TSTP Solution File: SYN195-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN195-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 : Thu Sep 29 23:54:09 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 81
% Syntax : Number of formulae : 162 ( 33 unt; 17 typ; 0 def)
% Number of atoms : 661 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 870 ( 401 ~; 391 |; 0 &)
% ( 78 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 47 ( 47 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 14 >; 13 *; 0 +; 0 <<)
% Number of predicates : 22 ( 20 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 328 ( 295 !; 0 ?; 328 :)
% Comments :
%------------------------------------------------------------------------------
tff(p3_type,type,
p3: ( $i * $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(n2_type,type,
n2: $i > $o ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(k1_type,type,
k1: $i > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(s4_type,type,
s4: $i > $o ).
tff(n3_type,type,
n3: $i > $o ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(r5_type,type,
r5: ( $i * $i ) > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(l1_type,type,
l1: ( $i * $i ) > $o ).
tff(1,plain,
^ [B: $i,C: $i] :
refl(
( ( ~ p0(C,B)
| p1(B,B,B) )
<=> ( ~ p0(C,B)
| p1(B,B,B) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [B: $i,C: $i] :
rewrite(
( ( p1(B,B,B)
| ~ p0(C,B) )
<=> ( ~ p0(C,B)
| p1(B,B,B) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [B: $i,C: $i] :
( p1(B,B,B)
| ~ p0(C,B) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [B: $i,C: $i] :
( p1(B,B,B)
| ~ p0(C,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_085) ).
tff(7,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( p0(b,d)
<=> p0(b,d) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
p0(b,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_10) ).
tff(13,plain,
p0(b,d),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) )
<=> ( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
p1(d,d,d),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( n2(A)
| ~ p1(B,C,A) )
<=> ( n2(A)
| ~ p1(B,C,A) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
<=> ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
<=> ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_137) ).
tff(22,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(d)
| ~ p1(d,d,d) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(d)
| ~ p1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(d)
| ~ p1(d,d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(d)
| ~ p1(d,d,d) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
n2(d),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
^ [H: $i] :
refl(
( ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
<=> ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
<=> ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
<=> ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [H: $i] :
trans(
monotonicity(
rewrite(
( ( p3(H,H,H)
| ~ k1(H) )
<=> ( ~ k1(H)
| p3(H,H,H) ) )),
( ( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) )
<=> ( ~ k1(H)
| p3(H,H,H)
| ~ n2(H) ) )),
rewrite(
( ( ~ k1(H)
| p3(H,H,H)
| ~ n2(H) )
<=> ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) )),
( ( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) )
<=> ( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [H: $i] :
( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) )
<=> ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [H: $i] :
( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_249) ).
tff(35,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
^ [I: $i,J: $i] :
refl(
( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(43,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( n0(c,d)
<=> n0(c,d) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
n0(c,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_34) ).
tff(48,plain,
n0(c,d),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(d)
| ~ n0(c,d) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(d)
| ~ n0(c,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(d)
| ~ n0(c,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(d)
| ~ n0(c,d) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
k1(d),
inference(unit_resolution,[status(thm)],[51,48,45]) ).
tff(53,plain,
( ( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(d)
| ~ n2(d)
| p3(d,d,d) )
<=> ( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(d)
| ~ n2(d)
| p3(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(d)
| ~ n2(d)
| p3(d,d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(d)
| ~ n2(d)
| p3(d,d,d) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
p3(d,d,d),
inference(unit_resolution,[status(thm)],[55,52,38,28]) ).
tff(57,plain,
^ [D: $i,E: $i,F: $i] :
refl(
( ( n3(D)
| ~ p2(E,F,D) )
<=> ( n3(D)
| ~ p2(E,F,D) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
<=> ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
<=> ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,axiom,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_240) ).
tff(61,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
^ [B: $i] :
refl(
( ( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ( p2(B,B,B)
| ~ n1(d,d,B) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_153) ).
tff(68,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( n1(d,d,d)
<=> n1(d,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( n1(d,d,d)
| $false )
<=> n1(d,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
q0(d,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_25) ).
tff(75,plain,
( q0(d,d)
<=> $true ),
inference(iff_true,[status(thm)],[74]) ).
tff(76,plain,
( ~ q0(d,d)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ~ q0(d,d)
<=> $false ),
inference(transitivity,[status(thm)],[76,73]) ).
tff(78,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> ( n1(d,d,d)
| $false ) ),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> n1(d,d,d) ),
inference(transitivity,[status(thm)],[78,72]) ).
tff(80,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> ( n1(d,d,d)
| ~ q0(d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,axiom,
( n1(d,d,d)
| ~ q0(d,d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_045) ).
tff(82,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[82,80]) ).
tff(84,plain,
n1(d,d,d),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
n1(d,d,d),
inference(modus_ponens,[status(thm)],[84,71]) ).
tff(86,plain,
( ( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) )
<=> ( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
p2(d,d,d),
inference(unit_resolution,[status(thm)],[88,85,70]) ).
tff(90,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(d)
| ~ p2(d,d,d) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(d)
| ~ p2(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(d)
| ~ p2(d,d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(d)
| ~ p2(d,d,d) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
n3(d),
inference(unit_resolution,[status(thm)],[92,89,63]) ).
tff(94,plain,
( ~ r5(d,d)
<=> ~ r5(d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(95,axiom,
~ r5(d,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(96,plain,
~ r5(d,d),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
^ [D: $i,C: $i] :
refl(
( ( ~ n3(D)
| ~ s4(C)
| r5(C,D) )
<=> ( ~ n3(D)
| ~ s4(C)
| r5(C,D) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [D: $i,C: $i] :
( ~ n3(D)
| ~ s4(C)
| r5(C,D) )
<=> ! [D: $i,C: $i] :
( ~ n3(D)
| ~ s4(C)
| r5(C,D) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [D: $i,C: $i] :
( ~ n3(D)
| ~ s4(C)
| r5(C,D) )
<=> ! [D: $i,C: $i] :
( ~ n3(D)
| ~ s4(C)
| r5(C,D) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
^ [D: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(asserted(k0(b)),
( k0(b)
<=> $true )),
( ~ k0(b)
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ k0(b)
<=> $false )),
( ( ~ k0(b)
| ~ n3(D)
| ~ s4(C)
| r5(C,D) )
<=> ( $false
| ~ n3(D)
| ~ s4(C)
| r5(C,D) ) )),
rewrite(
( ( $false
| ~ n3(D)
| ~ s4(C)
| r5(C,D) )
<=> ( ~ n3(D)
| ~ s4(C)
| r5(C,D) ) )),
( ( ~ k0(b)
| ~ n3(D)
| ~ s4(C)
| r5(C,D) )
<=> ( ~ n3(D)
| ~ s4(C)
| r5(C,D) ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [D: $i,C: $i] :
( ~ k0(b)
| ~ n3(D)
| ~ s4(C)
| r5(C,D) )
<=> ! [D: $i,C: $i] :
( ~ n3(D)
| ~ s4(C)
| r5(C,D) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
^ [D: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( r5(C,D)
| ~ s4(C) )
<=> ( ~ s4(C)
| r5(C,D) ) )),
( ( r5(C,D)
| ~ s4(C)
| ~ k0(b) )
<=> ( ~ s4(C)
| r5(C,D)
| ~ k0(b) ) )),
rewrite(
( ( ~ s4(C)
| r5(C,D)
| ~ k0(b) )
<=> ( ~ k0(b)
| ~ s4(C)
| r5(C,D) ) )),
( ( r5(C,D)
| ~ s4(C)
| ~ k0(b) )
<=> ( ~ k0(b)
| ~ s4(C)
| r5(C,D) ) )),
( ( r5(C,D)
| ~ s4(C)
| ~ k0(b)
| ~ n3(D) )
<=> ( ~ k0(b)
| ~ s4(C)
| r5(C,D)
| ~ n3(D) ) )),
rewrite(
( ( ~ k0(b)
| ~ s4(C)
| r5(C,D)
| ~ n3(D) )
<=> ( ~ k0(b)
| ~ n3(D)
| ~ s4(C)
| r5(C,D) ) )),
( ( r5(C,D)
| ~ s4(C)
| ~ k0(b)
| ~ n3(D) )
<=> ( ~ k0(b)
| ~ n3(D)
| ~ s4(C)
| r5(C,D) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [D: $i,C: $i] :
( r5(C,D)
| ~ s4(C)
| ~ k0(b)
| ~ n3(D) )
<=> ! [D: $i,C: $i] :
( ~ k0(b)
| ~ n3(D)
| ~ s4(C)
| r5(C,D) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,axiom,
! [D: $i,C: $i] :
( r5(C,D)
| ~ s4(C)
| ~ k0(b)
| ~ n3(D) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_327) ).
tff(105,plain,
! [D: $i,C: $i] :
( ~ k0(b)
| ~ n3(D)
| ~ s4(C)
| r5(C,D) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [D: $i,C: $i] :
( ~ n3(D)
| ~ s4(C)
| r5(C,D) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
! [D: $i,C: $i] :
( ~ n3(D)
| ~ s4(C)
| r5(C,D) ),
inference(modus_ponens,[status(thm)],[106,99]) ).
tff(108,plain,
! [D: $i,C: $i] :
( ~ n3(D)
| ~ s4(C)
| r5(C,D) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [D: $i,C: $i] :
( ~ n3(D)
| ~ s4(C)
| r5(C,D) ),
inference(modus_ponens,[status(thm)],[108,98]) ).
tff(110,plain,
( ( ~ ! [D: $i,C: $i] :
( ~ n3(D)
| ~ s4(C)
| r5(C,D) )
| ~ n3(d)
| ~ s4(d)
| r5(d,d) )
<=> ( ~ ! [D: $i,C: $i] :
( ~ n3(D)
| ~ s4(C)
| r5(C,D) )
| ~ n3(d)
| ~ s4(d)
| r5(d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ~ ! [D: $i,C: $i] :
( ~ n3(D)
| ~ s4(C)
| r5(C,D) )
| ~ n3(d)
| ~ s4(d)
| r5(d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
( ~ ! [D: $i,C: $i] :
( ~ n3(D)
| ~ s4(C)
| r5(C,D) )
| ~ n3(d)
| ~ s4(d)
| r5(d,d) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
( ~ n3(d)
| ~ s4(d) ),
inference(unit_resolution,[status(thm)],[112,109,96]) ).
tff(114,plain,
~ s4(d),
inference(unit_resolution,[status(thm)],[113,93]) ).
tff(115,plain,
^ [H: $i,G: $i] :
refl(
( ( ~ n0(H,G)
| l1(G,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],]) ).
tff(116,plain,
( ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
^ [H: $i,G: $i] :
rewrite(
( ( l1(G,G)
| ~ n0(H,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],]) ).
tff(119,plain,
( ! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,axiom,
! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_002) ).
tff(121,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[121,117]) ).
tff(123,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[123,116]) ).
tff(125,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(c,d)
| l1(d,d) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(c,d)
| l1(d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(c,d)
| l1(d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(c,d)
| l1(d,d) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
l1(d,d),
inference(unit_resolution,[status(thm)],[127,48,124]) ).
tff(129,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(
( ( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
<=> ( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) )),
inference(bind,[status(th)],]) ).
tff(130,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
rewrite(
( ( s4(A)
| ~ p3(B,C,D)
| ~ l1(A,C) )
<=> ( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) )),
inference(bind,[status(th)],]) ).
tff(133,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( s4(A)
| ~ p3(B,C,D)
| ~ l1(A,C) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( s4(A)
| ~ p3(B,C,D)
| ~ l1(A,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_299) ).
tff(135,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(skolemize,[status(sab)],[136]) ).
tff(138,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[137,130]) ).
tff(139,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(d,d)
| s4(d)
| ~ p3(d,d,d) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(d,d)
| s4(d)
| ~ p3(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(140,plain,
( ( ~ l1(d,d)
| ~ p3(d,d,d)
| s4(d) )
<=> ( ~ l1(d,d)
| s4(d)
| ~ p3(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(141,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(d,d)
| ~ p3(d,d,d)
| s4(d) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(d,d)
| s4(d)
| ~ p3(d,d,d) ) ),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(d,d)
| ~ p3(d,d,d)
| s4(d) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(d,d)
| s4(d)
| ~ p3(d,d,d) ) ),
inference(transitivity,[status(thm)],[141,139]) ).
tff(143,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(d,d)
| ~ p3(d,d,d)
| s4(d) ),
inference(quant_inst,[status(thm)],]) ).
tff(144,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(d,d)
| s4(d)
| ~ p3(d,d,d) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
$false,
inference(unit_resolution,[status(thm)],[144,138,128,114,56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN195-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 02:16:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------