%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWC002-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:50 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 23
% Syntax : Number of formulae : 64 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 83 ( 65 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 8 ~; 4 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 104 ( 96 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
tff(circuit_type,type,
circuit: ( $i * $i * $i ) > $o ).
tff(bottom_type,type,
bottom: $i > $i ).
tff(connect_type,type,
connect: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(table_type,type,
table: ( $i * $i * $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(n0_type,type,
n0: $i ).
tff(top_type,type,
top: $i > $i ).
tff(and_type,type,
and: ( $i * $i ) > $i ).
tff(1,plain,
( ( and(n1,n1) = n1 )
<=> ( and(n1,n1) = n1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
and(n1,n1) = n1,
file('/export/starexec/sandbox/benchmark/Axioms/HWC001-0.ax',and_definition4) ).
tff(3,plain,
and(n1,n1) = n1,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
n1 = and(n1,n1),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( and(n1,n0) = n0 )
<=> ( and(n1,n0) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
and(n1,n0) = n0,
file('/export/starexec/sandbox/benchmark/Axioms/HWC001-0.ax',and_definition3) ).
tff(7,plain,
and(n1,n0) = n0,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
n0 = and(n1,n0),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
table(n0,n0,n1,n1) = table(and(n1,n0),and(n1,n0),and(n1,n1),and(n1,n1)),
inference(monotonicity,[status(thm)],[8,8,4,4]) ).
tff(10,plain,
table(and(n1,n0),and(n1,n0),and(n1,n1),and(n1,n1)) = table(n0,n0,n1,n1),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] :
refl(( ( and(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(and(X1,Y1),and(X2,Y2),and(X3,Y3),and(X4,Y4)) )
<=> ( and(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(and(X1,Y1),and(X2,Y2),and(X3,Y3),and(X4,Y4)) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] : ( and(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(and(X1,Y1),and(X2,Y2),and(X3,Y3),and(X4,Y4)) )
<=> ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] : ( and(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(and(X1,Y1),and(X2,Y2),and(X3,Y3),and(X4,Y4)) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] : ( and(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(and(X1,Y1),and(X2,Y2),and(X3,Y3),and(X4,Y4)) )
<=> ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] : ( and(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(and(X1,Y1),and(X2,Y2),and(X3,Y3),and(X4,Y4)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] : ( and(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(and(X1,Y1),and(X2,Y2),and(X3,Y3),and(X4,Y4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_table_definition) ).
tff(15,plain,
! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] : ( and(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(and(X1,Y1),and(X2,Y2),and(X3,Y3),and(X4,Y4)) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] : ( and(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(and(X1,Y1),and(X2,Y2),and(X3,Y3),and(X4,Y4)) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] : ( and(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(and(X1,Y1),and(X2,Y2),and(X3,Y3),and(X4,Y4)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] : ( and(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(and(X1,Y1),and(X2,Y2),and(X3,Y3),and(X4,Y4)) )
| ( and(table(n1,n1,n1,n1),table(n0,n0,n1,n1)) = table(and(n1,n0),and(n1,n0),and(n1,n1),and(n1,n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
and(table(n1,n1,n1,n1),table(n0,n0,n1,n1)) = table(and(n1,n0),and(n1,n0),and(n1,n1),and(n1,n1)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( ( table(n0,n0,n0,n0) = nil )
<=> ( table(n0,n0,n0,n0) = nil ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
table(n0,n0,n0,n0) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_table) ).
tff(22,plain,
table(n0,n0,n0,n0) = nil,
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
nil = table(n0,n0,n0,n0),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( ( table(n1,n1,n1,n1) = nil )
<=> ( table(n1,n1,n1,n1) = nil ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
table(n1,n1,n1,n1) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',full_table) ).
tff(26,plain,
table(n1,n1,n1,n1) = nil,
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
table(n1,n1,n1,n1) = table(n0,n0,n0,n0),
inference(transitivity,[status(thm)],[26,23]) ).
tff(28,plain,
and(table(n1,n1,n1,n1),table(n0,n0,n1,n1)) = and(table(n0,n0,n0,n0),table(n0,n0,n1,n1)),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
and(table(n0,n0,n0,n0),table(n0,n0,n1,n1)) = and(table(n1,n1,n1,n1),table(n0,n0,n1,n1)),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] : ( and(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(and(X1,Y1),and(X2,Y2),and(X3,Y3),and(X4,Y4)) )
| ( and(table(n0,n0,n0,n0),table(n0,n0,n1,n1)) = table(and(n0,n0),and(n0,n0),and(n0,n1),and(n0,n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
and(table(n0,n0,n0,n0),table(n0,n0,n1,n1)) = table(and(n0,n0),and(n0,n0),and(n0,n1),and(n0,n1)),
inference(unit_resolution,[status(thm)],[30,17]) ).
tff(32,plain,
table(and(n0,n0),and(n0,n0),and(n0,n1),and(n0,n1)) = and(table(n0,n0,n0,n0),table(n0,n0,n1,n1)),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ( and(n0,n1) = n0 )
<=> ( and(n0,n1) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
and(n0,n1) = n0,
file('/export/starexec/sandbox/benchmark/Axioms/HWC001-0.ax',and_definition2) ).
tff(35,plain,
and(n0,n1) = n0,
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
( ( and(n0,n0) = n0 )
<=> ( and(n0,n0) = n0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
and(n0,n0) = n0,
file('/export/starexec/sandbox/benchmark/Axioms/HWC001-0.ax',and_definition1) ).
tff(38,plain,
and(n0,n0) = n0,
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
table(and(n0,n0),and(n0,n0),and(n0,n1),and(n0,n1)) = table(n0,n0,n0,n0),
inference(monotonicity,[status(thm)],[38,38,35,35]) ).
tff(40,plain,
table(n0,n0,n0,n0) = table(and(n0,n0),and(n0,n0),and(n0,n1),and(n0,n1)),
inference(symmetry,[status(thm)],[39]) ).
tff(41,plain,
table(and(n0,n0),and(n0,n1),and(n0,n0),and(n0,n1)) = table(n0,n0,n0,n0),
inference(monotonicity,[status(thm)],[38,35,38,35]) ).
tff(42,plain,
( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] : ( and(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(and(X1,Y1),and(X2,Y2),and(X3,Y3),and(X4,Y4)) )
| ( and(table(n0,n0,n0,n0),table(n0,n1,n0,n1)) = table(and(n0,n0),and(n0,n1),and(n0,n0),and(n0,n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
and(table(n0,n0,n0,n0),table(n0,n1,n0,n1)) = table(and(n0,n0),and(n0,n1),and(n0,n0),and(n0,n1)),
inference(unit_resolution,[status(thm)],[42,17]) ).
tff(44,plain,
and(table(n1,n1,n1,n1),table(n0,n1,n0,n1)) = and(table(n0,n0,n0,n0),table(n0,n1,n0,n1)),
inference(monotonicity,[status(thm)],[27]) ).
tff(45,plain,
( ~ ! [Y4: $i,Y2: $i,Y1: $i,Y3: $i,X4: $i,X3: $i,X2: $i,X1: $i] : ( and(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(and(X1,Y1),and(X2,Y2),and(X3,Y3),and(X4,Y4)) )
| ( and(table(n1,n1,n1,n1),table(n0,n1,n0,n1)) = table(and(n1,n0),and(n1,n1),and(n1,n0),and(n1,n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
and(table(n1,n1,n1,n1),table(n0,n1,n0,n1)) = table(and(n1,n0),and(n1,n1),and(n1,n0),and(n1,n1)),
inference(unit_resolution,[status(thm)],[45,17]) ).
tff(47,plain,
table(and(n1,n0),and(n1,n1),and(n1,n0),and(n1,n1)) = and(table(n1,n1,n1,n1),table(n0,n1,n0,n1)),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
table(n0,n1,n0,n1) = table(and(n1,n0),and(n1,n1),and(n1,n0),and(n1,n1)),
inference(monotonicity,[status(thm)],[8,4,8,4]) ).
tff(49,plain,
table(n0,n1,n0,n1) = table(n0,n0,n1,n1),
inference(transitivity,[status(thm)],[48,47,44,43,41,40,32,29,19,10]) ).
tff(50,plain,
connect(table(n0,n1,n0,n1),nil) = connect(table(n0,n0,n1,n1),nil),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
top(connect(table(n0,n1,n0,n1),nil)) = top(connect(table(n0,n0,n1,n1),nil)),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( circuit(top(connect(table(n0,n1,n0,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil)))
<=> circuit(top(connect(table(n0,n0,n1,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil))) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
( circuit(top(connect(table(n0,n0,n1,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil)))
<=> circuit(top(connect(table(n0,n1,n0,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil))) ),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
bottom(connect(table(n0,n1,n0,n1),nil)) = bottom(connect(table(n0,n0,n1,n1),nil)),
inference(monotonicity,[status(thm)],[50]) ).
tff(55,plain,
( circuit(top(connect(table(n0,n0,n1,n1),nil)),nil,bottom(connect(table(n0,n1,n0,n1),nil)))
<=> circuit(top(connect(table(n0,n0,n1,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil))) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( circuit(top(connect(table(n0,n0,n1,n1),nil)),nil,bottom(connect(table(n0,n1,n0,n1),nil)))
<=> circuit(top(connect(table(n0,n0,n1,n1),nil)),nil,bottom(connect(table(n0,n1,n0,n1),nil))) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
circuit(top(connect(table(n0,n0,n1,n1),nil)),nil,bottom(connect(table(n0,n1,n0,n1),nil))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',input_configuration) ).
tff(58,plain,
circuit(top(connect(table(n0,n0,n1,n1),nil)),nil,bottom(connect(table(n0,n1,n0,n1),nil))),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
circuit(top(connect(table(n0,n0,n1,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil))),
inference(modus_ponens,[status(thm)],[58,55]) ).
tff(60,plain,
circuit(top(connect(table(n0,n1,n0,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil))),
inference(modus_ponens,[status(thm)],[59,53]) ).
tff(61,plain,
( ~ circuit(top(connect(table(n0,n1,n0,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil)))
<=> ~ circuit(top(connect(table(n0,n1,n0,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil))) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
~ circuit(top(connect(table(n0,n1,n0,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_output_configuration) ).
tff(63,plain,
~ circuit(top(connect(table(n0,n1,n0,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil))),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
$false,
inference(unit_resolution,[status(thm)],[63,60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HWC002-1 : TPTP v9.0.0. Released v1.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n013.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 17:18:08 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Unsatisfiable
% 0.11/0.38 % SZS output start Proof
% See solution above
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------