TSTP Solution File: SYN192-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN192-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 23:54:08 EDT 2022
% Result : Unsatisfiable 0.76s 0.74s
% Output : Proof 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 78
% Syntax : Number of formulae : 152 ( 36 unt; 18 typ; 0 def)
% Number of atoms : 690 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 972 ( 451 ~; 444 |; 0 &)
% ( 77 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 35 ( 35 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 13 >; 12 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 340 ( 308 !; 0 ?; 340 :)
% Comments :
%------------------------------------------------------------------------------
tff(n3_type,type,
n3: $i > $o ).
tff(a_type,type,
a: $i ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(l0_type,type,
l0: $i > $o ).
tff(s0_type,type,
s0: $i > $o ).
tff(d_type,type,
d: $i ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(r4_type,type,
r4: $i > $o ).
tff(q3_type,type,
q3: ( $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(l1_type,type,
l1: ( $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,
^ [D: $i,E: $i,F: $i] :
refl(
( ( n3(D)
| ~ p2(E,F,D) )
<=> ( n3(D)
| ~ p2(E,F,D) ) )),
inference(bind,[status(th)],]) ).
tff(2,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)],[1]) ).
tff(3,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(4,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(5,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,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(9,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)],[8]) ).
tff(10,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(11,axiom,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_176) ).
tff(12,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( m1(a,a,a)
<=> m1(a,a,a) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ( m1(a,a,a)
| $false
| $false )
<=> m1(a,a,a) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_20) ).
tff(19,plain,
( l0(a)
<=> $true ),
inference(iff_true,[status(thm)],[18]) ).
tff(20,plain,
( ~ l0(a)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( ~ l0(a)
<=> $false ),
inference(transitivity,[status(thm)],[20,17]) ).
tff(22,axiom,
s0(d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_1) ).
tff(23,plain,
( s0(d)
<=> $true ),
inference(iff_true,[status(thm)],[22]) ).
tff(24,plain,
( ~ s0(d)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ~ s0(d)
<=> $false ),
inference(transitivity,[status(thm)],[24,17]) ).
tff(26,plain,
( ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) )
<=> ( m1(a,a,a)
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[25,21]) ).
tff(27,plain,
( ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) )
<=> m1(a,a,a) ),
inference(transitivity,[status(thm)],[26,16]) ).
tff(28,plain,
( ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( m1(a,a,a)
| ~ l0(a) )
<=> ( m1(a,a,a)
| ~ l0(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) )
<=> ( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,axiom,
( m1(a,a,a)
| ~ l0(a)
| ~ s0(d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_023) ).
tff(34,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( m1(a,a,a)
| ~ s0(d)
| ~ l0(a) ),
inference(modus_ponens,[status(thm)],[34,28]) ).
tff(36,plain,
m1(a,a,a),
inference(modus_ponens,[status(thm)],[35,27]) ).
tff(37,plain,
m1(a,a,a),
inference(modus_ponens,[status(thm)],[36,15]) ).
tff(38,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(a,a,a)
| ~ m1(a,a,a) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
p2(a,a,a),
inference(unit_resolution,[status(thm)],[40,37,14]) ).
tff(42,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(a)
| ~ p2(a,a,a) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(a)
| ~ p2(a,a,a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(a)
| ~ p2(a,a,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(a)
| ~ p2(a,a,a) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
n3(a),
inference(unit_resolution,[status(thm)],[44,41,7]) ).
tff(46,plain,
^ [X: $i] :
refl(
( p0(b,X)
<=> p0(b,X) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [X: $i] : p0(b,X)
<=> ! [X: $i] : p0(b,X) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [X: $i] : p0(b,X)
<=> ! [X: $i] : p0(b,X) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
! [X: $i] : p0(b,X),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_14) ).
tff(50,plain,
! [X: $i] : p0(b,X),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [X: $i] : p0(b,X),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [X: $i] : p0(b,X),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [X: $i] : p0(b,X)
| p0(b,a) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
p0(b,a),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ r4(a)
<=> ~ r4(a) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
~ r4(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(57,plain,
~ r4(a),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
^ [I: $i,J: $i,H: $i,G: $i] :
refl(
( ( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
<=> ( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
<=> ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
<=> ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
^ [I: $i,J: $i,H: $i,G: $i] :
trans(
monotonicity(
rewrite(
( ( r4(G)
| ~ n3(G)
| ~ q3(H,I) )
<=> ( ~ n3(G)
| ~ q3(H,I)
| r4(G) ) )),
( ( r4(G)
| ~ n3(G)
| ~ q3(H,I)
| ~ p0(J,G) )
<=> ( ~ n3(G)
| ~ q3(H,I)
| r4(G)
| ~ p0(J,G) ) )),
rewrite(
( ( ~ n3(G)
| ~ q3(H,I)
| r4(G)
| ~ p0(J,G) )
<=> ( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) )),
( ( r4(G)
| ~ n3(G)
| ~ q3(H,I)
| ~ p0(J,G) )
<=> ( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [I: $i,J: $i,H: $i,G: $i] :
( r4(G)
| ~ n3(G)
| ~ q3(H,I)
| ~ p0(J,G) )
<=> ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [I: $i,J: $i,H: $i,G: $i] :
( r4(G)
| ~ n3(G)
| ~ q3(H,I)
| ~ p0(J,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_298) ).
tff(64,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,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(69,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)],[68]) ).
tff(70,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(71,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(72,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)],[71]) ).
tff(73,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(74,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)],[73,72]) ).
tff(75,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)],[74,70]) ).
tff(76,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)],[75]) ).
tff(77,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)],[76,69]) ).
tff(78,plain,
( m0(e,b,c)
<=> m0(e,b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
m0(e,b,c),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_27) ).
tff(80,plain,
m0(e,b,c),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
( p0(c,b)
<=> p0(c,b) ),
inference(rewrite,[status(thm)],]) ).
tff(82,axiom,
p0(c,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_18) ).
tff(83,plain,
p0(c,b),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
( r0(b)
<=> r0(b) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
r0(b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
tff(86,plain,
r0(b),
inference(modus_ponens,[status(thm)],[85,84]) ).
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) )
<=> ( ~ ! [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(88,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(89,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)],[88]) ).
tff(90,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)],[89,87]) ).
tff(91,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(92,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)],[91,90]) ).
tff(93,plain,
l1(b,e),
inference(unit_resolution,[status(thm)],[92,86,83,80,77]) ).
tff(94,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(95,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)],[94]) ).
tff(96,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(97,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(98,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)],[97]) ).
tff(99,axiom,
! [H: $i,G: $i] :
( q2(G,G,H)
| ~ l1(H,G) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_186) ).
tff(100,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) ),
inference(modus_ponens,[status(thm)],[102,95]) ).
tff(104,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(105,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(106,plain,
( ~ ! [H: $i,G: $i] :
( ~ l1(H,G)
| q2(G,G,H) )
| ~ l1(b,e)
| q2(e,e,b) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
q2(e,e,b),
inference(unit_resolution,[status(thm)],[106,103,93]) ).
tff(108,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(109,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)],[108]) ).
tff(110,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(111,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(112,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)],[111]) ).
tff(113,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(114,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[116,109]) ).
tff(118,plain,
( n0(e,e)
<=> n0(e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(119,axiom,
n0(e,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_30) ).
tff(120,plain,
n0(e,e),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,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(122,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(123,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)],[122]) ).
tff(124,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)],[123,121]) ).
tff(125,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(126,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)],[125,124]) ).
tff(127,plain,
q3(e,b),
inference(unit_resolution,[status(thm)],[126,120,117,107]) ).
tff(128,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,a)
| ~ q3(e,b)
| ~ n3(a)
| r4(a) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,a)
| ~ q3(e,b)
| ~ n3(a)
| r4(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(129,plain,
( ( ~ p0(b,a)
| ~ n3(a)
| ~ q3(e,b)
| r4(a) )
<=> ( ~ p0(b,a)
| ~ q3(e,b)
| ~ n3(a)
| r4(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,a)
| ~ n3(a)
| ~ q3(e,b)
| r4(a) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,a)
| ~ q3(e,b)
| ~ n3(a)
| r4(a) ) ),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,a)
| ~ n3(a)
| ~ q3(e,b)
| r4(a) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,a)
| ~ q3(e,b)
| ~ n3(a)
| r4(a) ) ),
inference(transitivity,[status(thm)],[130,128]) ).
tff(132,plain,
( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,a)
| ~ n3(a)
| ~ q3(e,b)
| r4(a) ),
inference(quant_inst,[status(thm)],]) ).
tff(133,plain,
( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,a)
| ~ q3(e,b)
| ~ n3(a)
| r4(a) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
$false,
inference(unit_resolution,[status(thm)],[133,127,67,57,54,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN192-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 02:02:34 EDT 2022
% 0.13/0.35 % 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.
% 0.76/0.74 % SZS status Unsatisfiable
% 0.76/0.74 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------