TSTP Solution File: SYN177-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN177-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 23:54:04 EDT 2022
% Result : Unsatisfiable 0.20s 0.51s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 42
% Syntax : Number of formulae : 79 ( 23 unt; 10 typ; 0 def)
% Number of atoms : 379 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 542 ( 257 ~; 245 |; 0 &)
% ( 40 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 25 ( 25 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 7 >; 8 *; 0 +; 0 <<)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 191 ( 172 !; 0 ?; 191 :)
% Comments :
%------------------------------------------------------------------------------
tff(q3_type,type,
q3: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(e_type,type,
e: $i ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(l1_type,type,
l1: ( $i * $i ) > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(1,plain,
^ [X: $i] :
refl(
( ~ q3(X,b)
<=> ~ q3(X,b) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ~ q3(X,b)
<=> ! [X: $i] : ~ q3(X,b) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ~ q3(X,b)
<=> ! [X: $i] : ~ q3(X,b) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ~ q3(X,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(5,plain,
! [X: $i] : ~ q3(X,b),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ~ q3(X,b),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ~ q3(X,b),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,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(9,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)],[8]) ).
tff(10,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(11,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(12,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)],[11]) ).
tff(13,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(14,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)],[13,12]) ).
tff(15,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)],[14,10]) ).
tff(16,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)],[15]) ).
tff(17,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)],[16,9]) ).
tff(18,plain,
( m0(e,b,c)
<=> m0(e,b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
m0(e,b,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_27) ).
tff(20,plain,
m0(e,b,c),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( p0(c,b)
<=> p0(c,b) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
p0(c,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_18) ).
tff(23,plain,
p0(c,b),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( r0(b)
<=> r0(b) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
r0(b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
tff(26,plain,
r0(b),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,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(28,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(29,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)],[28]) ).
tff(30,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)],[29,27]) ).
tff(31,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(32,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)],[31,30]) ).
tff(33,plain,
l1(b,e),
inference(unit_resolution,[status(thm)],[32,26,23,20,17]) ).
tff(34,plain,
^ [H: $i,G: $i] :
refl(
( ( ~ l1(H,G)
| q2(G,G,H) )
<=> ( ~ l1(H,G)
| q2(G,G,H) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
<=> ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
<=> ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
^ [H: $i,G: $i] :
rewrite(
( ( q2(G,G,H)
| ~ l1(H,G) )
<=> ( ~ l1(H,G)
| q2(G,G,H) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [H: $i,G: $i] :
( q2(G,G,H)
| ~ l1(H,G) )
<=> ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,axiom,
! [H: $i,G: $i] :
( q2(G,G,H)
| ~ l1(H,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_186) ).
tff(40,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[42,35]) ).
tff(44,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
q2(e,e,b),
inference(unit_resolution,[status(thm)],[46,43,33]) ).
tff(48,plain,
^ [I: $i,H: $i,G: $i] :
refl(
( ( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
<=> ( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
^ [I: $i,H: $i,G: $i] :
trans(
monotonicity(
rewrite(
( ( q3(G,H)
| ~ q2(I,G,H) )
<=> ( ~ q2(I,G,H)
| q3(G,H) ) )),
( ( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) )
<=> ( ~ q2(I,G,H)
| q3(G,H)
| ~ n0(I,G) ) )),
rewrite(
( ( ~ q2(I,G,H)
| q3(G,H)
| ~ n0(I,G) )
<=> ( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) )),
( ( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) )
<=> ( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [I: $i,H: $i,G: $i] :
( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) )
<=> ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,axiom,
! [I: $i,H: $i,G: $i] :
( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_255) ).
tff(54,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[56,49]) ).
tff(58,plain,
( n0(e,e)
<=> n0(e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
n0(e,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_30) ).
tff(60,plain,
n0(e,e),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ( ~ q2(e,e,b)
| ~ n0(e,e)
| q3(e,b) )
<=> ( q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,b)
| ~ n0(e,e)
| q3(e,b) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,b)
| ~ n0(e,e)
| q3(e,b) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ) ),
inference(transitivity,[status(thm)],[63,61]) ).
tff(65,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,b)
| ~ n0(e,e)
| q3(e,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,b)
| ~ n0(e,e)
| ~ q2(e,e,b) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
q3(e,b),
inference(unit_resolution,[status(thm)],[66,60,57,47]) ).
tff(68,plain,
( ~ ! [X: $i] : ~ q3(X,b)
| ~ q3(e,b) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
$false,
inference(unit_resolution,[status(thm)],[68,67,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN177-1 : 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 : n014.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 02:03:44 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.
% 0.20/0.51 % SZS status Unsatisfiable
% 0.20/0.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------