%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : REL046-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:23:49 AM UTC 2025
% Result : Unsatisfiable 5.74s 5.95s
% Output : Proof 5.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 67 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 90 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 14 ~; 10 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 4 ( 4 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 86 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk2_type,type,
sk2: $i ).
tff(join_type,type,
join: ( $i * $i ) > $i ).
tff(sk1_type,type,
sk1: $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(meet_type,type,
meet: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
<=> ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
<=> ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
<=> ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux3_a_kind_of_de_Morgan_3) ).
tff(5,plain,
! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
| ( sk2 = join(complement(join(complement(sk2),complement(sk3))),complement(join(complement(sk2),sk3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
sk2 = join(complement(join(complement(sk2),complement(sk3))),complement(join(complement(sk2),sk3))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
join(complement(join(complement(sk2),complement(sk3))),complement(join(complement(sk2),sk3))) = sk2,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i] :
refl(( ( meet(A,B) = complement(join(complement(A),complement(B))) )
<=> ( meet(A,B) = complement(join(complement(A),complement(B))) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) )
<=> ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) )
<=> ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux4_definiton_of_meet_4) ).
tff(15,plain,
! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i] : ( meet(A,B) = complement(join(complement(A),complement(B))) )
| ( meet(sk2,sk3) = complement(join(complement(sk2),complement(sk3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
meet(sk2,sk3) = complement(join(complement(sk2),complement(sk3))),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( ( join(sk1,meet(sk2,sk3)) = meet(sk2,sk3) )
<=> ( join(sk1,meet(sk2,sk3)) = meet(sk2,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
join(sk1,meet(sk2,sk3)) = meet(sk2,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
tff(22,plain,
join(sk1,meet(sk2,sk3)) = meet(sk2,sk3),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
join(sk1,meet(sk2,sk3)) = complement(join(complement(sk2),complement(sk3))),
inference(transitivity,[status(thm)],[22,19]) ).
tff(24,plain,
join(join(sk1,meet(sk2,sk3)),complement(join(complement(sk2),sk3))) = join(complement(join(complement(sk2),complement(sk3))),complement(join(complement(sk2),sk3))),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( join(A,join(B,C)) = join(join(A,B),C) )
<=> ( join(A,join(B,C)) = join(join(A,B),C) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux2_join_associativity_2) ).
tff(29,plain,
! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
| ( join(sk1,join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))) = join(join(sk1,meet(sk2,sk3)),complement(join(complement(sk2),sk3))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
join(sk1,join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))) = join(join(sk1,meet(sk2,sk3)),complement(join(complement(sk2),sk3))),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
join(meet(sk2,sk3),complement(join(complement(sk2),sk3))) = join(complement(join(complement(sk2),complement(sk3))),complement(join(complement(sk2),sk3))),
inference(monotonicity,[status(thm)],[19]) ).
tff(35,plain,
join(complement(join(complement(sk2),complement(sk3))),complement(join(complement(sk2),sk3))) = join(meet(sk2,sk3),complement(join(complement(sk2),sk3))),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
sk2 = join(meet(sk2,sk3),complement(join(complement(sk2),sk3))),
inference(transitivity,[status(thm)],[9,35]) ).
tff(37,plain,
join(sk1,sk2) = join(sk1,join(meet(sk2,sk3),complement(join(complement(sk2),sk3)))),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
join(sk1,sk2) = sk2,
inference(transitivity,[status(thm)],[37,33,24,10]) ).
tff(39,plain,
( ~ ! [B: $i,A: $i] : ( A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) )
| ( sk3 = join(complement(join(complement(sk3),complement(sk2))),complement(join(complement(sk3),sk2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
sk3 = join(complement(join(complement(sk3),complement(sk2))),complement(join(complement(sk3),sk2))),
inference(unit_resolution,[status(thm)],[39,7]) ).
tff(41,plain,
join(complement(join(complement(sk3),complement(sk2))),complement(join(complement(sk3),sk2))) = sk3,
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
^ [B: $i,A: $i] :
refl(( ( join(A,B) = join(B,A) )
<=> ( join(A,B) = join(B,A) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
<=> ! [B: $i,A: $i] : ( join(A,B) = join(B,A) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
<=> ! [B: $i,A: $i] : ( join(A,B) = join(B,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
! [B: $i,A: $i] : ( join(A,B) = join(B,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux1_join_commutativity_1) ).
tff(46,plain,
! [B: $i,A: $i] : ( join(A,B) = join(B,A) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [B: $i,A: $i] : ( join(A,B) = join(B,A) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [B: $i,A: $i] : ( join(A,B) = join(B,A) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i] : ( join(A,B) = join(B,A) )
| ( join(complement(sk2),complement(sk3)) = join(complement(sk3),complement(sk2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
join(complement(sk2),complement(sk3)) = join(complement(sk3),complement(sk2)),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
join(complement(sk3),complement(sk2)) = join(complement(sk2),complement(sk3)),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
complement(join(complement(sk3),complement(sk2))) = complement(join(complement(sk2),complement(sk3))),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
complement(join(complement(sk2),complement(sk3))) = complement(join(complement(sk3),complement(sk2))),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
join(sk1,meet(sk2,sk3)) = complement(join(complement(sk3),complement(sk2))),
inference(transitivity,[status(thm)],[22,19,53]) ).
tff(55,plain,
join(join(sk1,meet(sk2,sk3)),complement(join(complement(sk3),sk2))) = join(complement(join(complement(sk3),complement(sk2))),complement(join(complement(sk3),sk2))),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( join(A,join(B,C)) = join(join(A,B),C) )
| ( join(sk1,join(meet(sk2,sk3),complement(join(complement(sk3),sk2)))) = join(join(sk1,meet(sk2,sk3)),complement(join(complement(sk3),sk2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
join(sk1,join(meet(sk2,sk3),complement(join(complement(sk3),sk2)))) = join(join(sk1,meet(sk2,sk3)),complement(join(complement(sk3),sk2))),
inference(unit_resolution,[status(thm)],[56,31]) ).
tff(58,plain,
meet(sk2,sk3) = complement(join(complement(sk3),complement(sk2))),
inference(transitivity,[status(thm)],[19,53]) ).
tff(59,plain,
join(meet(sk2,sk3),complement(join(complement(sk3),sk2))) = join(complement(join(complement(sk3),complement(sk2))),complement(join(complement(sk3),sk2))),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
join(complement(join(complement(sk3),complement(sk2))),complement(join(complement(sk3),sk2))) = join(meet(sk2,sk3),complement(join(complement(sk3),sk2))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
sk3 = join(meet(sk2,sk3),complement(join(complement(sk3),sk2))),
inference(transitivity,[status(thm)],[40,60]) ).
tff(62,plain,
join(sk1,sk3) = join(sk1,join(meet(sk2,sk3),complement(join(complement(sk3),sk2)))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
join(sk1,sk3) = sk3,
inference(transitivity,[status(thm)],[62,57,55,41]) ).
tff(64,plain,
( ( ( join(sk1,sk2) != sk2 )
| ( join(sk1,sk3) != sk3 ) )
<=> ( ( join(sk1,sk2) != sk2 )
| ( join(sk1,sk3) != sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
( ( join(sk1,sk2) != sk2 )
| ( join(sk1,sk3) != sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_15) ).
tff(66,plain,
( ( join(sk1,sk2) != sk2 )
| ( join(sk1,sk3) != sk3 ) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
$false,
inference(unit_resolution,[status(thm)],[66,63,38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : REL046-1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 03:03:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 5.74/5.95 % SZS status Unsatisfiable
% 5.74/5.95 % SZS output start Proof
% See solution above
% 5.82/5.98 % E exiting
%------------------------------------------------------------------------------