TSTP Solution File: GRP767-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP767-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 : Fri Sep 16 22:29:48 EDT 2022
% Result : Unsatisfiable 11.08s 7.33s
% Output : Proof 11.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 78
% Syntax : Number of formulae : 232 ( 168 unt; 9 typ; 0 def)
% Number of atoms : 304 ( 290 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 100 ( 32 ~; 28 |; 0 &)
% ( 40 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 13 ( 13 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 6 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 264 ( 240 !; 0 ?; 264 :)
% Comments :
%------------------------------------------------------------------------------
tff(j_type,type,
j: $i > $i ).
tff(x1_type,type,
x1: $i ).
tff(product_type,type,
product: ( $i * $i ) > $i ).
tff(x0_type,type,
x0: $i ).
tff(quotient_type,type,
quotient: ( $i * $i ) > $i ).
tff(one_type,type,
one: $i ).
tff(difference_type,type,
difference: ( $i * $i ) > $i ).
tff(i_type,type,
i: $i > $i ).
tff(eta_type,type,
eta: $i > $i ).
tff(1,plain,
^ [A: $i] :
refl(
( ( j(A) = quotient(one,A) )
<=> ( j(A) = quotient(one,A) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i] : ( j(A) = quotient(one,A) )
<=> ! [A: $i] : ( j(A) = quotient(one,A) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( j(A) = quotient(one,A) )
<=> ! [A: $i] : ( j(A) = quotient(one,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [A: $i] : ( j(A) = quotient(one,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
tff(5,plain,
! [A: $i] : ( j(A) = quotient(one,A) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( j(A) = quotient(one,A) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( j(A) = quotient(one,A) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
| ( j(x1) = quotient(one,x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
j(x1) = quotient(one,x1),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
quotient(one,x1) = j(x1),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i] :
refl(
( ( difference(A,product(A,B)) = B )
<=> ( difference(A,product(A,B)) = B ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
<=> ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
<=> ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
tff(15,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i] : ( difference(A,product(A,B)) = B ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(x0,j(x0)),product(product(x0,j(x0)),quotient(one,x1))) = quotient(one,x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
difference(product(x0,j(x0)),product(product(x0,j(x0)),quotient(one,x1))) = quotient(one,x1),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
^ [A: $i] :
refl(
( ( product(A,one) = A )
<=> ( product(A,one) = A ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [A: $i] : ( product(A,one) = A )
<=> ! [A: $i] : ( product(A,one) = A ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [A: $i] : ( product(A,one) = A )
<=> ! [A: $i] : ( product(A,one) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
! [A: $i] : ( product(A,one) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
tff(24,plain,
! [A: $i] : ( product(A,one) = A ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [A: $i] : ( product(A,one) = A ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [A: $i] : ( product(A,one) = A ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [A: $i] : ( product(A,one) = A )
| ( product(x0,one) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
product(x0,one) = x0,
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
^ [B: $i,A: $i] :
refl(
( ( product(quotient(A,B),B) = A )
<=> ( product(quotient(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
tff(33,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [B: $i,A: $i] : ( product(quotient(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(one,x0),x0) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
product(quotient(one,x0),x0) = one,
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
product(x0,product(quotient(one,x0),x0)) = product(x0,one),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
^ [B: $i,A: $i] :
refl(
( ( product(A,difference(A,B)) = B )
<=> ( product(A,difference(A,B)) = B ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
<=> ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
<=> ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
tff(43,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [B: $i,A: $i] : ( product(A,difference(A,B)) = B ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(product(x0,j(x0)),difference(product(x0,j(x0)),product(x0,product(quotient(one,x0),x0)))) = product(x0,product(quotient(one,x0),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
product(product(x0,j(x0)),difference(product(x0,j(x0)),product(x0,product(quotient(one,x0),x0)))) = product(x0,product(quotient(one,x0),x0)),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
| ( j(x0) = quotient(one,x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
j(x0) = quotient(one,x0),
inference(unit_resolution,[status(thm)],[48,7]) ).
tff(50,plain,
quotient(one,x0) = j(x0),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
product(x0,quotient(one,x0)) = product(x0,j(x0)),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
product(x0,j(x0)) = product(x0,quotient(one,x0)),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
difference(product(x0,j(x0)),product(x0,product(quotient(one,x0),x0))) = difference(product(x0,quotient(one,x0)),product(x0,product(quotient(one,x0),x0))),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
difference(product(x0,quotient(one,x0)),product(x0,product(quotient(one,x0),x0))) = difference(product(x0,j(x0)),product(x0,product(quotient(one,x0),x0))),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
<=> ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
tff(59,plain,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(product(A,B),product(A,product(B,C))) = quotient(quotient(product(C,product(A,B)),B),A) )
| ( difference(product(x0,quotient(one,x0)),product(x0,product(quotient(one,x0),x0))) = quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
difference(product(x0,quotient(one,x0)),product(x0,product(quotient(one,x0),x0))) = quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0) = difference(product(x0,quotient(one,x0)),product(x0,product(quotient(one,x0),x0))),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0) = difference(product(x0,j(x0)),product(x0,product(quotient(one,x0),x0))),
inference(transitivity,[status(thm)],[64,54]) ).
tff(66,plain,
product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)) = product(product(x0,j(x0)),difference(product(x0,j(x0)),product(x0,product(quotient(one,x0),x0)))),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)) = x0,
inference(transitivity,[status(thm)],[66,47,38,28]) ).
tff(68,plain,
product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0))) = product(x0,j(product(x1,x0))),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
product(x0,j(product(x1,x0))) = product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0))),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
^ [B: $i,A: $i] :
refl(
( ( quotient(product(A,B),B) = A )
<=> ( quotient(product(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(71,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)],[70]) ).
tff(72,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(73,axiom,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
tff(74,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [B: $i,A: $i] : ( quotient(product(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(x0,j(product(x1,x0))),x1),x1) = product(x0,j(product(x1,x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
quotient(product(product(x0,j(product(x1,x0))),x1),x1) = product(x0,j(product(x1,x0))),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
( ~ ! [B: $i,A: $i] : ( product(A,difference(A,B)) = B )
| ( product(x0,difference(x0,product(product(x0,j(product(x1,x0))),x1))) = product(product(x0,j(product(x1,x0))),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
product(x0,difference(x0,product(product(x0,j(product(x1,x0))),x1))) = product(product(x0,j(product(x1,x0))),x1),
inference(unit_resolution,[status(thm)],[79,45]) ).
tff(81,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(one,product(x1,x0)),product(x1,x0)) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
product(quotient(one,product(x1,x0)),product(x1,x0)) = one,
inference(unit_resolution,[status(thm)],[81,35]) ).
tff(83,plain,
( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
| ( j(product(x1,x0)) = quotient(one,product(x1,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
j(product(x1,x0)) = quotient(one,product(x1,x0)),
inference(unit_resolution,[status(thm)],[83,7]) ).
tff(85,plain,
product(j(product(x1,x0)),product(x1,x0)) = product(quotient(one,product(x1,x0)),product(x1,x0)),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
product(j(product(x1,x0)),product(x1,x0)) = one,
inference(transitivity,[status(thm)],[85,82]) ).
tff(87,plain,
quotient(product(j(product(x1,x0)),product(x1,x0)),x0) = quotient(one,x0),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
<=> ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
<=> ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,axiom,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
tff(92,plain,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( difference(A,product(product(A,B),C)) = quotient(product(B,product(C,A)),A) )
| ( difference(x0,product(product(x0,j(product(x1,x0))),x1)) = quotient(product(j(product(x1,x0)),product(x1,x0)),x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
difference(x0,product(product(x0,j(product(x1,x0))),x1)) = quotient(product(j(product(x1,x0)),product(x1,x0)),x0),
inference(unit_resolution,[status(thm)],[95,94]) ).
tff(97,plain,
difference(x0,product(product(x0,j(product(x1,x0))),x1)) = j(x0),
inference(transitivity,[status(thm)],[96,87,50]) ).
tff(98,plain,
product(x0,difference(x0,product(product(x0,j(product(x1,x0))),x1))) = product(x0,j(x0)),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
product(x0,j(x0)) = product(x0,difference(x0,product(product(x0,j(product(x1,x0))),x1))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
^ [A: $i] :
refl(
( ( product(i(A),A) = product(A,j(A)) )
<=> ( product(i(A),A) = product(A,j(A)) ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
<=> ! [A: $i] : ( product(i(A),A) = product(A,j(A)) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
<=> ! [A: $i] : ( product(i(A),A) = product(A,j(A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,axiom,
! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
tff(104,plain,
! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
inference(skolemize,[status(sab)],[104]) ).
tff(106,plain,
! [A: $i] : ( product(i(A),A) = product(A,j(A)) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
( ~ ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
| ( product(i(x0),x0) = product(x0,j(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
product(i(x0),x0) = product(x0,j(x0)),
inference(unit_resolution,[status(thm)],[107,106]) ).
tff(109,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(quotient(one,x0),product(quotient(one,x0),x0)) = x0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
difference(quotient(one,x0),product(quotient(one,x0),x0)) = x0,
inference(unit_resolution,[status(thm)],[109,17]) ).
tff(111,plain,
one = product(quotient(one,x0),x0),
inference(symmetry,[status(thm)],[37]) ).
tff(112,plain,
difference(quotient(one,x0),one) = difference(quotient(one,x0),product(quotient(one,x0),x0)),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
^ [A: $i] :
refl(
( ( i(A) = difference(A,one) )
<=> ( i(A) = difference(A,one) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [A: $i] : ( i(A) = difference(A,one) )
<=> ! [A: $i] : ( i(A) = difference(A,one) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [A: $i] : ( i(A) = difference(A,one) )
<=> ! [A: $i] : ( i(A) = difference(A,one) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,axiom,
! [A: $i] : ( i(A) = difference(A,one) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
tff(117,plain,
! [A: $i] : ( i(A) = difference(A,one) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [A: $i] : ( i(A) = difference(A,one) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [A: $i] : ( i(A) = difference(A,one) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
( ~ ! [A: $i] : ( i(A) = difference(A,one) )
| ( i(quotient(one,x0)) = difference(quotient(one,x0),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
i(quotient(one,x0)) = difference(quotient(one,x0),one),
inference(unit_resolution,[status(thm)],[120,119]) ).
tff(122,plain,
i(quotient(one,x0)) = x0,
inference(transitivity,[status(thm)],[121,112,110]) ).
tff(123,plain,
i(i(quotient(one,x0))) = i(x0),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
product(i(i(quotient(one,x0))),x0) = product(i(x0),x0),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
^ [B: $i,A: $i] :
refl(
( ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
<=> ( product(i(i(A)),B) = product(eta(A),product(A,B)) ) )),
inference(bind,[status(th)],]) ).
tff(126,plain,
( ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
<=> ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
<=> ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,axiom,
! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos13) ).
tff(129,plain,
! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ),
inference(skolemize,[status(sab)],[129]) ).
tff(131,plain,
! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) ),
inference(modus_ponens,[status(thm)],[130,126]) ).
tff(132,plain,
( ~ ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
| ( product(i(i(quotient(one,x0))),x0) = product(eta(quotient(one,x0)),product(quotient(one,x0),x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
product(i(i(quotient(one,x0))),x0) = product(eta(quotient(one,x0)),product(quotient(one,x0),x0)),
inference(unit_resolution,[status(thm)],[132,131]) ).
tff(134,plain,
product(eta(quotient(one,x0)),product(quotient(one,x0),x0)) = product(i(i(quotient(one,x0))),x0),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
^ [A: $i] :
refl(
( ( eta(A) = product(i(A),A) )
<=> ( eta(A) = product(i(A),A) ) )),
inference(bind,[status(th)],]) ).
tff(136,plain,
( ! [A: $i] : ( eta(A) = product(i(A),A) )
<=> ! [A: $i] : ( eta(A) = product(i(A),A) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
( ! [A: $i] : ( eta(A) = product(i(A),A) )
<=> ! [A: $i] : ( eta(A) = product(i(A),A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,axiom,
! [A: $i] : ( eta(A) = product(i(A),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
tff(139,plain,
! [A: $i] : ( eta(A) = product(i(A),A) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
! [A: $i] : ( eta(A) = product(i(A),A) ),
inference(skolemize,[status(sab)],[139]) ).
tff(141,plain,
! [A: $i] : ( eta(A) = product(i(A),A) ),
inference(modus_ponens,[status(thm)],[140,136]) ).
tff(142,plain,
( ~ ! [A: $i] : ( eta(A) = product(i(A),A) )
| ( eta(quotient(one,x0)) = product(i(quotient(one,x0)),quotient(one,x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
eta(quotient(one,x0)) = product(i(quotient(one,x0)),quotient(one,x0)),
inference(unit_resolution,[status(thm)],[142,141]) ).
tff(144,plain,
product(i(quotient(one,x0)),quotient(one,x0)) = eta(quotient(one,x0)),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
i(j(x0)) = i(quotient(one,x0)),
inference(monotonicity,[status(thm)],[49]) ).
tff(146,plain,
i(quotient(one,x0)) = i(j(x0)),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
product(i(quotient(one,x0)),quotient(one,x0)) = product(i(j(x0)),j(x0)),
inference(monotonicity,[status(thm)],[146,50]) ).
tff(148,plain,
product(i(j(x0)),j(x0)) = product(i(quotient(one,x0)),quotient(one,x0)),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
i(j(x0)) = x0,
inference(transitivity,[status(thm)],[145,121,112,110]) ).
tff(150,plain,
product(i(j(x0)),j(x0)) = product(x0,j(x0)),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
product(x0,j(x0)) = product(i(j(x0)),j(x0)),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
product(x0,j(x0)) = eta(quotient(one,x0)),
inference(transitivity,[status(thm)],[151,148,144]) ).
tff(153,plain,
product(product(x0,j(x0)),product(quotient(one,x0),x0)) = product(eta(quotient(one,x0)),product(quotient(one,x0),x0)),
inference(monotonicity,[status(thm)],[152]) ).
tff(154,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(one,x1),x1) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(155,plain,
product(quotient(one,x1),x1) = one,
inference(unit_resolution,[status(thm)],[154,35]) ).
tff(156,plain,
product(quotient(one,x1),x1) = product(quotient(one,x0),x0),
inference(transitivity,[status(thm)],[155,111]) ).
tff(157,plain,
eta(quotient(one,x0)) = product(x0,j(x0)),
inference(transitivity,[status(thm)],[143,147,150]) ).
tff(158,plain,
product(eta(quotient(one,x0)),product(quotient(one,x1),x1)) = product(product(x0,j(x0)),product(quotient(one,x0),x0)),
inference(monotonicity,[status(thm)],[157,156]) ).
tff(159,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
<=> ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ) )),
inference(bind,[status(th)],]) ).
tff(160,plain,
( ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,plain,
( ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(162,axiom,
! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
tff(163,plain,
! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
inference(skolemize,[status(sab)],[163]) ).
tff(165,plain,
! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) ),
inference(modus_ponens,[status(thm)],[164,160]) ).
tff(166,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( product(eta(A),product(B,C)) = product(product(eta(A),B),C) )
| ( product(eta(quotient(one,x0)),product(quotient(one,x1),x1)) = product(product(eta(quotient(one,x0)),quotient(one,x1)),x1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(167,plain,
product(eta(quotient(one,x0)),product(quotient(one,x1),x1)) = product(product(eta(quotient(one,x0)),quotient(one,x1)),x1),
inference(unit_resolution,[status(thm)],[166,165]) ).
tff(168,plain,
product(product(eta(quotient(one,x0)),quotient(one,x1)),x1) = product(eta(quotient(one,x0)),product(quotient(one,x1),x1)),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
product(eta(quotient(one,x0)),quotient(one,x1)) = product(product(x0,j(x0)),quotient(one,x1)),
inference(monotonicity,[status(thm)],[157]) ).
tff(170,plain,
product(product(x0,j(x0)),quotient(one,x1)) = product(eta(quotient(one,x0)),quotient(one,x1)),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
product(product(product(x0,j(x0)),quotient(one,x1)),x1) = product(product(eta(quotient(one,x0)),quotient(one,x1)),x1),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
product(product(product(x0,j(x0)),quotient(one,x1)),x1) = product(product(x0,j(product(x1,x0))),x1),
inference(transitivity,[status(thm)],[171,168,158,153,134,124,108,99,80]) ).
tff(173,plain,
quotient(product(product(product(x0,j(x0)),quotient(one,x1)),x1),x1) = quotient(product(product(x0,j(product(x1,x0))),x1),x1),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
( ~ ! [B: $i,A: $i] : ( quotient(product(A,B),B) = A )
| ( quotient(product(product(product(x0,j(x0)),quotient(one,x1)),x1),x1) = product(product(x0,j(x0)),quotient(one,x1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(175,plain,
quotient(product(product(product(x0,j(x0)),quotient(one,x1)),x1),x1) = product(product(x0,j(x0)),quotient(one,x1)),
inference(unit_resolution,[status(thm)],[174,76]) ).
tff(176,plain,
product(product(x0,j(x0)),quotient(one,x1)) = quotient(product(product(product(x0,j(x0)),quotient(one,x1)),x1),x1),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
product(product(x0,j(x0)),quotient(one,x1)) = product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0))),
inference(transitivity,[status(thm)],[176,173,78,69]) ).
tff(178,plain,
difference(product(x0,j(x0)),product(product(x0,j(x0)),quotient(one,x1))) = difference(product(x0,j(x0)),product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0)))),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
difference(product(x0,j(x0)),product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0)))) = difference(product(x0,j(x0)),product(product(x0,j(x0)),quotient(one,x1))),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
( ~ ! [A: $i] : ( eta(A) = product(i(A),A) )
| ( eta(j(j(x0))) = product(i(j(j(x0))),j(j(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(181,plain,
eta(j(j(x0))) = product(i(j(j(x0))),j(j(x0))),
inference(unit_resolution,[status(thm)],[180,141]) ).
tff(182,plain,
product(i(j(j(x0))),j(j(x0))) = eta(j(j(x0))),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(j(j(x0)),product(j(j(x0)),quotient(one,x0))) = quotient(one,x0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(184,plain,
difference(j(j(x0)),product(j(j(x0)),quotient(one,x0))) = quotient(one,x0),
inference(unit_resolution,[status(thm)],[183,17]) ).
tff(185,plain,
quotient(one,quotient(one,x0)) = quotient(one,j(x0)),
inference(monotonicity,[status(thm)],[50]) ).
tff(186,plain,
quotient(one,j(x0)) = quotient(one,quotient(one,x0)),
inference(symmetry,[status(thm)],[185]) ).
tff(187,plain,
( ~ ! [A: $i] : ( j(A) = quotient(one,A) )
| ( j(j(x0)) = quotient(one,j(x0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
j(j(x0)) = quotient(one,j(x0)),
inference(unit_resolution,[status(thm)],[187,7]) ).
tff(189,plain,
j(j(x0)) = quotient(one,quotient(one,x0)),
inference(transitivity,[status(thm)],[188,186]) ).
tff(190,plain,
product(j(j(x0)),quotient(one,x0)) = product(quotient(one,quotient(one,x0)),quotient(one,x0)),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
product(quotient(one,quotient(one,x0)),quotient(one,x0)) = product(j(j(x0)),quotient(one,x0)),
inference(symmetry,[status(thm)],[190]) ).
tff(192,plain,
( ~ ! [B: $i,A: $i] : ( product(quotient(A,B),B) = A )
| ( product(quotient(one,quotient(one,x0)),quotient(one,x0)) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(193,plain,
product(quotient(one,quotient(one,x0)),quotient(one,x0)) = one,
inference(unit_resolution,[status(thm)],[192,35]) ).
tff(194,plain,
one = product(quotient(one,quotient(one,x0)),quotient(one,x0)),
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
one = product(j(j(x0)),quotient(one,x0)),
inference(transitivity,[status(thm)],[194,191]) ).
tff(196,plain,
difference(j(j(x0)),one) = difference(j(j(x0)),product(j(j(x0)),quotient(one,x0))),
inference(monotonicity,[status(thm)],[195]) ).
tff(197,plain,
( ~ ! [A: $i] : ( i(A) = difference(A,one) )
| ( i(j(j(x0))) = difference(j(j(x0)),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(198,plain,
i(j(j(x0))) = difference(j(j(x0)),one),
inference(unit_resolution,[status(thm)],[197,119]) ).
tff(199,plain,
i(j(j(x0))) = j(x0),
inference(transitivity,[status(thm)],[198,196,184,50]) ).
tff(200,plain,
product(i(j(j(x0))),j(j(x0))) = product(j(x0),j(j(x0))),
inference(monotonicity,[status(thm)],[199]) ).
tff(201,plain,
product(j(x0),j(j(x0))) = product(i(j(j(x0))),j(j(x0))),
inference(symmetry,[status(thm)],[200]) ).
tff(202,plain,
( ~ ! [A: $i] : ( product(i(A),A) = product(A,j(A)) )
| ( product(i(j(x0)),j(x0)) = product(j(x0),j(j(x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(203,plain,
product(i(j(x0)),j(x0)) = product(j(x0),j(j(x0))),
inference(unit_resolution,[status(thm)],[202,106]) ).
tff(204,plain,
product(x0,j(x0)) = eta(j(j(x0))),
inference(transitivity,[status(thm)],[151,203,201,182]) ).
tff(205,plain,
product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))) = product(eta(j(j(x0))),product(j(j(x0)),j(product(x1,x0)))),
inference(monotonicity,[status(thm)],[204]) ).
tff(206,plain,
product(eta(j(j(x0))),product(j(j(x0)),j(product(x1,x0)))) = product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
( ~ ! [B: $i,A: $i] : ( product(i(i(A)),B) = product(eta(A),product(A,B)) )
| ( product(i(i(j(j(x0)))),j(product(x1,x0))) = product(eta(j(j(x0))),product(j(j(x0)),j(product(x1,x0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(208,plain,
product(i(i(j(j(x0)))),j(product(x1,x0))) = product(eta(j(j(x0))),product(j(j(x0)),j(product(x1,x0)))),
inference(unit_resolution,[status(thm)],[207,131]) ).
tff(209,plain,
i(i(j(j(x0)))) = i(j(x0)),
inference(monotonicity,[status(thm)],[199]) ).
tff(210,plain,
i(i(j(j(x0)))) = x0,
inference(transitivity,[status(thm)],[209,145,121,112,110]) ).
tff(211,plain,
product(i(i(j(j(x0)))),j(product(x1,x0))) = product(x0,j(product(x1,x0))),
inference(monotonicity,[status(thm)],[210]) ).
tff(212,plain,
product(x0,j(product(x1,x0))) = product(i(i(j(j(x0)))),j(product(x1,x0))),
inference(symmetry,[status(thm)],[211]) ).
tff(213,plain,
product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0))) = product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0)))),
inference(transitivity,[status(thm)],[68,212,208,206]) ).
tff(214,plain,
difference(product(x0,j(x0)),product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0)))) = difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))),
inference(monotonicity,[status(thm)],[213]) ).
tff(215,plain,
difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))) = difference(product(x0,j(x0)),product(product(product(x0,j(x0)),quotient(quotient(product(x0,product(x0,quotient(one,x0))),quotient(one,x0)),x0)),j(product(x1,x0)))),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
( ~ ! [B: $i,A: $i] : ( difference(A,product(A,B)) = B )
| ( difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))) = product(j(j(x0)),j(product(x1,x0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(217,plain,
difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))) = product(j(j(x0)),j(product(x1,x0))),
inference(unit_resolution,[status(thm)],[216,17]) ).
tff(218,plain,
product(j(j(x0)),j(product(x1,x0))) = difference(product(x0,j(x0)),product(product(x0,j(x0)),product(j(j(x0)),j(product(x1,x0))))),
inference(symmetry,[status(thm)],[217]) ).
tff(219,plain,
product(j(j(x0)),j(product(x1,x0))) = j(x1),
inference(transitivity,[status(thm)],[218,215,179,19,10]) ).
tff(220,plain,
( ( product(j(j(x0)),j(product(x1,x0))) != j(x1) )
<=> ( product(j(j(x0)),j(product(x1,x0))) != j(x1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(221,axiom,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(222,plain,
product(j(j(x0)),j(product(x1,x0))) != j(x1),
inference(modus_ponens,[status(thm)],[221,220]) ).
tff(223,plain,
$false,
inference(unit_resolution,[status(thm)],[222,219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP767-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 20:54:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 11.08/7.33 % SZS status Unsatisfiable
% 11.08/7.33 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------