TSTP Solution File: SYN183-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN183-1 : 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 23:54:06 EDT 2022
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 102
% Syntax : Number of formulae : 217 ( 39 unt; 18 typ; 0 def)
% Number of atoms : 997 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1363 ( 623 ~; 615 |; 0 &)
% ( 125 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 58 ( 58 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 16 >; 19 *; 0 +; 0 <<)
% Number of predicates : 24 ( 22 usr; 2 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 351 ( 319 !; 0 ?; 351 :)
% Comments :
%------------------------------------------------------------------------------
tff(m3_type,type,
m3: ( $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(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(q4_type,type,
q4: ( $i * $i ) > $o ).
tff(q5_type,type,
q5: ( $i * $i ) > $o ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $o ).
tff(k3_type,type,
k3: ( $i * $i * $i ) > $o ).
tff(r1_type,type,
r1: $i > $o ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(s0_type,type,
s0: $i > $o ).
tff(n1_type,type,
n1: ( $i * $i * $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,
^ [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(36,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)],[35]) ).
tff(37,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(38,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(39,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( m1(e,e,e)
<=> m1(e,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( $false
| m1(e,e,e) )
<=> m1(e,e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( ~ r0(e)
| m1(e,e,e) )
<=> ( $false
| m1(e,e,e) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(45,plain,
( ( ~ r0(e)
| m1(e,e,e) )
<=> m1(e,e,e) ),
inference(transitivity,[status(thm)],[44,43]) ).
tff(46,plain,
( ( m1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
( m1(e,e,e)
| ~ r0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_012) ).
tff(48,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
m1(e,e,e),
inference(modus_ponens,[status(thm)],[48,45]) ).
tff(50,plain,
m1(e,e,e),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| p2(e,e,e)
| ~ m1(e,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) )
| ~ m1(e,e,e)
| p2(e,e,e) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
p2(e,e,e),
inference(unit_resolution,[status(thm)],[56,50,41]) ).
tff(58,plain,
^ [D: $i] :
refl(
( ( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
<=> ( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
<=> ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
<=> ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
^ [D: $i] :
trans(
monotonicity(
rewrite(
( ( m3(D,e,e)
| ~ n2(e) )
<=> ( ~ n2(e)
| m3(D,e,e) ) )),
( ( m3(D,e,e)
| ~ n2(e)
| ~ p2(D,e,e) )
<=> ( ~ n2(e)
| m3(D,e,e)
| ~ p2(D,e,e) ) )),
rewrite(
( ( ~ n2(e)
| m3(D,e,e)
| ~ p2(D,e,e) )
<=> ( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) )),
( ( m3(D,e,e)
| ~ n2(e)
| ~ p2(D,e,e) )
<=> ( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [D: $i] :
( m3(D,e,e)
| ~ n2(e)
| ~ p2(D,e,e) )
<=> ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [D: $i] :
( m3(D,e,e)
| ~ n2(e)
| ~ p2(D,e,e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_234) ).
tff(64,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
( ( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(e,e,e)
| m3(e,e,e) )
<=> ( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(e,e,e)
| m3(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(e,e,e)
| m3(e,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
( ~ ! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) )
| ~ n2(e)
| ~ p2(e,e,e)
| m3(e,e,e) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
m3(e,e,e),
inference(unit_resolution,[status(thm)],[70,67,57,34]) ).
tff(72,plain,
( ~ q5(e,e)
<=> ~ q5(e,e) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
~ q5(e,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(74,plain,
~ q5(e,e),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
^ [H: $i] :
refl(
( ( q5(H,H)
| ~ q4(H,H) )
<=> ( q5(H,H)
| ~ q4(H,H) ) )),
inference(bind,[status(th)],]) ).
tff(76,plain,
( ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) )
<=> ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) )
<=> ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
! [H: $i] :
( q5(H,H)
| ~ q4(H,H) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_325) ).
tff(79,plain,
! [H: $i] :
( q5(H,H)
| ~ q4(H,H) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [H: $i] :
( q5(H,H)
| ~ q4(H,H) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [H: $i] :
( q5(H,H)
| ~ q4(H,H) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
( ( ~ ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) )
| q5(e,e)
| ~ q4(e,e) )
<=> ( ~ ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) )
| q5(e,e)
| ~ q4(e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ~ ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) )
| q5(e,e)
| ~ q4(e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
( ~ ! [H: $i] :
( q5(H,H)
| ~ q4(H,H) )
| q5(e,e)
| ~ q4(e,e) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
~ q4(e,e),
inference(unit_resolution,[status(thm)],[84,81,74]) ).
tff(86,plain,
^ [I: $i] :
refl(
( ( q2(I,I,I)
| ~ p1(I,I,I) )
<=> ( q2(I,I,I)
| ~ p1(I,I,I) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
<=> ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
( ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
<=> ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,axiom,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_181) ).
tff(90,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[91,87]) ).
tff(93,plain,
( ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) )
<=> ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ( q2(e,e,e)
| ~ p1(e,e,e) )
<=> ( ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| q2(e,e,e)
| ~ p1(e,e,e) )
<=> ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| q2(e,e,e)
| ~ p1(e,e,e) )
<=> ( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(transitivity,[status(thm)],[95,93]) ).
tff(97,plain,
( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| q2(e,e,e)
| ~ p1(e,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
q2(e,e,e),
inference(unit_resolution,[status(thm)],[98,30,92]) ).
tff(100,plain,
^ [I: $i,A: $i,J: $i] :
refl(
( ( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
<=> ( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
^ [I: $i,A: $i,J: $i] :
trans(
monotonicity(
rewrite(
( ( k3(I,I,I)
| ~ r1(I) )
<=> ( ~ r1(I)
| k3(I,I,I) ) )),
( ( k3(I,I,I)
| ~ r1(I)
| ~ p2(J,A,A) )
<=> ( ~ r1(I)
| k3(I,I,I)
| ~ p2(J,A,A) ) )),
rewrite(
( ( ~ r1(I)
| k3(I,I,I)
| ~ p2(J,A,A) )
<=> ( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ) )),
( ( k3(I,I,I)
| ~ r1(I)
| ~ p2(J,A,A) )
<=> ( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ) )),
inference(bind,[status(th)],]) ).
tff(104,plain,
( ! [I: $i,A: $i,J: $i] :
( k3(I,I,I)
| ~ r1(I)
| ~ p2(J,A,A) )
<=> ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,axiom,
! [I: $i,A: $i,J: $i] :
( k3(I,I,I)
| ~ r1(I)
| ~ p2(J,A,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_213) ).
tff(106,plain,
! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) ),
inference(modus_ponens,[status(thm)],[108,101]) ).
tff(110,plain,
^ [D: $i,E: $i] :
refl(
( ( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) )
<=> ( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) ) )),
inference(bind,[status(th)],]) ).
tff(111,plain,
( ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) )
<=> ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,plain,
( ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) )
<=> ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
^ [D: $i,E: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(asserted(s0(d)),
( s0(d)
<=> $true )),
( ~ s0(d)
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ s0(d)
<=> $false )),
( ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
<=> ( ~ q0(D,E)
| $false
| ~ q1(d,E,d)
| r1(D) ) )),
rewrite(
( ( ~ q0(D,E)
| $false
| ~ q1(d,E,d)
| r1(D) )
<=> ( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) ) )),
( ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
<=> ( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) )
<=> ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
^ [D: $i,E: $i] :
trans(
monotonicity(
rewrite(
( ( r1(D)
| ~ q0(D,E)
| ~ s0(d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| r1(D) ) )),
( ( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| r1(D)
| ~ q1(d,E,d) ) )),
rewrite(
( ( ~ q0(D,E)
| ~ s0(d)
| r1(D)
| ~ q1(d,E,d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) )),
( ( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) )
<=> ( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) )),
inference(bind,[status(th)],]) ).
tff(116,plain,
( ! [D: $i,E: $i] :
( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) )
<=> ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,axiom,
! [D: $i,E: $i] :
( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_124) ).
tff(118,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d)
| r1(D) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) ),
inference(modus_ponens,[status(thm)],[119,112]) ).
tff(121,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) ),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) ),
inference(modus_ponens,[status(thm)],[121,111]) ).
tff(123,plain,
( q1(d,d,d)
<=> q1(d,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ( $false
| $false
| q1(d,d,d) )
<=> q1(d,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(125,axiom,
s0(d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_1) ).
tff(126,plain,
( s0(d)
<=> $true ),
inference(iff_true,[status(thm)],[125]) ).
tff(127,plain,
( ~ s0(d)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
( ~ s0(d)
<=> $false ),
inference(transitivity,[status(thm)],[127,10]) ).
tff(129,plain,
( ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) )
<=> ( $false
| $false
| q1(d,d,d) ) ),
inference(monotonicity,[status(thm)],[128,14]) ).
tff(130,plain,
( ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) )
<=> q1(d,d,d) ),
inference(transitivity,[status(thm)],[129,124]) ).
tff(131,plain,
( ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,plain,
( ( ~ k0(e)
| q1(d,d,d)
| ~ s0(d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
( ( q1(d,d,d)
| ~ k0(e) )
<=> ( ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) )
<=> ( ~ k0(e)
| q1(d,d,d)
| ~ s0(d) ) ),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
( ( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(transitivity,[status(thm)],[134,132]) ).
tff(136,axiom,
( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_117) ).
tff(137,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[137,131]) ).
tff(139,plain,
q1(d,d,d),
inference(modus_ponens,[status(thm)],[138,130]) ).
tff(140,plain,
q1(d,d,d),
inference(modus_ponens,[status(thm)],[139,123]) ).
tff(141,plain,
( q0(e,d)
<=> q0(e,d) ),
inference(rewrite,[status(thm)],]) ).
tff(142,axiom,
q0(e,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_2) ).
tff(143,plain,
q0(e,d),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) )
| r1(e)
| ~ q1(d,d,d)
| ~ q0(e,d) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) )
| r1(e)
| ~ q1(d,d,d)
| ~ q0(e,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(145,plain,
( ( ~ q0(e,d)
| ~ q1(d,d,d)
| r1(e) )
<=> ( r1(e)
| ~ q1(d,d,d)
| ~ q0(e,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(146,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) )
| ~ q0(e,d)
| ~ q1(d,d,d)
| r1(e) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) )
| r1(e)
| ~ q1(d,d,d)
| ~ q0(e,d) ) ),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
( ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) )
| ~ q0(e,d)
| ~ q1(d,d,d)
| r1(e) )
<=> ( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) )
| r1(e)
| ~ q1(d,d,d)
| ~ q0(e,d) ) ),
inference(transitivity,[status(thm)],[146,144]) ).
tff(148,plain,
( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) )
| ~ q0(e,d)
| ~ q1(d,d,d)
| r1(e) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
( ~ ! [D: $i,E: $i] :
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) )
| r1(e)
| ~ q1(d,d,d)
| ~ q0(e,d) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
r1(e),
inference(unit_resolution,[status(thm)],[149,143,140,122]) ).
tff(151,plain,
^ [B: $i] :
refl(
( ( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ( p2(B,B,B)
| ~ n1(d,d,B) ) )),
inference(bind,[status(th)],]) ).
tff(152,plain,
( ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ) ),
inference(quant_intro,[status(thm)],[151]) ).
tff(153,plain,
( ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
<=> ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(154,axiom,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_153) ).
tff(155,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(skolemize,[status(sab)],[155]) ).
tff(157,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(modus_ponens,[status(thm)],[156,152]) ).
tff(158,plain,
( n1(d,d,d)
<=> n1(d,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(159,plain,
( ( n1(d,d,d)
| $false )
<=> n1(d,d,d) ),
inference(rewrite,[status(thm)],]) ).
tff(160,axiom,
q0(d,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_25) ).
tff(161,plain,
( q0(d,d)
<=> $true ),
inference(iff_true,[status(thm)],[160]) ).
tff(162,plain,
( ~ q0(d,d)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
( ~ q0(d,d)
<=> $false ),
inference(transitivity,[status(thm)],[162,10]) ).
tff(164,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> ( n1(d,d,d)
| $false ) ),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> n1(d,d,d) ),
inference(transitivity,[status(thm)],[164,159]) ).
tff(166,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> ( n1(d,d,d)
| ~ q0(d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(167,axiom,
( n1(d,d,d)
| ~ q0(d,d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_045) ).
tff(168,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[168,166]) ).
tff(170,plain,
n1(d,d,d),
inference(modus_ponens,[status(thm)],[169,165]) ).
tff(171,plain,
n1(d,d,d),
inference(modus_ponens,[status(thm)],[170,158]) ).
tff(172,plain,
( ( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) )
<=> ( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(173,plain,
( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
p2(d,d,d),
inference(unit_resolution,[status(thm)],[174,171,157]) ).
tff(176,plain,
( ( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ r1(e)
| k3(e,e,e)
| ~ p2(d,d,d) )
<=> ( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ r1(e)
| k3(e,e,e)
| ~ p2(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(177,plain,
( ( ~ p2(d,d,d)
| ~ r1(e)
| k3(e,e,e) )
<=> ( ~ r1(e)
| k3(e,e,e)
| ~ p2(d,d,d) ) ),
inference(rewrite,[status(thm)],]) ).
tff(178,plain,
( ( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ p2(d,d,d)
| ~ r1(e)
| k3(e,e,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ r1(e)
| k3(e,e,e)
| ~ p2(d,d,d) ) ),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( ( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ p2(d,d,d)
| ~ r1(e)
| k3(e,e,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ r1(e)
| k3(e,e,e)
| ~ p2(d,d,d) ) ),
inference(transitivity,[status(thm)],[178,176]) ).
tff(180,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ p2(d,d,d)
| ~ r1(e)
| k3(e,e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(181,plain,
( ~ ! [I: $i,A: $i,J: $i] :
( ~ p2(J,A,A)
| ~ r1(I)
| k3(I,I,I) )
| ~ r1(e)
| k3(e,e,e)
| ~ p2(d,d,d) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
k3(e,e,e),
inference(unit_resolution,[status(thm)],[181,175,150,109]) ).
tff(183,plain,
^ [B: $i,D: $i,E: $i,F: $i,C: $i] :
refl(
( ( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
<=> ( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
inference(bind,[status(th)],]) ).
tff(184,plain,
( ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
<=> ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) ),
inference(quant_intro,[status(thm)],[183]) ).
tff(185,plain,
( ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
<=> ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(186,plain,
^ [B: $i,D: $i,E: $i,F: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( q4(B,C)
| ~ k3(D,D,B) )
<=> ( ~ k3(D,D,B)
| q4(B,C) ) )),
( ( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B) )
<=> ( ~ k3(D,D,B)
| q4(B,C)
| ~ q2(E,C,B) ) )),
rewrite(
( ( ~ k3(D,D,B)
| q4(B,C)
| ~ q2(E,C,B) )
<=> ( ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
( ( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B) )
<=> ( ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
( ( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B)
| ~ m3(E,F,E) )
<=> ( ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C)
| ~ m3(E,F,E) ) )),
rewrite(
( ( ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C)
| ~ m3(E,F,E) )
<=> ( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
( ( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B)
| ~ m3(E,F,E) )
<=> ( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) )),
inference(bind,[status(th)],]) ).
tff(187,plain,
( ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B)
| ~ m3(E,F,E) )
<=> ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ) ),
inference(quant_intro,[status(thm)],[186]) ).
tff(188,axiom,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B)
| ~ m3(E,F,E) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_295) ).
tff(189,plain,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
inference(modus_ponens,[status(thm)],[189,185]) ).
tff(191,plain,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
inference(skolemize,[status(sab)],[190]) ).
tff(192,plain,
! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) ),
inference(modus_ponens,[status(thm)],[191,184]) ).
tff(193,plain,
( ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ k3(e,e,e)
| q4(e,e)
| ~ q2(e,e,e)
| ~ m3(e,e,e) )
<=> ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ k3(e,e,e)
| q4(e,e)
| ~ q2(e,e,e)
| ~ m3(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(194,plain,
( ( ~ m3(e,e,e)
| ~ q2(e,e,e)
| ~ k3(e,e,e)
| q4(e,e) )
<=> ( ~ k3(e,e,e)
| q4(e,e)
| ~ q2(e,e,e)
| ~ m3(e,e,e) ) ),
inference(rewrite,[status(thm)],]) ).
tff(195,plain,
( ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ m3(e,e,e)
| ~ q2(e,e,e)
| ~ k3(e,e,e)
| q4(e,e) )
<=> ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ k3(e,e,e)
| q4(e,e)
| ~ q2(e,e,e)
| ~ m3(e,e,e) ) ),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
( ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ m3(e,e,e)
| ~ q2(e,e,e)
| ~ k3(e,e,e)
| q4(e,e) )
<=> ( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ k3(e,e,e)
| q4(e,e)
| ~ q2(e,e,e)
| ~ m3(e,e,e) ) ),
inference(transitivity,[status(thm)],[195,193]) ).
tff(197,plain,
( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ m3(e,e,e)
| ~ q2(e,e,e)
| ~ k3(e,e,e)
| q4(e,e) ),
inference(quant_inst,[status(thm)],]) ).
tff(198,plain,
( ~ ! [B: $i,D: $i,E: $i,F: $i,C: $i] :
( ~ m3(E,F,E)
| ~ q2(E,C,B)
| ~ k3(D,D,B)
| q4(B,C) )
| ~ k3(e,e,e)
| q4(e,e)
| ~ q2(e,e,e)
| ~ m3(e,e,e) ),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
$false,
inference(unit_resolution,[status(thm)],[198,192,182,99,85,71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN183-1 : TPTP v8.1.0. Released v1.1.0.
% 0.06/0.13 % 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 02:04:59 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.
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------