%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT005-10 : TPTP v9.0.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:13:42 AM UTC 2025
% Result : Unsatisfiable 13.14s 13.37s
% Output : Proof 13.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 72
% Syntax : Number of formulae : 228 ( 170 unt; 0 typ; 0 def)
% Number of atoms : 308 ( 296 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 106 ( 37 ~; 33 |; 0 &)
% ( 36 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 11 ( 11 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 : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 313 ( 287 !; 0 ?; 313 :)
% Comments :
%------------------------------------------------------------------------------
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(r2_type,type,
r2: $i ).
tff(r1_type,type,
r1: $i ).
tff(b_type,type,
b: $i ).
tff(ifeq3_type,type,
ifeq3: ( $i * $i * $i * $i ) > $i ).
tff(n0_type,type,
n0: $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(true_type,type,
true: $i ).
tff(complement_type,type,
complement: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq3(A,A,B,C) = B )
<=> ( ifeq3(A,A,B,C) = B ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(5,plain,
! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B )
| ( ifeq3(r1,r1,meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),join(r1,meet(meet(r2,b),join(r1,meet(r2,a))))) = meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq3(r1,r1,meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),join(r1,meet(meet(r2,b),join(r1,meet(r2,a))))) = meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,Y) = meet(Y,X) )
<=> ( meet(X,Y) = meet(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
<=> ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
<=> ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
tff(14,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))) = meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))) = meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))) = meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [Y: $i,X: $i] :
refl(( ( meet(X,join(X,Y)) = X )
<=> ( meet(X,join(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption1) ).
tff(24,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(r1,join(r1,meet(r2,a))) = r1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
meet(r1,join(r1,meet(r2,a))) = r1,
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
r1 = meet(r1,join(r1,meet(r2,a))),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
ifeq3(r1,r1,meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),join(r1,meet(meet(r2,b),join(r1,meet(r2,a))))) = ifeq3(meet(r1,join(r1,meet(r2,a))),r1,meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))),join(r1,meet(meet(r2,b),join(r1,meet(r2,a))))),
inference(monotonicity,[status(thm)],[29,19]) ).
tff(31,plain,
ifeq3(meet(r1,join(r1,meet(r2,a))),r1,meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))),join(r1,meet(meet(r2,b),join(r1,meet(r2,a))))) = ifeq3(r1,r1,meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),join(r1,meet(meet(r2,b),join(r1,meet(r2,a))))),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ifeq3(meet(X,Z),X,meet(Z,join(X,Y)),join(X,meet(Y,Z))) = join(X,meet(Y,Z)) )
<=> ( ifeq3(meet(X,Z),X,meet(Z,join(X,Y)),join(X,meet(Y,Z))) = join(X,meet(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [Z: $i,Y: $i,X: $i] : ( ifeq3(meet(X,Z),X,meet(Z,join(X,Y)),join(X,meet(Y,Z))) = join(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( ifeq3(meet(X,Z),X,meet(Z,join(X,Y)),join(X,meet(Y,Z))) = join(X,meet(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [Z: $i,Y: $i,X: $i] : ( ifeq3(meet(X,Z),X,meet(Z,join(X,Y)),join(X,meet(Y,Z))) = join(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( ifeq3(meet(X,Z),X,meet(Z,join(X,Y)),join(X,meet(Y,Z))) = join(X,meet(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
! [Z: $i,Y: $i,X: $i] : ( ifeq3(meet(X,Z),X,meet(Z,join(X,Y)),join(X,meet(Y,Z))) = join(X,meet(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modular) ).
tff(36,plain,
! [Z: $i,Y: $i,X: $i] : ( ifeq3(meet(X,Z),X,meet(Z,join(X,Y)),join(X,meet(Y,Z))) = join(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [Z: $i,Y: $i,X: $i] : ( ifeq3(meet(X,Z),X,meet(Z,join(X,Y)),join(X,meet(Y,Z))) = join(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Z: $i,Y: $i,X: $i] : ( ifeq3(meet(X,Z),X,meet(Z,join(X,Y)),join(X,meet(Y,Z))) = join(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( ifeq3(meet(X,Z),X,meet(Z,join(X,Y)),join(X,meet(Y,Z))) = join(X,meet(Y,Z)) )
| ( ifeq3(meet(r1,join(r1,meet(r2,a))),r1,meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))),join(r1,meet(meet(r2,b),join(r1,meet(r2,a))))) = join(r1,meet(meet(r2,b),join(r1,meet(r2,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
ifeq3(meet(r1,join(r1,meet(r2,a))),r1,meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))),join(r1,meet(meet(r2,b),join(r1,meet(r2,a))))) = join(r1,meet(meet(r2,b),join(r1,meet(r2,a)))),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
join(r1,meet(meet(r2,b),join(r1,meet(r2,a)))) = ifeq3(meet(r1,join(r1,meet(r2,a))),r1,meet(join(r1,meet(r2,a)),join(r1,meet(r2,b))),join(r1,meet(meet(r2,b),join(r1,meet(r2,a))))),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(join(a,b),r1) = meet(r1,join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
meet(join(a,b),r1) = meet(r1,join(a,b)),
inference(unit_resolution,[status(thm)],[42,16]) ).
tff(44,plain,
meet(join(a,b),meet(r1,join(r1,meet(r2,a)))) = meet(join(a,b),r1),
inference(monotonicity,[status(thm)],[28]) ).
tff(45,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_meet) ).
tff(49,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(a,b),r1),join(r1,meet(r2,a))) = meet(join(a,b),meet(r1,join(r1,meet(r2,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
meet(meet(join(a,b),r1),join(r1,meet(r2,a))) = meet(join(a,b),meet(r1,join(r1,meet(r2,a)))),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
meet(r1,join(a,b)) = meet(join(a,b),r1),
inference(symmetry,[status(thm)],[43]) ).
tff(55,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq(A,A,B,C) = B )
<=> ( ifeq(A,A,B,C) = B ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
tff(59,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,meet(r1,join(a,b)),n0) = meet(r1,join(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
ifeq(true,true,meet(r1,join(a,b)),n0) = meet(r1,join(a,b)),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
( ( complement(r1,join(a,b)) = true )
<=> ( complement(r1,join(a,b)) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
complement(r1,join(a,b)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_join_b) ).
tff(66,plain,
complement(r1,join(a,b)) = true,
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
true = complement(r1,join(a,b)),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
ifeq(true,true,meet(r1,join(a,b)),n0) = ifeq(complement(r1,join(a,b)),true,meet(r1,join(a,b)),n0),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
ifeq(complement(r1,join(a,b)),true,meet(r1,join(a,b)),n0) = ifeq(true,true,meet(r1,join(a,b)),n0),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
^ [Y: $i,X: $i] :
refl(( ( ifeq(complement(X,Y),true,meet(X,Y),n0) = n0 )
<=> ( ifeq(complement(X,Y),true,meet(X,Y),n0) = n0 ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [Y: $i,X: $i] : ( ifeq(complement(X,Y),true,meet(X,Y),n0) = n0 )
<=> ! [Y: $i,X: $i] : ( ifeq(complement(X,Y),true,meet(X,Y),n0) = n0 ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [Y: $i,X: $i] : ( ifeq(complement(X,Y),true,meet(X,Y),n0) = n0 )
<=> ! [Y: $i,X: $i] : ( ifeq(complement(X,Y),true,meet(X,Y),n0) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
! [Y: $i,X: $i] : ( ifeq(complement(X,Y),true,meet(X,Y),n0) = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_meet) ).
tff(74,plain,
! [Y: $i,X: $i] : ( ifeq(complement(X,Y),true,meet(X,Y),n0) = n0 ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [Y: $i,X: $i] : ( ifeq(complement(X,Y),true,meet(X,Y),n0) = n0 ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [Y: $i,X: $i] : ( ifeq(complement(X,Y),true,meet(X,Y),n0) = n0 ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq(complement(X,Y),true,meet(X,Y),n0) = n0 )
| ( ifeq(complement(r1,join(a,b)),true,meet(r1,join(a,b)),n0) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
ifeq(complement(r1,join(a,b)),true,meet(r1,join(a,b)),n0) = n0,
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
n0 = ifeq(complement(r1,join(a,b)),true,meet(r1,join(a,b)),n0),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
n0 = meet(join(a,b),r1),
inference(transitivity,[status(thm)],[79,69,63,54]) ).
tff(81,plain,
meet(n0,join(r1,meet(r2,a))) = meet(meet(join(a,b),r1),join(r1,meet(r2,a))),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq(complement(X,Y),true,meet(X,Y),n0) = n0 )
| ( ifeq(complement(r2,meet(a,b)),true,meet(r2,meet(a,b)),n0) = n0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
ifeq(complement(r2,meet(a,b)),true,meet(r2,meet(a,b)),n0) = n0,
inference(unit_resolution,[status(thm)],[82,76]) ).
tff(84,plain,
( ( complement(r2,meet(a,b)) = true )
<=> ( complement(r2,meet(a,b)) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,axiom,
complement(r2,meet(a,b)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_meet_b) ).
tff(86,plain,
complement(r2,meet(a,b)) = true,
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
true = complement(r2,meet(a,b)),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
ifeq(true,true,meet(r2,meet(a,b)),n0) = ifeq(complement(r2,meet(a,b)),true,meet(r2,meet(a,b)),n0),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,meet(r2,meet(a,b)),n0) = meet(r2,meet(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
ifeq(true,true,meet(r2,meet(a,b)),n0) = meet(r2,meet(a,b)),
inference(unit_resolution,[status(thm)],[89,61]) ).
tff(91,plain,
meet(r2,meet(a,b)) = ifeq(true,true,meet(r2,meet(a,b)),n0),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
meet(r2,meet(a,b)) = n0,
inference(transitivity,[status(thm)],[91,88,83]) ).
tff(93,plain,
meet(meet(r2,meet(a,b)),join(r1,meet(r2,a))) = meet(n0,join(r1,meet(r2,a))),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,meet(a,b)),join(r1,meet(r2,a))) = meet(r2,meet(meet(a,b),join(r1,meet(r2,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
meet(meet(r2,meet(a,b)),join(r1,meet(r2,a))) = meet(r2,meet(meet(a,b),join(r1,meet(r2,a)))),
inference(unit_resolution,[status(thm)],[94,51]) ).
tff(96,plain,
meet(r2,meet(meet(a,b),join(r1,meet(r2,a)))) = meet(meet(r2,meet(a,b)),join(r1,meet(r2,a))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(a,b),join(r1,meet(r2,a))) = meet(a,meet(b,join(r1,meet(r2,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
meet(meet(a,b),join(r1,meet(r2,a))) = meet(a,meet(b,join(r1,meet(r2,a)))),
inference(unit_resolution,[status(thm)],[97,51]) ).
tff(99,plain,
meet(a,meet(b,join(r1,meet(r2,a)))) = meet(meet(a,b),join(r1,meet(r2,a))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(b,join(r1,meet(r2,a))) = meet(join(r1,meet(r2,a)),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
meet(b,join(r1,meet(r2,a))) = meet(join(r1,meet(r2,a)),b),
inference(unit_resolution,[status(thm)],[100,16]) ).
tff(102,plain,
meet(a,meet(b,join(r1,meet(r2,a)))) = meet(a,meet(join(r1,meet(r2,a)),b)),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
meet(a,meet(join(r1,meet(r2,a)),b)) = meet(a,meet(b,join(r1,meet(r2,a)))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(join(r1,meet(r2,a)),b),a) = meet(a,meet(join(r1,meet(r2,a)),b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
meet(meet(join(r1,meet(r2,a)),b),a) = meet(a,meet(join(r1,meet(r2,a)),b)),
inference(unit_resolution,[status(thm)],[104,16]) ).
tff(106,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B )
| ( ifeq3(a,a,meet(join(a,b),join(r1,a)),a) = meet(join(a,b),join(r1,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
ifeq3(a,a,meet(join(a,b),join(r1,a)),a) = meet(join(a,b),join(r1,a)),
inference(unit_resolution,[status(thm)],[106,7]) ).
tff(108,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(meet(a,b),r2) = meet(r2,meet(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
meet(meet(a,b),r2) = meet(r2,meet(a,b)),
inference(unit_resolution,[status(thm)],[108,16]) ).
tff(110,plain,
meet(r2,meet(a,b)) = meet(meet(a,b),r2),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
ifeq(complement(r2,meet(a,b)),true,meet(r2,meet(a,b)),n0) = ifeq(true,true,meet(r2,meet(a,b)),n0),
inference(symmetry,[status(thm)],[88]) ).
tff(112,plain,
n0 = ifeq(complement(r2,meet(a,b)),true,meet(r2,meet(a,b)),n0),
inference(symmetry,[status(thm)],[83]) ).
tff(113,plain,
meet(r1,join(a,b)) = ifeq(true,true,meet(r1,join(a,b)),n0),
inference(symmetry,[status(thm)],[63]) ).
tff(114,plain,
meet(r1,join(a,b)) = meet(meet(a,b),r2),
inference(transitivity,[status(thm)],[113,68,78,112,111,90,110]) ).
tff(115,plain,
join(a,meet(r1,join(a,b))) = join(a,meet(meet(a,b),r2)),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
join(a,meet(meet(a,b),r2)) = join(a,meet(r1,join(a,b))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
meet(meet(a,b),r2) = n0,
inference(transitivity,[status(thm)],[109,91,88,83]) ).
tff(118,plain,
join(a,meet(meet(a,b),r2)) = join(a,n0),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
join(a,n0) = join(a,meet(meet(a,b),r2)),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
^ [X: $i] :
refl(( ( join(X,n0) = X )
<=> ( join(X,n0) = X ) )),
inference(bind,[status(th)],[]) ).
tff(121,plain,
( ! [X: $i] : ( join(X,n0) = X )
<=> ! [X: $i] : ( join(X,n0) = X ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
( ! [X: $i] : ( join(X,n0) = X )
<=> ! [X: $i] : ( join(X,n0) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,axiom,
! [X: $i] : ( join(X,n0) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_join_0) ).
tff(124,plain,
! [X: $i] : ( join(X,n0) = X ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [X: $i] : ( join(X,n0) = X ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [X: $i] : ( join(X,n0) = X ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
( ~ ! [X: $i] : ( join(X,n0) = X )
| ( join(a,n0) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
join(a,n0) = a,
inference(unit_resolution,[status(thm)],[127,126]) ).
tff(129,plain,
a = join(a,n0),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
a = join(a,meet(r1,join(a,b))),
inference(transitivity,[status(thm)],[129,119,116]) ).
tff(131,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,Y) = join(Y,X) )
<=> ( join(X,Y) = join(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(132,plain,
( ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
<=> ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ) ),
inference(quant_intro,[status(thm)],[131]) ).
tff(133,plain,
( ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
<=> ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,axiom,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
tff(135,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(skolemize,[status(sab)],[135]) ).
tff(137,plain,
! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) ),
inference(modus_ponens,[status(thm)],[136,132]) ).
tff(138,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,r1) = join(r1,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
join(a,r1) = join(r1,a),
inference(unit_resolution,[status(thm)],[138,137]) ).
tff(140,plain,
meet(join(a,b),join(a,r1)) = meet(join(a,b),join(r1,a)),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
meet(join(a,b),join(r1,a)) = meet(join(a,b),join(a,r1)),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(a,join(a,b)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(143,plain,
meet(a,join(a,b)) = a,
inference(unit_resolution,[status(thm)],[142,26]) ).
tff(144,plain,
a = meet(a,join(a,b)),
inference(symmetry,[status(thm)],[143]) ).
tff(145,plain,
ifeq3(a,a,meet(join(a,b),join(r1,a)),a) = ifeq3(meet(a,join(a,b)),a,meet(join(a,b),join(a,r1)),join(a,meet(r1,join(a,b)))),
inference(monotonicity,[status(thm)],[144,141,130]) ).
tff(146,plain,
ifeq3(meet(a,join(a,b)),a,meet(join(a,b),join(a,r1)),join(a,meet(r1,join(a,b)))) = ifeq3(a,a,meet(join(a,b),join(r1,a)),a),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( ifeq3(meet(X,Z),X,meet(Z,join(X,Y)),join(X,meet(Y,Z))) = join(X,meet(Y,Z)) )
| ( ifeq3(meet(a,join(a,b)),a,meet(join(a,b),join(a,r1)),join(a,meet(r1,join(a,b)))) = join(a,meet(r1,join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,plain,
ifeq3(meet(a,join(a,b)),a,meet(join(a,b),join(a,r1)),join(a,meet(r1,join(a,b)))) = join(a,meet(r1,join(a,b))),
inference(unit_resolution,[status(thm)],[147,38]) ).
tff(149,plain,
join(a,meet(r1,join(a,b))) = ifeq3(meet(a,join(a,b)),a,meet(join(a,b),join(a,r1)),join(a,meet(r1,join(a,b)))),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
a = meet(join(a,b),join(r1,a)),
inference(transitivity,[status(thm)],[129,119,116,149,146,107]) ).
tff(151,plain,
meet(meet(join(r1,meet(r2,a)),b),a) = meet(meet(join(r1,meet(r2,a)),b),meet(join(a,b),join(r1,a))),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
meet(meet(join(r1,meet(r2,a)),b),meet(join(a,b),join(r1,a))) = meet(meet(join(r1,meet(r2,a)),b),a),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(meet(join(r1,meet(r2,a)),b),join(a,b)),join(r1,a)) = meet(meet(join(r1,meet(r2,a)),b),meet(join(a,b),join(r1,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
meet(meet(meet(join(r1,meet(r2,a)),b),join(a,b)),join(r1,a)) = meet(meet(join(r1,meet(r2,a)),b),meet(join(a,b),join(r1,a))),
inference(unit_resolution,[status(thm)],[153,51]) ).
tff(155,plain,
join(r1,a) = join(a,r1),
inference(symmetry,[status(thm)],[139]) ).
tff(156,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(b,join(b,a)) = b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
meet(b,join(b,a)) = b,
inference(unit_resolution,[status(thm)],[156,26]) ).
tff(158,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(b,a) = join(a,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
join(b,a) = join(a,b),
inference(unit_resolution,[status(thm)],[158,137]) ).
tff(160,plain,
join(a,b) = join(b,a),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
meet(b,join(a,b)) = meet(b,join(b,a)),
inference(monotonicity,[status(thm)],[160]) ).
tff(162,plain,
meet(b,join(a,b)) = b,
inference(transitivity,[status(thm)],[161,157]) ).
tff(163,plain,
meet(join(r1,meet(r2,a)),meet(b,join(a,b))) = meet(join(r1,meet(r2,a)),b),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(join(r1,meet(r2,a)),b),join(a,b)) = meet(join(r1,meet(r2,a)),meet(b,join(a,b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
meet(meet(join(r1,meet(r2,a)),b),join(a,b)) = meet(join(r1,meet(r2,a)),meet(b,join(a,b))),
inference(unit_resolution,[status(thm)],[164,51]) ).
tff(166,plain,
meet(meet(join(r1,meet(r2,a)),b),join(a,b)) = meet(join(r1,meet(r2,a)),b),
inference(transitivity,[status(thm)],[165,163]) ).
tff(167,plain,
meet(meet(meet(join(r1,meet(r2,a)),b),join(a,b)),join(r1,a)) = meet(meet(join(r1,meet(r2,a)),b),join(a,r1)),
inference(monotonicity,[status(thm)],[166,155]) ).
tff(168,plain,
meet(meet(join(r1,meet(r2,a)),b),join(a,r1)) = meet(meet(meet(join(r1,meet(r2,a)),b),join(a,b)),join(r1,a)),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
meet(join(r1,meet(r2,a)),b) = meet(b,join(r1,meet(r2,a))),
inference(symmetry,[status(thm)],[101]) ).
tff(170,plain,
meet(meet(join(r1,meet(r2,a)),b),join(a,r1)) = meet(meet(b,join(r1,meet(r2,a))),join(r1,a)),
inference(monotonicity,[status(thm)],[169,139]) ).
tff(171,plain,
meet(meet(b,join(r1,meet(r2,a))),join(r1,a)) = meet(meet(join(r1,meet(r2,a)),b),join(a,r1)),
inference(symmetry,[status(thm)],[170]) ).
tff(172,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(b,join(r1,meet(r2,a))),join(r1,a)) = meet(b,meet(join(r1,meet(r2,a)),join(r1,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
meet(meet(b,join(r1,meet(r2,a))),join(r1,a)) = meet(b,meet(join(r1,meet(r2,a)),join(r1,a))),
inference(unit_resolution,[status(thm)],[172,51]) ).
tff(174,plain,
meet(b,meet(join(r1,meet(r2,a)),join(r1,a))) = meet(meet(b,join(r1,meet(r2,a))),join(r1,a)),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,join(X,Y)) = X )
| ( meet(join(r1,meet(r2,a)),join(join(r1,meet(r2,a)),a)) = join(r1,meet(r2,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
meet(join(r1,meet(r2,a)),join(join(r1,meet(r2,a)),a)) = join(r1,meet(r2,a)),
inference(unit_resolution,[status(thm)],[175,26]) ).
tff(177,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(a,join(r1,meet(r2,a))) = join(join(r1,meet(r2,a)),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(178,plain,
join(a,join(r1,meet(r2,a))) = join(join(r1,meet(r2,a)),a),
inference(unit_resolution,[status(thm)],[177,137]) ).
tff(179,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,Y) = join(Y,X) )
| ( join(meet(r2,a),r1) = join(r1,meet(r2,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(180,plain,
join(meet(r2,a),r1) = join(r1,meet(r2,a)),
inference(unit_resolution,[status(thm)],[179,137]) ).
tff(181,plain,
join(r1,meet(r2,a)) = join(meet(r2,a),r1),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
join(a,join(r1,meet(r2,a))) = join(a,join(meet(r2,a),r1)),
inference(monotonicity,[status(thm)],[181]) ).
tff(183,plain,
join(a,join(meet(r2,a),r1)) = join(a,join(r1,meet(r2,a))),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(185,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[184]) ).
tff(186,plain,
( ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,axiom,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_join) ).
tff(188,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(skolemize,[status(sab)],[188]) ).
tff(190,plain,
! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) ),
inference(modus_ponens,[status(thm)],[189,185]) ).
tff(191,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( join(join(X,Y),Z) = join(X,join(Y,Z)) )
| ( join(join(a,meet(r2,a)),r1) = join(a,join(meet(r2,a),r1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,plain,
join(join(a,meet(r2,a)),r1) = join(a,join(meet(r2,a),r1)),
inference(unit_resolution,[status(thm)],[191,190]) ).
tff(193,plain,
^ [Y: $i,X: $i] :
refl(( ( join(X,meet(X,Y)) = X )
<=> ( join(X,meet(X,Y)) = X ) )),
inference(bind,[status(th)],[]) ).
tff(194,plain,
( ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ) ),
inference(quant_intro,[status(thm)],[193]) ).
tff(195,plain,
( ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
<=> ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(196,axiom,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
tff(197,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(skolemize,[status(sab)],[197]) ).
tff(199,plain,
! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X ),
inference(modus_ponens,[status(thm)],[198,194]) ).
tff(200,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(a,meet(a,r2)) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(201,plain,
join(a,meet(a,r2)) = a,
inference(unit_resolution,[status(thm)],[200,199]) ).
tff(202,plain,
( ~ ! [Y: $i,X: $i] : ( meet(X,Y) = meet(Y,X) )
| ( meet(a,r2) = meet(r2,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(203,plain,
meet(a,r2) = meet(r2,a),
inference(unit_resolution,[status(thm)],[202,16]) ).
tff(204,plain,
meet(r2,a) = meet(a,r2),
inference(symmetry,[status(thm)],[203]) ).
tff(205,plain,
join(a,meet(r2,a)) = join(a,meet(a,r2)),
inference(monotonicity,[status(thm)],[204]) ).
tff(206,plain,
join(a,meet(r2,a)) = a,
inference(transitivity,[status(thm)],[205,201]) ).
tff(207,plain,
join(join(a,meet(r2,a)),r1) = join(a,r1),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
join(a,r1) = join(join(a,meet(r2,a)),r1),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
join(r1,a) = join(join(r1,meet(r2,a)),a),
inference(transitivity,[status(thm)],[155,208,192,183,178]) ).
tff(210,plain,
meet(join(r1,meet(r2,a)),join(r1,a)) = meet(join(r1,meet(r2,a)),join(join(r1,meet(r2,a)),a)),
inference(monotonicity,[status(thm)],[209]) ).
tff(211,plain,
meet(join(r1,meet(r2,a)),join(r1,a)) = join(r1,meet(r2,a)),
inference(transitivity,[status(thm)],[210,176]) ).
tff(212,plain,
meet(b,meet(join(r1,meet(r2,a)),join(r1,a))) = meet(b,join(r1,meet(r2,a))),
inference(monotonicity,[status(thm)],[211]) ).
tff(213,plain,
meet(b,join(r1,meet(r2,a))) = meet(b,meet(join(r1,meet(r2,a)),join(r1,a))),
inference(symmetry,[status(thm)],[212]) ).
tff(214,plain,
meet(b,join(r1,meet(r2,a))) = meet(meet(a,b),join(r1,meet(r2,a))),
inference(transitivity,[status(thm)],[213,174,171,168,154,152,105,103,99]) ).
tff(215,plain,
meet(r2,meet(b,join(r1,meet(r2,a)))) = meet(r2,meet(meet(a,b),join(r1,meet(r2,a)))),
inference(monotonicity,[status(thm)],[214]) ).
tff(216,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) )
| ( meet(meet(r2,b),join(r1,meet(r2,a))) = meet(r2,meet(b,join(r1,meet(r2,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
meet(meet(r2,b),join(r1,meet(r2,a))) = meet(r2,meet(b,join(r1,meet(r2,a)))),
inference(unit_resolution,[status(thm)],[216,51]) ).
tff(218,plain,
meet(meet(r2,b),join(r1,meet(r2,a))) = meet(r1,join(a,b)),
inference(transitivity,[status(thm)],[217,215,96,93,81,53,44,43]) ).
tff(219,plain,
join(r1,meet(meet(r2,b),join(r1,meet(r2,a)))) = join(r1,meet(r1,join(a,b))),
inference(monotonicity,[status(thm)],[218]) ).
tff(220,plain,
join(r1,meet(r1,join(a,b))) = join(r1,meet(meet(r2,b),join(r1,meet(r2,a)))),
inference(symmetry,[status(thm)],[219]) ).
tff(221,plain,
( ~ ! [Y: $i,X: $i] : ( join(X,meet(X,Y)) = X )
| ( join(r1,meet(r1,join(a,b))) = r1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(222,plain,
join(r1,meet(r1,join(a,b))) = r1,
inference(unit_resolution,[status(thm)],[221,199]) ).
tff(223,plain,
r1 = join(r1,meet(r1,join(a,b))),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
r1 = meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
inference(transitivity,[status(thm)],[223,220,41,31,9]) ).
tff(225,plain,
( ( r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))) )
<=> ( r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(226,axiom,
r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lemma) ).
tff(227,plain,
r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
inference(modus_ponens,[status(thm)],[226,225]) ).
tff(228,plain,
$false,
inference(unit_resolution,[status(thm)],[227,224]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT005-10 : TPTP v9.0.0. Released v7.5.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 19:25:26 EDT 2025
% 0.11/0.33 % CPUTime :
% 13.14/13.37 % SZS status Unsatisfiable
% 13.14/13.37 % SZS output start Proof
% See solution above
% 13.22/13.39 % E exiting
%------------------------------------------------------------------------------