%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CAT010-10 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:00:21 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 35
% Syntax : Number of formulae : 97 ( 71 unt; 0 typ; 0 def)
% Number of atoms : 137 ( 129 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 47 ( 14 ~; 10 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 7 ( 7 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 : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 158 ( 143 !; 0 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
tff(codomain_type,type,
codomain: $i > $i ).
tff(a_type,type,
a: $i ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(ifeq2_type,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(domain_type,type,
domain: $i > $i ).
tff(true_type,type,
true: $i ).
tff(there_exists_type,type,
there_exists: $i > $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) )
<=> ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) )
<=> ! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) )
<=> ! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
tff(5,plain,
! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) )
| ( ifeq2(there_exists(compose(codomain(a),a)),true,domain(codomain(a)),codomain(a)) = codomain(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq2(there_exists(compose(codomain(a),a)),true,domain(codomain(a)),codomain(a)) = codomain(a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true )
<=> ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true )
<=> ! [X: $i] : ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true )
<=> ! [X: $i] : ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
tff(14,plain,
! [X: $i] : ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( ifeq(there_exists(domain(X)),true,there_exists(X),true) = true )
| ( ifeq(there_exists(domain(a)),true,there_exists(a),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ifeq(there_exists(domain(a)),true,there_exists(a),true) = true,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,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(20,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)],[19]) ).
tff(21,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(22,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
tff(23,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,there_exists(domain(a)),true) = there_exists(domain(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
ifeq(true,true,there_exists(domain(a)),true) = there_exists(domain(a)),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
( ( there_exists(compose(a,b)) = true )
<=> ( there_exists(compose(a,b)) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
there_exists(compose(a,b)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_exists) ).
tff(30,plain,
there_exists(compose(a,b)) = true,
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
true = there_exists(compose(a,b)),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
ifeq(true,true,there_exists(domain(a)),true) = ifeq(there_exists(compose(a,b)),true,there_exists(domain(a)),true),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
ifeq(there_exists(compose(a,b)),true,there_exists(domain(a)),true) = ifeq(true,true,there_exists(domain(a)),true),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
^ [Y: $i,X: $i] :
refl(( ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true )
<=> ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true )
<=> ! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true )
<=> ! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
tff(38,plain,
! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq(there_exists(compose(X,Y)),true,there_exists(domain(X)),true) = true )
| ( ifeq(there_exists(compose(a,b)),true,there_exists(domain(a)),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
ifeq(there_exists(compose(a,b)),true,there_exists(domain(a)),true) = true,
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
true = ifeq(there_exists(compose(a,b)),true,there_exists(domain(a)),true),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
true = there_exists(domain(a)),
inference(transitivity,[status(thm)],[43,33,27]) ).
tff(45,plain,
ifeq(true,true,there_exists(a),true) = ifeq(there_exists(domain(a)),true,there_exists(a),true),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,there_exists(a),true) = there_exists(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
ifeq(true,true,there_exists(a),true) = there_exists(a),
inference(unit_resolution,[status(thm)],[46,25]) ).
tff(48,plain,
there_exists(a) = ifeq(true,true,there_exists(a),true),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
^ [X: $i] :
refl(( ( compose(codomain(X),X) = X )
<=> ( compose(codomain(X),X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i] : ( compose(codomain(X),X) = X )
<=> ! [X: $i] : ( compose(codomain(X),X) = X ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [X: $i] : ( compose(codomain(X),X) = X )
<=> ! [X: $i] : ( compose(codomain(X),X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
! [X: $i] : ( compose(codomain(X),X) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
tff(53,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ~ ! [X: $i] : ( compose(codomain(X),X) = X )
| ( compose(codomain(a),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
compose(codomain(a),a) = a,
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
there_exists(compose(codomain(a),a)) = there_exists(a),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
there_exists(compose(codomain(a),a)) = true,
inference(transitivity,[status(thm)],[58,48,45,18]) ).
tff(60,plain,
ifeq2(there_exists(compose(codomain(a),a)),true,domain(codomain(a)),codomain(a)) = ifeq2(true,true,domain(codomain(a)),codomain(a)),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
ifeq2(true,true,domain(codomain(a)),codomain(a)) = ifeq2(there_exists(compose(codomain(a),a)),true,domain(codomain(a)),codomain(a)),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq2(A,A,B,C) = B )
<=> ( ifeq2(A,A,B,C) = B ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
tff(66,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,domain(codomain(a)),codomain(a)) = domain(codomain(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
ifeq2(true,true,domain(codomain(a)),codomain(a)) = domain(codomain(a)),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
domain(codomain(a)) = ifeq2(true,true,domain(codomain(a)),codomain(a)),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,domain(codomain(a)),codomain(compose(a,b))) = domain(codomain(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
ifeq2(true,true,domain(codomain(a)),codomain(compose(a,b))) = domain(codomain(a)),
inference(unit_resolution,[status(thm)],[72,68]) ).
tff(74,plain,
compose(compose(codomain(a),a),b) = compose(a,b),
inference(monotonicity,[status(thm)],[57]) ).
tff(75,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
<=> ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).
tff(79,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( compose(codomain(a),compose(a,b)) = compose(compose(codomain(a),a),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
compose(codomain(a),compose(a,b)) = compose(compose(codomain(a),a),b),
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
compose(codomain(a),compose(a,b)) = compose(a,b),
inference(transitivity,[status(thm)],[83,74]) ).
tff(85,plain,
there_exists(compose(codomain(a),compose(a,b))) = there_exists(compose(a,b)),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
there_exists(compose(a,b)) = there_exists(compose(codomain(a),compose(a,b))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
true = there_exists(compose(codomain(a),compose(a,b))),
inference(transitivity,[status(thm)],[31,86]) ).
tff(88,plain,
ifeq2(true,true,domain(codomain(a)),codomain(compose(a,b))) = ifeq2(there_exists(compose(codomain(a),compose(a,b))),true,domain(codomain(a)),codomain(compose(a,b))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
ifeq2(there_exists(compose(codomain(a),compose(a,b))),true,domain(codomain(a)),codomain(compose(a,b))) = ifeq2(true,true,domain(codomain(a)),codomain(compose(a,b))),
inference(symmetry,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [Y: $i,X: $i] : ( ifeq2(there_exists(compose(X,Y)),true,domain(X),codomain(Y)) = codomain(Y) )
| ( ifeq2(there_exists(compose(codomain(a),compose(a,b))),true,domain(codomain(a)),codomain(compose(a,b))) = codomain(compose(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
ifeq2(there_exists(compose(codomain(a),compose(a,b))),true,domain(codomain(a)),codomain(compose(a,b))) = codomain(compose(a,b)),
inference(unit_resolution,[status(thm)],[90,7]) ).
tff(92,plain,
codomain(compose(a,b)) = ifeq2(there_exists(compose(codomain(a),compose(a,b))),true,domain(codomain(a)),codomain(compose(a,b))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
codomain(compose(a,b)) = codomain(a),
inference(transitivity,[status(thm)],[92,89,73,71,61,9]) ).
tff(94,plain,
( ( codomain(compose(a,b)) != codomain(a) )
<=> ( codomain(compose(a,b)) != codomain(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,axiom,
codomain(compose(a,b)) != codomain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
tff(96,plain,
codomain(compose(a,b)) != codomain(a),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
$false,
inference(unit_resolution,[status(thm)],[96,93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT010-10 : TPTP v9.0.0. Released v7.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 11:54:01 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------