%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN215-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 : Sat Jun 21 05:38:30 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.45s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 84
% Syntax : Number of formulae : 189 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 863 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1196 ( 556 ~; 552 |; 0 &)
% ( 88 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 34 ( 34 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 21 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 413 ( 376 !; 0 ?; 413 :)
% Comments :
%------------------------------------------------------------------------------
tff(r4_type,type,
r4: $i > $o ).
tff(d_type,type,
d: $i ).
tff(q3_type,type,
q3: ( $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(q2_type,type,
q2: ( $i * $i * $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(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(n3_type,type,
n3: $i > $o ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(l4_type,type,
l4: $i > $o ).
tff(p3_type,type,
p3: ( $i * $i * $i ) > $o ).
tff(n2_type,type,
n2: $i > $o ).
tff(k1_type,type,
k1: $i > $o ).
tff(c_type,type,
c: $i ).
tff(s5_type,type,
s5: $i > $o ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,axiom,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_181) ).
tff(5,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( k0(e)
<=> k0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(10,plain,
k0(e),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( r0(e)
<=> r0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
r0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(13,plain,
r0(e),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ( p1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) ) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(transitivity,[status(thm)],[17,15]) ).
tff(19,axiom,
( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_090) ).
tff(20,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[20,14]) ).
tff(22,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[22,14]) ).
tff(24,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[23,14]) ).
tff(25,plain,
p1(e,e,e),
inference(unit_resolution,[status(thm)],[24,13,10]) ).
tff(26,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(27,plain,
( ( q2(e,e,e)
| ~ p1(e,e,e) )
<=> ( ~ p1(e,e,e)
| q2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,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)],[27]) ).
tff(29,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)],[28,26]) ).
tff(30,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(31,plain,
( ~ ! [I: $i] :
( q2(I,I,I)
| ~ p1(I,I,I) )
| ~ p1(e,e,e)
| q2(e,e,e) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
q2(e,e,e),
inference(unit_resolution,[status(thm)],[31,25,7]) ).
tff(33,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(34,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)],[33]) ).
tff(35,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(36,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(37,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)],[36]) ).
tff(38,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(39,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( n0(e,e)
<=> n0(e,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
n0(e,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_30) ).
tff(45,plain,
n0(e,e),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ~ q2(e,e,e)
| ~ n0(e,e)
| q3(e,e) )
<=> ( q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,e)
| ~ n0(e,e)
| q3(e,e) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,e)
| ~ n0(e,e)
| q3(e,e) )
<=> ( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| ~ q2(e,e,e)
| ~ n0(e,e)
| q3(e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [I: $i,H: $i,G: $i] :
( ~ q2(I,G,H)
| ~ n0(I,G)
| q3(G,H) )
| q3(e,e)
| ~ q2(e,e,e)
| ~ n0(e,e) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
q3(e,e),
inference(unit_resolution,[status(thm)],[51,45,42,32]) ).
tff(53,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(54,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)],[53]) ).
tff(55,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(56,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(57,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,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(61,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)],[60]) ).
tff(62,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(63,axiom,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_153) ).
tff(64,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( q0(d,d)
<=> q0(d,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,axiom,
q0(d,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_25) ).
tff(69,plain,
q0(d,d),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( ( n1(d,d,d)
| ~ q0(d,d) )
<=> ( n1(d,d,d)
| ~ q0(d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
( n1(d,d,d)
| ~ q0(d,d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_045) ).
tff(72,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[72,70]) ).
tff(74,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[73,70]) ).
tff(75,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
( n1(d,d,d)
| ~ q0(d,d) ),
inference(modus_ponens,[status(thm)],[75,70]) ).
tff(77,plain,
n1(d,d,d),
inference(unit_resolution,[status(thm)],[76,69]) ).
tff(78,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(79,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(80,plain,
( ~ ! [B: $i] :
( p2(B,B,B)
| ~ n1(d,d,B) )
| p2(d,d,d)
| ~ n1(d,d,d) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
p2(d,d,d),
inference(unit_resolution,[status(thm)],[80,77,66]) ).
tff(82,plain,
( ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(d)
| ~ p2(d,d,d) )
<=> ( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(d)
| ~ p2(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(d)
| ~ p2(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [D: $i,E: $i,F: $i] :
( n3(D)
| ~ p2(E,F,D) )
| n3(d)
| ~ p2(d,d,d) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
n3(d),
inference(unit_resolution,[status(thm)],[84,81,59]) ).
tff(86,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(87,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)],[86]) ).
tff(88,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(89,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(90,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)],[89]) ).
tff(91,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(92,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) ),
inference(modus_ponens,[status(thm)],[94,87]) ).
tff(96,plain,
( p0(b,d)
<=> p0(b,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
p0(b,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_10) ).
tff(98,plain,
p0(b,d),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ q3(e,e)
| ~ n3(d)
| r4(d) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ q3(e,e)
| ~ n3(d)
| r4(d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ( ~ p0(b,d)
| ~ n3(d)
| ~ q3(e,e)
| r4(d) )
<=> ( ~ p0(b,d)
| ~ q3(e,e)
| ~ n3(d)
| r4(d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ n3(d)
| ~ q3(e,e)
| r4(d) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ q3(e,e)
| ~ n3(d)
| r4(d) ) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ n3(d)
| ~ q3(e,e)
| r4(d) )
<=> ( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ q3(e,e)
| ~ n3(d)
| r4(d) ) ),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,plain,
( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ n3(d)
| ~ q3(e,e)
| r4(d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [I: $i,J: $i,H: $i,G: $i] :
( ~ p0(J,G)
| ~ n3(G)
| ~ q3(H,I)
| r4(G) )
| ~ p0(b,d)
| ~ q3(e,e)
| ~ n3(d)
| r4(d) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
r4(d),
inference(unit_resolution,[status(thm)],[104,98,95,85,52]) ).
tff(106,plain,
^ [B: $i,C: $i] :
refl(( ( ~ p0(C,B)
| p1(B,B,B) )
<=> ( ~ p0(C,B)
| p1(B,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(107,plain,
( ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
^ [B: $i,C: $i] :
rewrite(( ( p1(B,B,B)
| ~ p0(C,B) )
<=> ( ~ p0(C,B)
| p1(B,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(110,plain,
( ! [B: $i,C: $i] :
( p1(B,B,B)
| ~ p0(C,B) )
<=> ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,axiom,
! [B: $i,C: $i] :
( p1(B,B,B)
| ~ p0(C,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_085) ).
tff(112,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[114,107]) ).
tff(116,plain,
( ( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) )
<=> ( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(b,d)
| p1(d,d,d) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
p1(d,d,d),
inference(unit_resolution,[status(thm)],[118,98,115]) ).
tff(120,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(121,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)],[120]) ).
tff(122,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(123,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(124,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(d)
| ~ p1(d,d,d) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(d)
| ~ p1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(d)
| ~ p1(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(d)
| ~ p1(d,d,d) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
n2(d),
inference(unit_resolution,[status(thm)],[129,126,119]) ).
tff(131,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(132,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)],[131]) ).
tff(133,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(134,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(135,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)],[134]) ).
tff(136,axiom,
! [H: $i] :
( p3(H,H,H)
| ~ k1(H)
| ~ n2(H) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_249) ).
tff(137,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[137,133]) ).
tff(139,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(skolemize,[status(sab)],[138]) ).
tff(140,plain,
! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) ),
inference(modus_ponens,[status(thm)],[139,132]) ).
tff(141,plain,
^ [I: $i,J: $i] :
refl(( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],[]) ).
tff(142,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(145,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[145]) ).
tff(147,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[146,142]) ).
tff(148,plain,
( n0(c,d)
<=> n0(c,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(149,axiom,
n0(c,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_34) ).
tff(150,plain,
n0(c,d),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(d)
| ~ n0(c,d) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(d)
| ~ n0(c,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(d)
| ~ n0(c,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(d)
| ~ n0(c,d) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
k1(d),
inference(unit_resolution,[status(thm)],[153,150,147]) ).
tff(155,plain,
( ( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(d)
| ~ n2(d)
| p3(d,d,d) )
<=> ( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(d)
| ~ n2(d)
| p3(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,plain,
( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(d)
| ~ n2(d)
| p3(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
( ~ ! [H: $i] :
( ~ k1(H)
| ~ n2(H)
| p3(H,H,H) )
| ~ k1(d)
| ~ n2(d)
| p3(d,d,d) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
p3(d,d,d),
inference(unit_resolution,[status(thm)],[157,154,140,130]) ).
tff(159,plain,
^ [B: $i,A: $i,J: $i] :
refl(( ( l4(J)
| ~ p3(A,B,J) )
<=> ( l4(J)
| ~ p3(A,B,J) ) )),
inference(bind,[status(th)],[]) ).
tff(160,plain,
( ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) )
<=> ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,plain,
( ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) )
<=> ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,axiom,
! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_277) ).
tff(163,plain,
! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) ),
inference(skolemize,[status(sab)],[163]) ).
tff(165,plain,
! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) ),
inference(modus_ponens,[status(thm)],[164,160]) ).
tff(166,plain,
( ( ~ ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) )
| l4(d)
| ~ p3(d,d,d) )
<=> ( ~ ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) )
| l4(d)
| ~ p3(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(167,plain,
( ~ ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) )
| l4(d)
| ~ p3(d,d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
( ~ ! [B: $i,A: $i,J: $i] :
( l4(J)
| ~ p3(A,B,J) )
| l4(d)
| ~ p3(d,d,d) ),
inference(modus_ponens,[status(thm)],[167,166]) ).
tff(169,plain,
l4(d),
inference(unit_resolution,[status(thm)],[168,165,158]) ).
tff(170,plain,
( ~ s5(d)
<=> ~ s5(d) ),
inference(rewrite,[status(thm)],[]) ).
tff(171,axiom,
~ s5(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(172,plain,
~ s5(d),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
^ [I: $i,H: $i] :
refl(( ( ~ l4(H)
| ~ r4(I)
| s5(H) )
<=> ( ~ l4(H)
| ~ r4(I)
| s5(H) ) )),
inference(bind,[status(th)],[]) ).
tff(174,plain,
( ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
<=> ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) ) ),
inference(quant_intro,[status(thm)],[173]) ).
tff(175,plain,
( ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
<=> ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,plain,
^ [I: $i,H: $i] :
rewrite(( ( s5(H)
| ~ l4(H)
| ~ r4(I) )
<=> ( ~ l4(H)
| ~ r4(I)
| s5(H) ) )),
inference(bind,[status(th)],[]) ).
tff(177,plain,
( ! [I: $i,H: $i] :
( s5(H)
| ~ l4(H)
| ~ r4(I) )
<=> ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) ) ),
inference(quant_intro,[status(thm)],[176]) ).
tff(178,axiom,
! [I: $i,H: $i] :
( s5(H)
| ~ l4(H)
| ~ r4(I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_329) ).
tff(179,plain,
! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) ),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) ),
inference(modus_ponens,[status(thm)],[179,175]) ).
tff(181,plain,
! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) ),
inference(skolemize,[status(sab)],[180]) ).
tff(182,plain,
! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) ),
inference(modus_ponens,[status(thm)],[181,174]) ).
tff(183,plain,
( ( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| s5(d)
| ~ r4(d)
| ~ l4(d) )
<=> ( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| s5(d)
| ~ r4(d)
| ~ l4(d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(184,plain,
( ( ~ l4(d)
| ~ r4(d)
| s5(d) )
<=> ( s5(d)
| ~ r4(d)
| ~ l4(d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(185,plain,
( ( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| ~ l4(d)
| ~ r4(d)
| s5(d) )
<=> ( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| s5(d)
| ~ r4(d)
| ~ l4(d) ) ),
inference(monotonicity,[status(thm)],[184]) ).
tff(186,plain,
( ( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| ~ l4(d)
| ~ r4(d)
| s5(d) )
<=> ( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| s5(d)
| ~ r4(d)
| ~ l4(d) ) ),
inference(transitivity,[status(thm)],[185,183]) ).
tff(187,plain,
( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| ~ l4(d)
| ~ r4(d)
| s5(d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(188,plain,
( ~ ! [I: $i,H: $i] :
( ~ l4(H)
| ~ r4(I)
| s5(H) )
| s5(d)
| ~ r4(d)
| ~ l4(d) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
$false,
inference(unit_resolution,[status(thm)],[188,182,172,169,105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYN215-1 : TPTP v9.0.0. Released v1.1.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:29:33 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.45 % SZS status Unsatisfiable
% 0.18/0.45 % SZS output start Proof
% See solution above
% 0.18/0.47 % E exiting
%------------------------------------------------------------------------------