TSTP Solution File: SYN210-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN210-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 23:54:13 EDT 2022
% Result : Unsatisfiable 0.21s 0.51s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 56
% Syntax : Number of formulae : 106 ( 24 unt; 13 typ; 0 def)
% Number of atoms : 425 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 579 ( 269 ~; 265 |; 0 &)
% ( 45 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 22 ( 22 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 9 >; 8 *; 0 +; 0 <<)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 251 ( 226 !; 0 ?; 251 :)
% Comments :
%------------------------------------------------------------------------------
tff(p3_type,type,
p3: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(n2_type,type,
n2: $i > $o ).
tff(k1_type,type,
k1: $i > $o ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(b_type,type,
b: $i ).
tff(e_type,type,
e: $i ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(l1_type,type,
l1: ( $i * $i ) > $o ).
tff(s4_type,type,
s4: $i > $o ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,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)],[4]) ).
tff(6,axiom,
! [H: $i] :
( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_249) ).
tff(7,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,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(12,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)],[11]) ).
tff(13,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(14,axiom,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_137) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
^ [I: $i,A: $i,J: $i] :
refl(
( ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
<=> ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [I: $i,A: $i,J: $i] :
trans(
monotonicity(
rewrite(
( ( p1(I,I,I)
| ~ l0(I) )
<=> ( ~ l0(I)
| p1(I,I,I) ) )),
( ( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) )
<=> ( ~ l0(I)
| p1(I,I,I)
| ~ m0(J,A,I) ) )),
rewrite(
( ( ~ l0(I)
| p1(I,I,I)
| ~ m0(J,A,I) )
<=> ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) )),
( ( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) )
<=> ( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [I: $i,A: $i,J: $i] :
( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [I: $i,A: $i,J: $i] :
( p1(I,I,I)
| ~ l0(I)
| ~ m0(J,A,I) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_086) ).
tff(24,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( m0(e,b,c)
<=> m0(e,b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
m0(e,b,c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_27) ).
tff(30,plain,
m0(e,b,c),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( l0(c)
<=> l0(c) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
l0(c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_24) ).
tff(33,plain,
l0(c),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
( ( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) )
<=> ( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ l0(I)
| ~ m0(J,A,I)
| p1(I,I,I) )
| ~ l0(c)
| ~ m0(e,b,c)
| p1(c,c,c) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
p1(c,c,c),
inference(unit_resolution,[status(thm)],[36,33,30,27]) ).
tff(38,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(c)
| ~ p1(c,c,c) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(c)
| ~ p1(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(c)
| ~ p1(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(c)
| ~ p1(c,c,c) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
n2(c),
inference(unit_resolution,[status(thm)],[40,37,17]) ).
tff(42,plain,
^ [I: $i,J: $i] :
refl(
( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(46,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( n0(d,c)
<=> n0(d,c) ),
inference(rewrite,[status(thm)],]) ).
tff(50,axiom,
n0(d,c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_26) ).
tff(51,plain,
n0(d,c),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(c)
| ~ n0(d,c) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
k1(c),
inference(unit_resolution,[status(thm)],[54,51,48]) ).
tff(56,plain,
( ( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(c)
| ~ n2(c)
| p3(c,c,c) )
<=> ( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(c)
| ~ n2(c)
| p3(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(c)
| ~ n2(c)
| p3(c,c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(c)
| ~ n2(c)
| p3(c,c,c) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
p3(c,c,c),
inference(unit_resolution,[status(thm)],[58,55,41,10]) ).
tff(60,plain,
^ [H: $i,G: $i] :
refl(
( ( ~ n0(H,G)
| l1(G,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],]) ).
tff(61,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)],[60]) ).
tff(62,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(63,plain,
^ [H: $i,G: $i] :
rewrite(
( ( l1(G,G)
| ~ n0(H,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],]) ).
tff(64,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)],[63]) ).
tff(65,axiom,
! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_002) ).
tff(66,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,c)
| l1(c,c) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,c)
| l1(c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,c)
| l1(c,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,c)
| l1(c,c) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
l1(c,c),
inference(unit_resolution,[status(thm)],[72,51,69]) ).
tff(74,plain,
( ~ s4(c)
<=> ~ s4(c) ),
inference(rewrite,[status(thm)],]) ).
tff(75,axiom,
~ s4(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(76,plain,
~ s4(c),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,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(78,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)],[77]) ).
tff(79,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(80,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(81,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)],[80]) ).
tff(82,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( s4(A)
| ~ p3(B,C,D)
| ~ l1(A,C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_299) ).
tff(83,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(skolemize,[status(sab)],[84]) ).
tff(86,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[85,78]) ).
tff(87,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(c,c)
| s4(c)
| ~ p3(c,c,c) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(c,c)
| s4(c)
| ~ p3(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( ~ l1(c,c)
| ~ p3(c,c,c)
| s4(c) )
<=> ( ~ l1(c,c)
| s4(c)
| ~ p3(c,c,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(c,c)
| ~ p3(c,c,c)
| s4(c) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(c,c)
| s4(c)
| ~ p3(c,c,c) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(c,c)
| ~ p3(c,c,c)
| s4(c) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(c,c)
| s4(c)
| ~ p3(c,c,c) ) ),
inference(transitivity,[status(thm)],[89,87]) ).
tff(91,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(c,c)
| ~ p3(c,c,c)
| s4(c) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(c,c)
| s4(c)
| ~ p3(c,c,c) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
$false,
inference(unit_resolution,[status(thm)],[92,86,76,73,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.13 % Problem : SYN210-1 : TPTP v8.1.0. Released v1.1.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n023.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Sep 5 02:30:32 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 0.21/0.51 % SZS status Unsatisfiable
% 0.21/0.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------