%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN266-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:38:37 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 79
% Syntax : Number of formulae : 177 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 851 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1167 ( 540 ~; 536 |; 0 &)
% ( 91 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 47 ( 47 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 403 ( 364 !; 0 ?; 403 :)
% Comments :
%------------------------------------------------------------------------------
tff(p2_type,type,
p2: ( $i * $i * $i ) > $o ).
tff(e_type,type,
e: $i ).
tff(b_type,type,
b: $i ).
tff(n1_type,type,
n1: ( $i * $i * $i ) > $o ).
tff(k1_type,type,
k1: $i > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(l1_type,type,
l1: ( $i * $i ) > $o ).
tff(m3_type,type,
m3: ( $i * $i * $i ) > $o ).
tff(n2_type,type,
n2: $i > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(r0_type,type,
r0: $i > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(p3_type,type,
p3: ( $i * $i * $i ) > $o ).
tff(1,plain,
^ [I: $i,J: $i] :
refl(( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(5,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( n0(d,b)
<=> n0(d,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
n0(d,b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_7) ).
tff(10,plain,
n0(d,b),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(b)
| ~ n0(d,b) )
<=> ( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(b)
| ~ n0(d,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(b)
| ~ n0(d,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(b)
| ~ n0(d,b) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
k1(b),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [D: $i,C: $i] :
refl(( ( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) )
<=> ( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) )
<=> ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) )
<=> ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
^ [D: $i,C: $i] :
trans(monotonicity(rewrite(( ( n1(C,e,e)
| ~ m0(C,D,e) )
<=> ( ~ m0(C,D,e)
| n1(C,e,e) ) )),
( ( n1(C,e,e)
| ~ m0(C,D,e)
| ~ k1(C) )
<=> ( ~ m0(C,D,e)
| n1(C,e,e)
| ~ k1(C) ) )),
rewrite(( ( ~ m0(C,D,e)
| n1(C,e,e)
| ~ k1(C) )
<=> ( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ) )),
( ( n1(C,e,e)
| ~ m0(C,D,e)
| ~ k1(C) )
<=> ( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [D: $i,C: $i] :
( n1(C,e,e)
| ~ m0(C,D,e)
| ~ k1(C) )
<=> ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [D: $i,C: $i] :
( n1(C,e,e)
| ~ m0(C,D,e)
| ~ k1(C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_040) ).
tff(21,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( m0(b,b,e)
<=> m0(b,b,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
m0(b,b,e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_31) ).
tff(27,plain,
m0(b,b,e),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ( ~ ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) )
| ~ k1(b)
| ~ m0(b,b,e)
| n1(b,e,e) )
<=> ( ~ ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) )
| ~ k1(b)
| ~ m0(b,b,e)
| n1(b,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) )
| ~ k1(b)
| ~ m0(b,b,e)
| n1(b,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [D: $i,C: $i] :
( ~ k1(C)
| ~ m0(C,D,e)
| n1(C,e,e) )
| ~ k1(b)
| ~ m0(b,b,e)
| n1(b,e,e) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( ~ k1(b)
| n1(b,e,e) ),
inference(unit_resolution,[status(thm)],[30,27,24]) ).
tff(32,plain,
n1(b,e,e),
inference(unit_resolution,[status(thm)],[31,14]) ).
tff(33,plain,
^ [C: $i] :
refl(( ( ~ n1(C,e,e)
| p2(C,e,C) )
<=> ( ~ n1(C,e,e)
| p2(C,e,C) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) )
<=> ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) )
<=> ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
^ [C: $i] :
rewrite(( ( p2(C,e,C)
| ~ n1(C,e,e) )
<=> ( ~ n1(C,e,e)
| p2(C,e,C) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [C: $i] :
( p2(C,e,C)
| ~ n1(C,e,e) )
<=> ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [C: $i] :
( p2(C,e,C)
| ~ n1(C,e,e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_170) ).
tff(39,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) )
| ~ n1(b,e,e)
| p2(b,e,b) )
<=> ( ~ ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) )
| ~ n1(b,e,e)
| p2(b,e,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) )
| ~ n1(b,e,e)
| p2(b,e,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [C: $i] :
( ~ n1(C,e,e)
| p2(C,e,C) )
| ~ n1(b,e,e)
| p2(b,e,b) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
p2(b,e,b),
inference(unit_resolution,[status(thm)],[45,42,32]) ).
tff(47,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(48,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)],[47]) ).
tff(49,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(50,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(51,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)],[50]) ).
tff(52,axiom,
! [B: $i,C: $i] :
( p1(B,B,B)
| ~ p0(C,B) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_085) ).
tff(53,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
( p0(c,b)
<=> p0(c,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
p0(c,b),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_18) ).
tff(59,plain,
p0(c,b),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( ( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(c,b)
| p1(b,b,b) )
<=> ( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(c,b)
| p1(b,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(c,b)
| p1(b,b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [B: $i,C: $i] :
( ~ p0(C,B)
| p1(B,B,B) )
| ~ p0(c,b)
| p1(b,b,b) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
p1(b,b,b),
inference(unit_resolution,[status(thm)],[62,59,56]) ).
tff(64,plain,
^ [H: $i,G: $i] :
refl(( ( ~ n0(H,G)
| l1(G,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
^ [H: $i,G: $i] :
rewrite(( ( l1(G,G)
| ~ n0(H,G) )
<=> ( ~ n0(H,G)
| l1(G,G) ) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) )
<=> ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,axiom,
! [H: $i,G: $i] :
( l1(G,G)
| ~ n0(H,G) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_002) ).
tff(70,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
( ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,b)
| l1(b,b) )
<=> ( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,b)
| l1(b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,b)
| l1(b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [H: $i,G: $i] :
( ~ n0(H,G)
| l1(G,G) )
| ~ n0(d,b)
| l1(b,b) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
l1(b,b),
inference(unit_resolution,[status(thm)],[76,10,73]) ).
tff(78,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
refl(( ( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
<=> ( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( p2(C,D,D)
| ~ p1(C,E,F) )
<=> ( ~ p1(C,E,F)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ p1(C,E,F)
| ~ l1(E,F) )
<=> ( ~ p1(C,E,F)
| p2(C,D,D)
| ~ l1(E,F) ) )),
rewrite(( ( ~ p1(C,E,F)
| p2(C,D,D)
| ~ l1(E,F) )
<=> ( ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ p1(C,E,F)
| ~ l1(E,F) )
<=> ( ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ p1(C,E,F)
| ~ l1(E,F)
| ~ p2(C,D,C) )
<=> ( ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D)
| ~ p2(C,D,C) ) )),
rewrite(( ( ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D)
| ~ p2(C,D,C) )
<=> ( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) )),
( ( p2(C,D,D)
| ~ p1(C,E,F)
| ~ l1(E,F)
| ~ p2(C,D,C) )
<=> ( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( p2(C,D,D)
| ~ p1(C,E,F)
| ~ l1(E,F)
| ~ p2(C,D,C) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [D: $i,E: $i,F: $i,C: $i] :
( p2(C,D,D)
| ~ p1(C,E,F)
| ~ l1(E,F)
| ~ p2(C,D,C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_146) ).
tff(84,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ),
inference(skolemize,[status(sab)],[85]) ).
tff(87,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) ),
inference(modus_ponens,[status(thm)],[86,79]) ).
tff(88,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p1(b,b,b)
| ~ p2(b,e,b)
| ~ l1(b,b)
| p2(b,e,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p1(b,b,b)
| ~ p2(b,e,b)
| ~ l1(b,b)
| p2(b,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ( ~ p2(b,e,b)
| ~ l1(b,b)
| ~ p1(b,b,b)
| p2(b,e,e) )
<=> ( ~ p1(b,b,b)
| ~ p2(b,e,b)
| ~ l1(b,b)
| p2(b,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p2(b,e,b)
| ~ l1(b,b)
| ~ p1(b,b,b)
| p2(b,e,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p1(b,b,b)
| ~ p2(b,e,b)
| ~ l1(b,b)
| p2(b,e,e) ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p2(b,e,b)
| ~ l1(b,b)
| ~ p1(b,b,b)
| p2(b,e,e) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p1(b,b,b)
| ~ p2(b,e,b)
| ~ l1(b,b)
| p2(b,e,e) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p2(b,e,b)
| ~ l1(b,b)
| ~ p1(b,b,b)
| p2(b,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ p2(C,D,C)
| ~ l1(E,F)
| ~ p1(C,E,F)
| p2(C,D,D) )
| ~ p1(b,b,b)
| ~ p2(b,e,b)
| ~ l1(b,b)
| p2(b,e,e) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
p2(b,e,e),
inference(unit_resolution,[status(thm)],[93,87,77,63,46]) ).
tff(95,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(96,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)],[95]) ).
tff(97,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(98,axiom,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_137) ).
tff(99,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
( k0(e)
<=> k0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,axiom,
k0(e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(104,plain,
k0(e),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
( r0(e)
<=> r0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,axiom,
r0(e),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',axiom_13) ).
tff(107,plain,
r0(e),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
( ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
( ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ( p1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| p1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| p1(e,e,e)
| ~ k0(e) ) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) )
<=> ( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ) ),
inference(transitivity,[status(thm)],[111,109]) ).
tff(113,axiom,
( p1(e,e,e)
| ~ r0(e)
| ~ k0(e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_090) ).
tff(114,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[114,108]) ).
tff(116,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[115,108]) ).
tff(117,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[116,108]) ).
tff(118,plain,
( ~ r0(e)
| ~ k0(e)
| p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[117,108]) ).
tff(119,plain,
p1(e,e,e),
inference(unit_resolution,[status(thm)],[118,107,104]) ).
tff(120,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(121,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(122,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( n2(A)
| ~ p1(B,C,A) )
| n2(e)
| ~ p1(e,e,e) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
n2(e),
inference(unit_resolution,[status(thm)],[122,119,101]) ).
tff(124,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(125,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)],[124]) ).
tff(126,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(127,axiom,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_176) ).
tff(128,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(skolemize,[status(sab)],[128]) ).
tff(130,plain,
! [D: $i,E: $i] :
( p2(D,E,D)
| ~ m1(E,D,E) ),
inference(modus_ponens,[status(thm)],[129,125]) ).
tff(131,plain,
( ( ~ r0(e)
| m1(e,e,e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,plain,
( ( m1(e,e,e)
| ~ r0(e) )
<=> ( ~ r0(e)
| m1(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,axiom,
( m1(e,e,e)
| ~ r0(e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_012) ).
tff(134,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
( ~ r0(e)
| m1(e,e,e) ),
inference(modus_ponens,[status(thm)],[134,131]) ).
tff(136,plain,
m1(e,e,e),
inference(unit_resolution,[status(thm)],[135,107]) ).
tff(137,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(138,plain,
( ( p2(e,e,e)
| ~ m1(e,e,e) )
<=> ( ~ m1(e,e,e)
| p2(e,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,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)],[138]) ).
tff(140,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)],[139,137]) ).
tff(141,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(142,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)],[141,140]) ).
tff(143,plain,
p2(e,e,e),
inference(unit_resolution,[status(thm)],[142,136,130]) ).
tff(144,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(145,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)],[144]) ).
tff(146,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(147,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(148,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)],[147]) ).
tff(149,axiom,
! [D: $i] :
( m3(D,e,e)
| ~ n2(e)
| ~ p2(D,e,e) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_234) ).
tff(150,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(skolemize,[status(sab)],[151]) ).
tff(153,plain,
! [D: $i] :
( ~ n2(e)
| ~ p2(D,e,e)
| m3(D,e,e) ),
inference(modus_ponens,[status(thm)],[152,145]) ).
tff(154,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(155,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(156,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)],[155,154]) ).
tff(157,plain,
m3(e,e,e),
inference(unit_resolution,[status(thm)],[156,153,143,123]) ).
tff(158,plain,
( ~ p3(b,e,e)
<=> ~ p3(b,e,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,axiom,
~ p3(b,e,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(160,plain,
~ p3(b,e,e),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
<=> ( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(162,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ) ),
inference(quant_intro,[status(thm)],[161]) ).
tff(163,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
trans(monotonicity(rewrite(( ( p3(A,B,B)
| ~ m3(B,C,D) )
<=> ( ~ m3(B,C,D)
| p3(A,B,B) ) )),
( ( p3(A,B,B)
| ~ m3(B,C,D)
| ~ p2(A,B,D) )
<=> ( ~ m3(B,C,D)
| p3(A,B,B)
| ~ p2(A,B,D) ) )),
rewrite(( ( ~ m3(B,C,D)
| p3(A,B,B)
| ~ p2(A,B,D) )
<=> ( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ) )),
( ( p3(A,B,B)
| ~ m3(B,C,D)
| ~ p2(A,B,D) )
<=> ( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ) )),
inference(bind,[status(th)],[]) ).
tff(165,plain,
( ! [B: $i,D: $i,A: $i,C: $i] :
( p3(A,B,B)
| ~ m3(B,C,D)
| ~ p2(A,B,D) )
<=> ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ) ),
inference(quant_intro,[status(thm)],[164]) ).
tff(166,axiom,
! [B: $i,D: $i,A: $i,C: $i] :
( p3(A,B,B)
| ~ m3(B,C,D)
| ~ p2(A,B,D) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN001-0.ax',rule_251) ).
tff(167,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ),
inference(modus_ponens,[status(thm)],[167,163]) ).
tff(169,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ),
inference(skolemize,[status(sab)],[168]) ).
tff(170,plain,
! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) ),
inference(modus_ponens,[status(thm)],[169,162]) ).
tff(171,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| p3(b,e,e)
| ~ m3(e,e,e)
| ~ p2(b,e,e) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| p3(b,e,e)
| ~ m3(e,e,e)
| ~ p2(b,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,plain,
( ( ~ p2(b,e,e)
| ~ m3(e,e,e)
| p3(b,e,e) )
<=> ( p3(b,e,e)
| ~ m3(e,e,e)
| ~ p2(b,e,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(173,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| ~ p2(b,e,e)
| ~ m3(e,e,e)
| p3(b,e,e) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| p3(b,e,e)
| ~ m3(e,e,e)
| ~ p2(b,e,e) ) ),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
( ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| ~ p2(b,e,e)
| ~ m3(e,e,e)
| p3(b,e,e) )
<=> ( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| p3(b,e,e)
| ~ m3(e,e,e)
| ~ p2(b,e,e) ) ),
inference(transitivity,[status(thm)],[173,171]) ).
tff(175,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| ~ p2(b,e,e)
| ~ m3(e,e,e)
| p3(b,e,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] :
( ~ p2(A,B,D)
| ~ m3(B,C,D)
| p3(A,B,B) )
| p3(b,e,e)
| ~ m3(e,e,e)
| ~ p2(b,e,e) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
$false,
inference(unit_resolution,[status(thm)],[176,170,160,157,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN266-1 : TPTP v9.0.0. Released v1.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:31:32 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% See solution above
% 0.19/0.49 % E exiting
%------------------------------------------------------------------------------