TSTP Solution File: SYN209-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN209-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 23:54:12 EDT 2022
% Result : Unsatisfiable 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 64
% Syntax : Number of formulae : 123 ( 27 unt; 15 typ; 0 def)
% Number of atoms : 539 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 755 ( 350 ~; 343 |; 0 &)
% ( 62 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 26 ( 26 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 11 >; 9 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 250 ( 227 !; 0 ?; 250 :)
% Comments :
%------------------------------------------------------------------------------
tff(p3_type,type,
p3: ( $i * $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(n2_type,type,
n2: $i > $o ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(k1_type,type,
k1: $i > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(l1_type,type,
l1: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(s4_type,type,
s4: $i > $o ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( p1(e,e,e)
<=> p1(e,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
( ( $false
| $false
| p1(e,e,e) )
<=> p1(e,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(12,plain,
( k0(e)
<=> $true ),
inference(iff_true,[status(thm)],[11]) ).
tff(13,plain,
( ~ k0(e)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ~ k0(e)
<=> $false ),
inference(transitivity,[status(thm)],[13,10]) ).
tff(15,axiom,
r0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(16,plain,
( r0(e)
<=> $true ),
inference(iff_true,[status(thm)],[15]) ).
tff(17,plain,
( ~ r0(e)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ~ r0(e)
<=> $false ),
inference(transitivity,[status(thm)],[17,10]) ).
tff(19,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( $false
| $false
| p1(e,e,e) ) ),
inference(monotonicity,[status(thm)],[18,14]) ).
tff(20,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> p1(e,e,e) ),
inference(transitivity,[status(thm)],[19,9]) ).
tff(21,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( p1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,axiom,
( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_090) ).
tff(27,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[27,21]) ).
tff(29,plain,
p1(e,e,e),
inference(modus_ponens,[status(thm)],[28,20]) ).
tff(30,plain,
p1(e,e,e),
inference(modus_ponens,[status(thm)],[29,8]) ).
tff(31,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
n2(e),
inference(unit_resolution,[status(thm)],[33,30,7]) ).
tff(35,plain,
^ [I: $i,J: $i] :
refl(
( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(39,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( n0(d,e)
<=> n0(d,e) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
n0(d,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_3) ).
tff(44,plain,
n0(d,e),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(e)
| ~ n0(d,e) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(e)
| ~ n0(d,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(e)
| ~ n0(d,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(e)
| ~ n0(d,e) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
k1(e),
inference(unit_resolution,[status(thm)],[47,44,41]) ).
tff(49,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(50,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)],[49]) ).
tff(51,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(52,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(53,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)],[52]) ).
tff(54,axiom,
! [H: $i] :
( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_249) ).
tff(55,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(e)
| ~ n2(e)
| p3(e,e,e) )
<=> ( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(e)
| ~ n2(e)
| p3(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(e)
| ~ n2(e)
| p3(e,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(e)
| ~ n2(e)
| p3(e,e,e) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
p3(e,e,e),
inference(unit_resolution,[status(thm)],[61,58,48,34]) ).
tff(63,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
refl(
( ( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
<=> ( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( l1(C,D)
| ~ p0(E,C) )
<=> ( ~ p0(E,C)
| l1(C,D) ) )),
( ( l1(C,D)
| ~ p0(E,C)
| ~ r0(F) )
<=> ( ~ p0(E,C)
| l1(C,D)
| ~ r0(F) ) )),
rewrite(
( ( ~ p0(E,C)
| l1(C,D)
| ~ r0(F) )
<=> ( ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
( ( l1(C,D)
| ~ p0(E,C)
| ~ r0(F) )
<=> ( ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
( ( l1(C,D)
| ~ p0(E,C)
| ~ r0(F)
| ~ m0(D,C,E) )
<=> ( ~ r0(F)
| ~ p0(E,C)
| l1(C,D)
| ~ m0(D,C,E) ) )),
rewrite(
( ( ~ r0(F)
| ~ p0(E,C)
| l1(C,D)
| ~ m0(D,C,E) )
<=> ( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
( ( l1(C,D)
| ~ p0(E,C)
| ~ r0(F)
| ~ m0(D,C,E) )
<=> ( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( l1(C,D)
| ~ p0(E,C)
| ~ r0(F)
| ~ m0(D,C,E) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,axiom,
! [D: $i,E: $i,F: $i,C: $i] :
( l1(C,D)
| ~ p0(E,C)
| ~ r0(F)
| ~ m0(D,C,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_003) ).
tff(69,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) ),
inference(modus_ponens,[status(thm)],[71,64]) ).
tff(73,plain,
( m0(e,b,c)
<=> m0(e,b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(74,axiom,
m0(e,b,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_27) ).
tff(75,plain,
m0(e,b,c),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
( p0(c,b)
<=> p0(c,b) ),
inference(rewrite,[status(thm)],]) ).
tff(77,axiom,
p0(c,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_18) ).
tff(78,plain,
p0(c,b),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
( r0(b)
<=> r0(b) ),
inference(rewrite,[status(thm)],]) ).
tff(80,axiom,
r0(b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
tff(81,plain,
r0(b),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( ~ m0(e,b,c)
| ~ r0(b)
| ~ p0(c,b)
| l1(b,e) )
<=> ( ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ m0(e,b,c)
| ~ r0(b)
| ~ p0(c,b)
| l1(b,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ m0(e,b,c)
| ~ r0(b)
| ~ p0(c,b)
| l1(b,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ m0(e,b,c)
| ~ r0(b)
| ~ p0(c,b)
| l1(b,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ m0(D,C,E)
| ~ r0(F)
| ~ p0(E,C)
| l1(C,D) )
| ~ r0(b)
| ~ p0(c,b)
| ~ m0(e,b,c)
| l1(b,e) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
l1(b,e),
inference(unit_resolution,[status(thm)],[87,81,78,75,72]) ).
tff(89,plain,
( ~ s4(b)
<=> ~ s4(b) ),
inference(rewrite,[status(thm)],]) ).
tff(90,axiom,
~ s4(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(91,plain,
~ s4(b),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,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(93,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)],[92]) ).
tff(94,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(95,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(96,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)],[95]) ).
tff(97,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(98,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| s4(b)
| ~ l1(b,e)
| ~ p3(e,e,e) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| s4(b)
| ~ l1(b,e)
| ~ p3(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ( ~ l1(b,e)
| ~ p3(e,e,e)
| s4(b) )
<=> ( s4(b)
| ~ l1(b,e)
| ~ p3(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(b,e)
| ~ p3(e,e,e)
| s4(b) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| s4(b)
| ~ l1(b,e)
| ~ p3(e,e,e) ) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(b,e)
| ~ p3(e,e,e)
| s4(b) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| s4(b)
| ~ l1(b,e)
| ~ p3(e,e,e) ) ),
inference(transitivity,[status(thm)],[104,102]) ).
tff(106,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| ~ l1(b,e)
| ~ p3(e,e,e)
| s4(b) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ l1(A,C)
| ~ p3(B,C,D)
| s4(A) )
| s4(b)
| ~ l1(b,e)
| ~ p3(e,e,e) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
$false,
inference(unit_resolution,[status(thm)],[107,101,91,88,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN209-1 : 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 : n029.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 02:19:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.50 % SZS status Unsatisfiable
% 0.20/0.50 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------