TSTP Solution File: SYN270-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN270-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 23:54:28 EDT 2022
% Result : Unsatisfiable 0.11s 0.41s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 69
% Syntax : Number of formulae : 130 ( 33 unt; 15 typ; 0 def)
% Number of atoms : 691 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 994 ( 465 ~; 460 |; 0 &)
% ( 69 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 25 ( 11 >; 14 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 300 ( 270 !; 0 ?; 300 :)
% Comments :
%------------------------------------------------------------------------------
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(c_type,type,
c: $i ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(s0_type,type,
s0: $i > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(e_type,type,
e: $i ).
tff(d_type,type,
d: $i ).
tff(r3_type,type,
r3: ( $i * $i * $i ) > $o ).
tff(p4_type,type,
p4: ( $i * $i * $i ) > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(1,plain,
^ [I: $i,H: $i] :
refl(
( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [I: $i,H: $i] :
trans(
monotonicity(
rewrite(
( ( m1(H,I,H)
| ~ p0(H,I) )
<=> ( m1(H,I,H)
| ~ p0(H,I) ) )),
( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
rewrite(
( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_029) ).
tff(7,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( p0(b,c)
<=> p0(b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
p0(b,c),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_22) ).
tff(13,plain,
p0(b,c),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( s0(b)
<=> s0(b) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
s0(b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_5) ).
tff(16,plain,
s0(b),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) )
<=> ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ( m1(b,c,b)
| ~ p0(b,c)
| ~ s0(b) )
<=> ( ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| m1(b,c,b)
| ~ p0(b,c)
| ~ s0(b) )
<=> ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| m1(b,c,b)
| ~ p0(b,c)
| ~ s0(b) )
<=> ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| m1(b,c,b)
| ~ p0(b,c)
| ~ s0(b) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,c)
| m1(b,c,b) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
m1(b,c,b),
inference(unit_resolution,[status(thm)],[22,16,13,10]) ).
tff(24,plain,
^ [D: $i,E: $i] :
refl(
( ( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ( p2(D,E,D)
| ~ m1(E,D,E) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
<=> ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_176) ).
tff(28,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,b,c)
| ~ m1(b,c,b) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,b,c)
| ~ m1(b,c,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,b,c)
| ~ m1(b,c,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(c,b,c)
| ~ m1(b,c,b) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
p2(c,b,c),
inference(unit_resolution,[status(thm)],[33,30,23]) ).
tff(35,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
refl(
( ( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
<=> ( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
^ [I: $i,A: $i,J: $i,H: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( n1(H,H,H)
| ~ m0(I,J,I) )
<=> ( n1(H,H,H)
| ~ m0(I,J,I) ) )),
( ( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H) )
<=> ( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H) ) )),
rewrite(
( ( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H) )
<=> ( ~ k0(H)
| n1(H,H,H)
| ~ m0(I,J,I) ) )),
( ( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H) )
<=> ( ~ k0(H)
| n1(H,H,H)
| ~ m0(I,J,I) ) )),
( ( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H)
| ~ q0(A,J) )
<=> ( ~ k0(H)
| n1(H,H,H)
| ~ m0(I,J,I)
| ~ q0(A,J) ) )),
rewrite(
( ( ~ k0(H)
| n1(H,H,H)
| ~ m0(I,J,I)
| ~ q0(A,J) )
<=> ( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ) )),
( ( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H)
| ~ q0(A,J) )
<=> ( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [I: $i,A: $i,J: $i,H: $i] :
( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H)
| ~ q0(A,J) )
<=> ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [I: $i,A: $i,J: $i,H: $i] :
( n1(H,H,H)
| ~ m0(I,J,I)
| ~ k0(H)
| ~ q0(A,J) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_042) ).
tff(41,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( k0(b)
<=> k0(b) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
k0(b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_32) ).
tff(47,plain,
k0(b),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( m0(e,d,e)
<=> m0(e,d,e) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
m0(e,d,e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_8) ).
tff(50,plain,
m0(e,d,e),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( q0(e,d)
<=> q0(e,d) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
q0(e,d),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_2) ).
tff(53,plain,
q0(e,d),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| n1(b,b,b)
| ~ m0(e,d,e)
| ~ q0(e,d) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| n1(b,b,b)
| ~ m0(e,d,e)
| ~ q0(e,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( ~ k0(b)
| ~ q0(e,d)
| n1(b,b,b)
| ~ m0(e,d,e) )
<=> ( ~ k0(b)
| n1(b,b,b)
| ~ m0(e,d,e)
| ~ q0(e,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| ~ q0(e,d)
| n1(b,b,b)
| ~ m0(e,d,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| n1(b,b,b)
| ~ m0(e,d,e)
| ~ q0(e,d) ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| ~ q0(e,d)
| n1(b,b,b)
| ~ m0(e,d,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| n1(b,b,b)
| ~ m0(e,d,e)
| ~ q0(e,d) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| ~ q0(e,d)
| n1(b,b,b)
| ~ m0(e,d,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i] :
( ~ k0(H)
| ~ q0(A,J)
| n1(H,H,H)
| ~ m0(I,J,I) )
| ~ k0(b)
| n1(b,b,b)
| ~ m0(e,d,e)
| ~ q0(e,d) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
n1(b,b,b),
inference(unit_resolution,[status(thm)],[59,53,50,47,44]) ).
tff(61,plain,
^ [D: $i,E: $i,C: $i] :
refl(
( ( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
<=> ( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
<=> ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
<=> ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
^ [D: $i,E: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p2(C,D,D)
| ~ n1(E,D,E) )
<=> ( ~ n1(E,D,E)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ n1(E,D,E)
| ~ p0(C,D) )
<=> ( ~ n1(E,D,E)
| p2(C,D,D)
| ~ p0(C,D) ) )),
rewrite(
( ( ~ n1(E,D,E)
| p2(C,D,D)
| ~ p0(C,D) )
<=> ( ~ n1(E,D,E)
| ~ p0(C,D)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ n1(E,D,E)
| ~ p0(C,D) )
<=> ( ~ n1(E,D,E)
| ~ p0(C,D)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ n1(E,D,E)
| ~ p0(C,D)
| ~ p2(C,D,C) )
<=> ( ~ n1(E,D,E)
| ~ p0(C,D)
| p2(C,D,D)
| ~ p2(C,D,C) ) )),
rewrite(
( ( ~ n1(E,D,E)
| ~ p0(C,D)
| p2(C,D,D)
| ~ p2(C,D,C) )
<=> ( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ n1(E,D,E)
| ~ p0(C,D)
| ~ p2(C,D,C) )
<=> ( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [D: $i,E: $i,C: $i] :
( p2(C,D,D)
| ~ n1(E,D,E)
| ~ p0(C,D)
| ~ p2(C,D,C) )
<=> ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,axiom,
! [D: $i,E: $i,C: $i] :
( p2(C,D,D)
| ~ n1(E,D,E)
| ~ p0(C,D)
| ~ p2(C,D,C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_152) ).
tff(67,plain,
! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
( p0(c,b)
<=> p0(c,b) ),
inference(rewrite,[status(thm)],]) ).
tff(72,axiom,
p0(c,b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_18) ).
tff(73,plain,
p0(c,b),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
( ( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p0(c,b)
| ~ p2(c,b,c)
| p2(c,b,b) )
<=> ( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p0(c,b)
| ~ p2(c,b,c)
| p2(c,b,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ( ~ n1(b,b,b)
| ~ p2(c,b,c)
| ~ p0(c,b)
| p2(c,b,b) )
<=> ( ~ n1(b,b,b)
| ~ p0(c,b)
| ~ p2(c,b,c)
| p2(c,b,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( ( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p2(c,b,c)
| ~ p0(c,b)
| p2(c,b,b) )
<=> ( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p0(c,b)
| ~ p2(c,b,c)
| p2(c,b,b) ) ),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p2(c,b,c)
| ~ p0(c,b)
| p2(c,b,b) )
<=> ( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p0(c,b)
| ~ p2(c,b,c)
| p2(c,b,b) ) ),
inference(transitivity,[status(thm)],[76,74]) ).
tff(78,plain,
( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p2(c,b,c)
| ~ p0(c,b)
| p2(c,b,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
( ~ ! [D: $i,E: $i,C: $i] :
( ~ n1(E,D,E)
| ~ p2(C,D,C)
| ~ p0(C,D)
| p2(C,D,D) )
| ~ n1(b,b,b)
| ~ p0(c,b)
| ~ p2(c,b,c)
| p2(c,b,b) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
( ~ p2(c,b,c)
| p2(c,b,b) ),
inference(unit_resolution,[status(thm)],[79,73,70,60]) ).
tff(81,plain,
p2(c,b,b),
inference(unit_resolution,[status(thm)],[80,34]) ).
tff(82,plain,
( ~ p4(b,b,c)
<=> ~ p4(b,b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(83,axiom,
~ p4(b,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(84,plain,
~ p4(b,b,c),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
^ [H: $i,G: $i] :
refl(
( ( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) )
<=> ( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) )
<=> ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) )
<=> ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
^ [H: $i,G: $i] :
trans(
monotonicity(
rewrite(
( ( p4(G,G,H)
| ~ r0(G) )
<=> ( ~ r0(G)
| p4(G,G,H) ) )),
( ( p4(G,G,H)
| ~ r0(G)
| ~ r3(H,G,H) )
<=> ( ~ r0(G)
| p4(G,G,H)
| ~ r3(H,G,H) ) )),
rewrite(
( ( ~ r0(G)
| p4(G,G,H)
| ~ r3(H,G,H) )
<=> ( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ) )),
( ( p4(G,G,H)
| ~ r0(G)
| ~ r3(H,G,H) )
<=> ( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [H: $i,G: $i] :
( p4(G,G,H)
| ~ r0(G)
| ~ r3(H,G,H) )
<=> ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,axiom,
! [H: $i,G: $i] :
( p4(G,G,H)
| ~ r0(G)
| ~ r3(H,G,H) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_285) ).
tff(91,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ),
inference(modus_ponens,[status(thm)],[91,87]) ).
tff(93,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) ),
inference(modus_ponens,[status(thm)],[93,86]) ).
tff(95,plain,
( r0(b)
<=> r0(b) ),
inference(rewrite,[status(thm)],]) ).
tff(96,axiom,
r0(b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
tff(97,plain,
r0(b),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) )
| ~ r0(b)
| ~ r3(c,b,c)
| p4(b,b,c) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) )
| ~ r0(b)
| ~ r3(c,b,c)
| p4(b,b,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) )
| ~ r0(b)
| ~ r3(c,b,c)
| p4(b,b,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
( ~ ! [H: $i,G: $i] :
( ~ r0(G)
| ~ r3(H,G,H)
| p4(G,G,H) )
| ~ r0(b)
| ~ r3(c,b,c)
| p4(b,b,c) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
~ r3(c,b,c),
inference(unit_resolution,[status(thm)],[100,97,94,84]) ).
tff(102,plain,
^ [B: $i,D: $i,C: $i] :
refl(
( ( ~ p2(B,D,C)
| r3(B,C,B) )
<=> ( ~ p2(B,D,C)
| r3(B,C,B) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
( ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
^ [B: $i,D: $i,C: $i] :
rewrite(
( ( r3(B,C,B)
| ~ p2(B,D,C) )
<=> ( ~ p2(B,D,C)
| r3(B,C,B) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [B: $i,D: $i,C: $i] :
( r3(B,C,B)
| ~ p2(B,D,C) )
<=> ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,axiom,
! [B: $i,D: $i,C: $i] :
( r3(B,C,B)
| ~ p2(B,D,C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_267) ).
tff(108,plain,
! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ),
inference(modus_ponens,[status(thm)],[108,104]) ).
tff(110,plain,
! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) ),
inference(modus_ponens,[status(thm)],[110,103]) ).
tff(112,plain,
( ( ~ ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
| ~ p2(c,b,b)
| r3(c,b,c) )
<=> ( ~ ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
| ~ p2(c,b,b)
| r3(c,b,c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
| ~ p2(c,b,b)
| r3(c,b,c) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
( ~ ! [B: $i,D: $i,C: $i] :
( ~ p2(B,D,C)
| r3(B,C,B) )
| ~ p2(c,b,b)
| r3(c,b,c) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
$false,
inference(unit_resolution,[status(thm)],[114,111,101,81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SYN270-1 : TPTP v8.1.0. Released v1.1.0.
% 0.00/0.08 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.07/0.27 % Computer : n002.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Mon Sep 5 02:32:03 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.07/0.27 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.07/0.27 Usage: tptp [options] [-file:]file
% 0.07/0.27 -h, -? prints this message.
% 0.07/0.27 -smt2 print SMT-LIB2 benchmark.
% 0.07/0.27 -m, -model generate model.
% 0.07/0.27 -p, -proof generate proof.
% 0.07/0.27 -c, -core generate unsat core of named formulas.
% 0.07/0.27 -st, -statistics display statistics.
% 0.07/0.27 -t:timeout set timeout (in second).
% 0.07/0.27 -smt2status display status in smt2 format instead of SZS.
% 0.07/0.27 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.07/0.27 -<param>:<value> configuration parameter and value.
% 0.07/0.27 -o:<output-file> file to place output in.
% 0.11/0.41 % SZS status Unsatisfiable
% 0.11/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------