%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MSC005-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:17:30 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 30
% Syntax : Number of formulae : 70 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 329 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 486 ( 234 ~; 222 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 136 ( 123 !; 0 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
tff(value_type,type,
value: ( $i * $i ) > $o ).
tff(falsity_type,type,
falsity: $i ).
tff(xor_type,type,
xor: ( $i * $i ) > $i ).
tff(truth_type,type,
truth: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
<=> ( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
<=> ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
<=> ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
rewrite(( ( ~ value(X,truth)
| ~ value(Y,falsity)
| value(xor(X,Y),truth) )
<=> ( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( ~ value(X,truth)
| ~ value(Y,falsity)
| value(xor(X,Y),truth) )
<=> ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [Y: $i,X: $i] :
( ~ value(X,truth)
| ~ value(Y,falsity)
| value(xor(X,Y),truth) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',true_xor_false) ).
tff(7,plain,
! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( value(falsity,falsity)
<=> value(falsity,falsity) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
value(falsity,falsity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_is_false) ).
tff(13,plain,
value(falsity,falsity),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( value(truth,truth)
<=> value(truth,truth) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
value(truth,truth),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',true_is_true) ).
tff(16,plain,
value(truth,truth),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(falsity,falsity)
| ~ value(truth,truth)
| value(xor(truth,falsity),truth) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(falsity,falsity)
| ~ value(truth,truth)
| value(xor(truth,falsity),truth) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ value(truth,truth)
| value(xor(truth,falsity),truth)
| ~ value(falsity,falsity) )
<=> ( ~ value(falsity,falsity)
| ~ value(truth,truth)
| value(xor(truth,falsity),truth) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(truth,truth)
| value(xor(truth,falsity),truth)
| ~ value(falsity,falsity) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(falsity,falsity)
| ~ value(truth,truth)
| value(xor(truth,falsity),truth) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(truth,truth)
| value(xor(truth,falsity),truth)
| ~ value(falsity,falsity) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(falsity,falsity)
| ~ value(truth,truth)
| value(xor(truth,falsity),truth) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(truth,truth)
| value(xor(truth,falsity),truth)
| ~ value(falsity,falsity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(falsity,falsity)
| ~ value(truth,truth)
| value(xor(truth,falsity),truth) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
value(xor(truth,falsity),truth),
inference(unit_resolution,[status(thm)],[22,16,13,10]) ).
tff(24,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(falsity,falsity)
| value(xor(xor(truth,falsity),falsity),truth)
| ~ value(xor(truth,falsity),truth) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(falsity,falsity)
| value(xor(xor(truth,falsity),falsity),truth)
| ~ value(xor(truth,falsity),truth) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ value(xor(truth,falsity),truth)
| value(xor(xor(truth,falsity),falsity),truth)
| ~ value(falsity,falsity) )
<=> ( ~ value(falsity,falsity)
| value(xor(xor(truth,falsity),falsity),truth)
| ~ value(xor(truth,falsity),truth) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(xor(truth,falsity),truth)
| value(xor(xor(truth,falsity),falsity),truth)
| ~ value(falsity,falsity) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(falsity,falsity)
| value(xor(xor(truth,falsity),falsity),truth)
| ~ value(xor(truth,falsity),truth) ) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(xor(truth,falsity),truth)
| value(xor(xor(truth,falsity),falsity),truth)
| ~ value(falsity,falsity) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(falsity,falsity)
| value(xor(xor(truth,falsity),falsity),truth)
| ~ value(xor(truth,falsity),truth) ) ),
inference(transitivity,[status(thm)],[26,24]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(xor(truth,falsity),truth)
| value(xor(xor(truth,falsity),falsity),truth)
| ~ value(falsity,falsity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [Y: $i,X: $i] :
( ~ value(X,truth)
| value(xor(X,Y),truth)
| ~ value(Y,falsity) )
| ~ value(falsity,falsity)
| value(xor(xor(truth,falsity),falsity),truth)
| ~ value(xor(truth,falsity),truth) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( value(xor(xor(truth,falsity),falsity),truth)
| ~ value(xor(truth,falsity),truth) ),
inference(unit_resolution,[status(thm)],[29,13,10]) ).
tff(31,plain,
value(xor(xor(truth,falsity),falsity),truth),
inference(unit_resolution,[status(thm)],[30,23]) ).
tff(32,plain,
^ [Y: $i,X: $i] :
refl(( ( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) )
<=> ( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) )
<=> ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) )
<=> ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [Y: $i,X: $i] :
rewrite(( ( ~ value(X,truth)
| ~ value(Y,truth)
| value(xor(X,Y),falsity) )
<=> ( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [Y: $i,X: $i] :
( ~ value(X,truth)
| ~ value(Y,truth)
| value(xor(X,Y),falsity) )
<=> ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [Y: $i,X: $i] :
( ~ value(X,truth)
| ~ value(Y,truth)
| value(xor(X,Y),falsity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',true_xor_true) ).
tff(38,plain,
! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) )
| value(xor(xor(xor(truth,falsity),falsity),truth),falsity)
| ~ value(truth,truth)
| ~ value(xor(xor(truth,falsity),falsity),truth) )
<=> ( ~ ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) )
| value(xor(xor(xor(truth,falsity),falsity),truth),falsity)
| ~ value(truth,truth)
| ~ value(xor(xor(truth,falsity),falsity),truth) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) )
| value(xor(xor(xor(truth,falsity),falsity),truth),falsity)
| ~ value(truth,truth)
| ~ value(xor(xor(truth,falsity),falsity),truth) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,truth)
| ~ value(X,truth) )
| value(xor(xor(xor(truth,falsity),falsity),truth),falsity)
| ~ value(truth,truth)
| ~ value(xor(xor(truth,falsity),falsity),truth) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( value(xor(xor(xor(truth,falsity),falsity),truth),falsity)
| ~ value(xor(xor(truth,falsity),falsity),truth) ),
inference(unit_resolution,[status(thm)],[44,16,41]) ).
tff(46,plain,
value(xor(xor(xor(truth,falsity),falsity),truth),falsity),
inference(unit_resolution,[status(thm)],[45,31]) ).
tff(47,plain,
^ [Y: $i,X: $i] :
refl(( ( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) )
<=> ( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) )
<=> ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) )
<=> ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
^ [Y: $i,X: $i] :
rewrite(( ( ~ value(X,falsity)
| ~ value(Y,falsity)
| value(xor(X,Y),falsity) )
<=> ( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [Y: $i,X: $i] :
( ~ value(X,falsity)
| ~ value(Y,falsity)
| value(xor(X,Y),falsity) )
<=> ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [Y: $i,X: $i] :
( ~ value(X,falsity)
| ~ value(Y,falsity)
| value(xor(X,Y),falsity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_xor_false) ).
tff(53,plain,
! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
( ( ~ ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) )
| value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),falsity)
| ~ value(falsity,falsity)
| ~ value(xor(xor(xor(truth,falsity),falsity),truth),falsity) )
<=> ( ~ ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) )
| value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),falsity)
| ~ value(falsity,falsity)
| ~ value(xor(xor(xor(truth,falsity),falsity),truth),falsity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) )
| value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),falsity)
| ~ value(falsity,falsity)
| ~ value(xor(xor(xor(truth,falsity),falsity),truth),falsity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [Y: $i,X: $i] :
( value(xor(X,Y),falsity)
| ~ value(Y,falsity)
| ~ value(X,falsity) )
| value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),falsity)
| ~ value(falsity,falsity)
| ~ value(xor(xor(xor(truth,falsity),falsity),truth),falsity) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),falsity)
| ~ value(xor(xor(xor(truth,falsity),falsity),truth),falsity) ),
inference(unit_resolution,[status(thm)],[59,13,56]) ).
tff(61,plain,
value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),falsity),
inference(unit_resolution,[status(thm)],[60,46]) ).
tff(62,plain,
^ [Value: $i] :
refl(( ~ value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),Value)
<=> ~ value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),Value) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [Value: $i] : ~ value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),Value)
<=> ! [Value: $i] : ~ value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),Value) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [Value: $i] : ~ value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),Value)
<=> ! [Value: $i] : ~ value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),Value) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
! [Value: $i] : ~ value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),Value),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',evaluate_expression) ).
tff(66,plain,
! [Value: $i] : ~ value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),Value),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [Value: $i] : ~ value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),Value),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [Value: $i] : ~ value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),Value),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
( ~ ! [Value: $i] : ~ value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),Value)
| ~ value(xor(xor(xor(xor(truth,falsity),falsity),truth),falsity),falsity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
$false,
inference(unit_resolution,[status(thm)],[69,68,61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : MSC005-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 23:32:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% See solution above
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------