product(b,b),product(a,b)))),
inference(symmetry,[status(thm)],[512]) ).
tff(514,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(product(product(a,b),x0),product(product(a,b),a)),product(product(c,product(c,c)),product(c,product(b,b)))),product(product(c,product(c,c)),product(c,product(b,b)))) = product(product(product(a,b),x0),product(product(a,b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(515,plain,
quotient(product(product(product(product(a,b),x0),product(product(a,b),a)),product(product(c,product(c,c)),product(c,product(b,b)))),product(product(c,product(c,c)),product(c,product(b,b)))) = product(product(product(a,b),x0),product(product(a,b),a)),
inference(unit_resolution,[status(thm)],[514,17]) ).
tff(516,plain,
product(product(product(a,b),x0),product(product(a,b),a)) = quotient(product(product(product(product(a,b),x0),product(product(a,b),a)),product(product(c,product(c,c)),product(c,product(b,b)))),product(product(c,product(c,c)),product(c,product(b,b)))),
inference(symmetry,[status(thm)],[515]) ).
tff(517,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( bigC(A,B,C) = product(product(A,B),product(C,A)) )
| ( bigC(a,b,x0) = product(product(a,b),product(x0,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(518,plain,
bigC(a,b,x0) = product(product(a,b),product(x0,a)),
inference(unit_resolution,[status(thm)],[517,7]) ).
tff(519,plain,
bigC(a,b,x0) = bigC(c,c,x0),
inference(transitivity,[status(thm)],[518,147,150,516,513,19,10]) ).
tff(520,plain,
( ( bigC(a,b,x0) != bigC(c,c,x0) )
<=> ( bigC(a,b,x0) != bigC(c,c,x0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(521,axiom,
bigC(a,b,x0) != bigC(c,c,x0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(522,plain,
bigC(a,b,x0) != bigC(c,c,x0),
inference(modus_ponens,[status(thm)],[521,520]) ).
tff(523,plain,
$false,
inference(unit_resolution,[status(thm)],[522,519]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP777-10 : TPTP v9.0.0. Released v8.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 17:10:33 EDT 2025
% 0.12/0.34 % CPUTime :
% 228.49/228.75 % SZS status Unsatisfiable
% 228.49/228.75 % SZS output start Proof
% See solution above
% 228.86/229.06 % E exiting
%------------------------------------------------------------------------------