%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN272-1 : TPTP v9.0.0. Released v1.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:38:38 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.46s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 89
% Syntax : Number of formulae : 191 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 938 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1321 ( 619 ~; 607 |; 0 &)
% ( 95 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 45 ( 45 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 459 ( 420 !; 0 ?; 459 :)
% Comments :
%------------------------------------------------------------------------------
tff(p4_type,type,
p4: ( $i * $i * $i ) > $o ).
tff(d_type,type,
d: $i ).
tff(e_type,type,
e: $i ).
tff(k3_type,type,
k3: ( $i * $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(k2_type,type,
k2: ( $i * $i ) > $o ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $o ).
tff(k0_type,type,
k0: $i > $o ).
tff(s0_type,type,
s0: $i > $o ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $o ).
tff(p0_type,type,
p0: ( $i * $i ) > $o ).
tff(k1_type,type,
k1: $i > $o ).
tff(n0_type,type,
n0: ( $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(r0_type,type,
r0: $i > $o ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $o ).
tff(q0_type,type,
q0: ( $i * $i ) > $o ).
tff(1,plain,
^ [A: $i,J: $i] :
refl(( ( ~ q1(A,J,J)
| k2(J,J) )
<=> ( ~ q1(A,J,J)
| k2(J,J) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
<=> ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
<=> ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [A: $i,J: $i] :
rewrite(( ( k2(J,J)
| ~ q1(A,J,J) )
<=> ( ~ q1(A,J,J)
| k2(J,J) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [A: $i,J: $i] :
( k2(J,J)
| ~ q1(A,J,J) )
<=> ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [A: $i,J: $i] :
( k2(J,J)
| ~ q1(A,J,J) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_129) ).
tff(7,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( k0(e)
<=> k0(e) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_28) ).
tff(13,plain,
k0(e),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( s0(d)
<=> s0(d) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
s0(d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_1) ).
tff(16,plain,
s0(d),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ k0(e)
| q1(d,d,d)
| ~ s0(d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( q1(d,d,d)
| ~ k0(e) )
<=> ( ~ k0(e)
| q1(d,d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) )
<=> ( ~ k0(e)
| q1(d,d,d)
| ~ s0(d) ) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( ( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) )
<=> ( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ) ),
inference(transitivity,[status(thm)],[20,18]) ).
tff(22,axiom,
( q1(d,d,d)
| ~ k0(e)
| ~ s0(d) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_117) ).
tff(23,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[23,17]) ).
tff(25,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[25,17]) ).
tff(27,plain,
( ~ s0(d)
| ~ k0(e)
| q1(d,d,d) ),
inference(modus_ponens,[status(thm)],[26,17]) ).
tff(28,plain,
q1(d,d,d),
inference(unit_resolution,[status(thm)],[27,16,13]) ).
tff(29,plain,
( ( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(d,d,d)
| k2(d,d) )
<=> ( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(d,d,d)
| k2(d,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(d,d,d)
| k2(d,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(d,d,d)
| k2(d,d) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
k2(d,d),
inference(unit_resolution,[status(thm)],[31,28,10]) ).
tff(33,plain,
^ [I: $i,H: $i] :
refl(( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
^ [I: $i,H: $i] :
trans(monotonicity(rewrite(( ( m1(H,I,H)
| ~ p0(H,I) )
<=> ( m1(H,I,H)
| ~ p0(H,I) ) )),
( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
rewrite(( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
( ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
<=> ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_029) ).
tff(39,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( p0(b,d)
<=> p0(b,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
p0(b,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_10) ).
tff(45,plain,
p0(b,d),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( s0(b)
<=> s0(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
s0(b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_5) ).
tff(48,plain,
s0(b),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,d)
| m1(b,d,b) )
<=> ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,d)
| m1(b,d,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( m1(b,d,b)
| ~ p0(b,d)
| ~ s0(b) )
<=> ( ~ s0(b)
| ~ p0(b,d)
| m1(b,d,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| m1(b,d,b)
| ~ p0(b,d)
| ~ s0(b) )
<=> ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,d)
| m1(b,d,b) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| m1(b,d,b)
| ~ p0(b,d)
| ~ s0(b) )
<=> ( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,d)
| m1(b,d,b) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| m1(b,d,b)
| ~ p0(b,d)
| ~ s0(b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [I: $i,H: $i] :
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) )
| ~ s0(b)
| ~ p0(b,d)
| m1(b,d,b) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
m1(b,d,b),
inference(unit_resolution,[status(thm)],[54,48,45,42]) ).
tff(56,plain,
^ [I: $i,J: $i] :
refl(( ( k1(I)
| ~ n0(J,I) )
<=> ( k1(I)
| ~ n0(J,I) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
<=> ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_001) ).
tff(60,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
( n0(c,d)
<=> n0(c,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,axiom,
n0(c,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_34) ).
tff(65,plain,
n0(c,d),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,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(67,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(d)
| ~ n0(c,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(d)
| ~ n0(c,d) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
k1(d),
inference(unit_resolution,[status(thm)],[68,65,62]) ).
tff(70,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
refl(( ( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
<=> ( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( k2(C,D)
| ~ m1(E,D,C) )
<=> ( ~ m1(E,D,C)
| k2(C,D) ) )),
( ( k2(C,D)
| ~ m1(E,D,C)
| ~ k1(F) )
<=> ( ~ m1(E,D,C)
| k2(C,D)
| ~ k1(F) ) )),
rewrite(( ( ~ m1(E,D,C)
| k2(C,D)
| ~ k1(F) )
<=> ( ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D) ) )),
( ( k2(C,D)
| ~ m1(E,D,C)
| ~ k1(F) )
<=> ( ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D) ) )),
( ( k2(C,D)
| ~ m1(E,D,C)
| ~ k1(F)
| ~ k2(F,D) )
<=> ( ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D)
| ~ k2(F,D) ) )),
rewrite(( ( ~ k1(F)
| ~ m1(E,D,C)
| k2(C,D)
| ~ k2(F,D) )
<=> ( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ) )),
( ( k2(C,D)
| ~ m1(E,D,C)
| ~ k1(F)
| ~ k2(F,D) )
<=> ( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [D: $i,E: $i,F: $i,C: $i] :
( k2(C,D)
| ~ m1(E,D,C)
| ~ k1(F)
| ~ k2(F,D) )
<=> ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,axiom,
! [D: $i,E: $i,F: $i,C: $i] :
( k2(C,D)
| ~ m1(E,D,C)
| ~ k1(F)
| ~ k2(F,D) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_127) ).
tff(76,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) ),
inference(modus_ponens,[status(thm)],[78,71]) ).
tff(80,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(d)
| ~ k2(d,d)
| ~ m1(b,d,b)
| k2(b,d) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(d)
| ~ k2(d,d)
| ~ m1(b,d,b)
| k2(b,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(d)
| ~ k2(d,d)
| ~ m1(b,d,b)
| k2(b,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(d)
| ~ k2(d,d)
| ~ m1(b,d,b)
| k2(b,d) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
k2(b,d),
inference(unit_resolution,[status(thm)],[82,79,69,55,32]) ).
tff(84,plain,
^ [F: $i,G: $i] :
refl(( ( ~ k2(G,F)
| k3(F,F,G) )
<=> ( ~ k2(G,F)
| k3(F,F,G) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [F: $i,G: $i] :
( ~ k2(G,F)
| k3(F,F,G) )
<=> ! [F: $i,G: $i] :
( ~ k2(G,F)
| k3(F,F,G) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [F: $i,G: $i] :
( ~ k2(G,F)
| k3(F,F,G) )
<=> ! [F: $i,G: $i] :
( ~ k2(G,F)
| k3(F,F,G) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
^ [F: $i,G: $i] :
rewrite(( ( k3(F,F,G)
| ~ k2(G,F) )
<=> ( ~ k2(G,F)
| k3(F,F,G) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [F: $i,G: $i] :
( k3(F,F,G)
| ~ k2(G,F) )
<=> ! [F: $i,G: $i] :
( ~ k2(G,F)
| k3(F,F,G) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,axiom,
! [F: $i,G: $i] :
( k3(F,F,G)
| ~ k2(G,F) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_194) ).
tff(90,plain,
! [F: $i,G: $i] :
( ~ k2(G,F)
| k3(F,F,G) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [F: $i,G: $i] :
( ~ k2(G,F)
| k3(F,F,G) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
! [F: $i,G: $i] :
( ~ k2(G,F)
| k3(F,F,G) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [F: $i,G: $i] :
( ~ k2(G,F)
| k3(F,F,G) ),
inference(modus_ponens,[status(thm)],[92,85]) ).
tff(94,plain,
( ( ~ ! [F: $i,G: $i] :
( ~ k2(G,F)
| k3(F,F,G) )
| ~ k2(b,d)
| k3(d,d,b) )
<=> ( ~ ! [F: $i,G: $i] :
( ~ k2(G,F)
| k3(F,F,G) )
| ~ k2(b,d)
| k3(d,d,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [F: $i,G: $i] :
( ~ k2(G,F)
| k3(F,F,G) )
| ~ k2(b,d)
| k3(d,d,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [F: $i,G: $i] :
( ~ k2(G,F)
| k3(F,F,G) )
| ~ k2(b,d)
| k3(d,d,b) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
k3(d,d,b),
inference(unit_resolution,[status(thm)],[96,93,83]) ).
tff(98,plain,
( r0(b)
<=> r0(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,axiom,
r0(b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_9) ).
tff(100,plain,
r0(b),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
( ( ~ r0(b)
| q1(b,b,b) )
<=> ( ~ r0(b)
| q1(b,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ( q1(b,b,b)
| ~ r0(b) )
<=> ( ~ r0(b)
| q1(b,b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,axiom,
( q1(b,b,b)
| ~ r0(b) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_120) ).
tff(104,plain,
( ~ r0(b)
| q1(b,b,b) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
( ~ r0(b)
| q1(b,b,b) ),
inference(modus_ponens,[status(thm)],[104,101]) ).
tff(106,plain,
q1(b,b,b),
inference(unit_resolution,[status(thm)],[105,100]) ).
tff(107,plain,
( ( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(b,b,b)
| k2(b,b) )
<=> ( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(b,b,b)
| k2(b,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(b,b,b)
| k2(b,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
( ~ ! [A: $i,J: $i] :
( ~ q1(A,J,J)
| k2(J,J) )
| ~ q1(b,b,b)
| k2(b,b) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
k2(b,b),
inference(unit_resolution,[status(thm)],[109,106,10]) ).
tff(111,plain,
^ [B: $i,C: $i] :
refl(( ( ~ m0(C,C,B)
| m1(B,C,B) )
<=> ( ~ m0(C,C,B)
| m1(B,C,B) ) )),
inference(bind,[status(th)],[]) ).
tff(112,plain,
( ! [B: $i,C: $i] :
( ~ m0(C,C,B)
| m1(B,C,B) )
<=> ! [B: $i,C: $i] :
( ~ m0(C,C,B)
| m1(B,C,B) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ! [B: $i,C: $i] :
( ~ m0(C,C,B)
| m1(B,C,B) )
<=> ! [B: $i,C: $i] :
( ~ m0(C,C,B)
| m1(B,C,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
^ [B: $i,C: $i] :
rewrite(( ( m1(B,C,B)
| ~ m0(C,C,B) )
<=> ( ~ m0(C,C,B)
| m1(B,C,B) ) )),
inference(bind,[status(th)],[]) ).
tff(115,plain,
( ! [B: $i,C: $i] :
( m1(B,C,B)
| ~ m0(C,C,B) )
<=> ! [B: $i,C: $i] :
( ~ m0(C,C,B)
| m1(B,C,B) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,axiom,
! [B: $i,C: $i] :
( m1(B,C,B)
| ~ m0(C,C,B) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_005) ).
tff(117,plain,
! [B: $i,C: $i] :
( ~ m0(C,C,B)
| m1(B,C,B) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [B: $i,C: $i] :
( ~ m0(C,C,B)
| m1(B,C,B) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
! [B: $i,C: $i] :
( ~ m0(C,C,B)
| m1(B,C,B) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [B: $i,C: $i] :
( ~ m0(C,C,B)
| m1(B,C,B) ),
inference(modus_ponens,[status(thm)],[119,112]) ).
tff(121,plain,
( m0(b,b,e)
<=> m0(b,b,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,axiom,
m0(b,b,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_31) ).
tff(123,plain,
m0(b,b,e),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
( ( ~ ! [B: $i,C: $i] :
( ~ m0(C,C,B)
| m1(B,C,B) )
| ~ m0(b,b,e)
| m1(e,b,e) )
<=> ( ~ ! [B: $i,C: $i] :
( ~ m0(C,C,B)
| m1(B,C,B) )
| ~ m0(b,b,e)
| m1(e,b,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [B: $i,C: $i] :
( ~ m0(C,C,B)
| m1(B,C,B) )
| ~ m0(b,b,e)
| m1(e,b,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [B: $i,C: $i] :
( ~ m0(C,C,B)
| m1(B,C,B) )
| ~ m0(b,b,e)
| m1(e,b,e) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
m1(e,b,e),
inference(unit_resolution,[status(thm)],[126,123,120]) ).
tff(128,plain,
( n0(d,b)
<=> n0(d,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,axiom,
n0(d,b),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_7) ).
tff(130,plain,
n0(d,b),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,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(132,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(b)
| ~ n0(d,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
( ~ ! [I: $i,J: $i] :
( k1(I)
| ~ n0(J,I) )
| k1(b)
| ~ n0(d,b) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
k1(b),
inference(unit_resolution,[status(thm)],[133,130,62]) ).
tff(135,plain,
( ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(b)
| ~ k2(b,b)
| ~ m1(e,b,e)
| k2(e,b) )
<=> ( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(b)
| ~ k2(b,b)
| ~ m1(e,b,e)
| k2(e,b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(b)
| ~ k2(b,b)
| ~ m1(e,b,e)
| k2(e,b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] :
( ~ k1(F)
| ~ k2(F,D)
| ~ m1(E,D,C)
| k2(C,D) )
| ~ k1(b)
| ~ k2(b,b)
| ~ m1(e,b,e)
| k2(e,b) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
k2(e,b),
inference(unit_resolution,[status(thm)],[137,79,134,127,110]) ).
tff(139,plain,
^ [I: $i,A: $i,J: $i,H: $i,G: $i] :
refl(( ( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
<=> ( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) ) )),
inference(bind,[status(th)],[]) ).
tff(140,plain,
( ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
<=> ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,plain,
( ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
<=> ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
^ [I: $i,A: $i,J: $i,H: $i,G: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( k3(G,G,H)
| ~ q0(I,H) )
<=> ( ~ q0(I,H)
| k3(G,G,H) ) )),
( ( k3(G,G,H)
| ~ q0(I,H)
| ~ k2(G,J) )
<=> ( ~ q0(I,H)
| k3(G,G,H)
| ~ k2(G,J) ) )),
rewrite(( ( ~ q0(I,H)
| k3(G,G,H)
| ~ k2(G,J) )
<=> ( ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) ) )),
( ( k3(G,G,H)
| ~ q0(I,H)
| ~ k2(G,J) )
<=> ( ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) ) )),
( ( k3(G,G,H)
| ~ q0(I,H)
| ~ k2(G,J)
| ~ k3(H,A,J) )
<=> ( ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H)
| ~ k3(H,A,J) ) )),
rewrite(( ( ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H)
| ~ k3(H,A,J) )
<=> ( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) ) )),
( ( k3(G,G,H)
| ~ q0(I,H)
| ~ k2(G,J)
| ~ k3(H,A,J) )
<=> ( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) ) )),
inference(bind,[status(th)],[]) ).
tff(143,plain,
( ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( k3(G,G,H)
| ~ q0(I,H)
| ~ k2(G,J)
| ~ k3(H,A,J) )
<=> ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,axiom,
! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( k3(G,G,H)
| ~ q0(I,H)
| ~ k2(G,J)
| ~ k3(H,A,J) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_202) ).
tff(145,plain,
! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) ),
inference(modus_ponens,[status(thm)],[145,141]) ).
tff(147,plain,
! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) ),
inference(skolemize,[status(sab)],[146]) ).
tff(148,plain,
! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) ),
inference(modus_ponens,[status(thm)],[147,140]) ).
tff(149,plain,
( q0(e,d)
<=> q0(e,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,axiom,
q0(e,d),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_2) ).
tff(151,plain,
q0(e,d),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ q0(e,d)
| ~ k2(e,b)
| ~ k3(d,d,b)
| k3(e,e,d) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ q0(e,d)
| ~ k2(e,b)
| ~ k3(d,d,b)
| k3(e,e,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(153,plain,
( ( ~ k3(d,d,b)
| ~ k2(e,b)
| ~ q0(e,d)
| k3(e,e,d) )
<=> ( ~ q0(e,d)
| ~ k2(e,b)
| ~ k3(d,d,b)
| k3(e,e,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(154,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ k3(d,d,b)
| ~ k2(e,b)
| ~ q0(e,d)
| k3(e,e,d) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ q0(e,d)
| ~ k2(e,b)
| ~ k3(d,d,b)
| k3(e,e,d) ) ),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ k3(d,d,b)
| ~ k2(e,b)
| ~ q0(e,d)
| k3(e,e,d) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ q0(e,d)
| ~ k2(e,b)
| ~ k3(d,d,b)
| k3(e,e,d) ) ),
inference(transitivity,[status(thm)],[154,152]) ).
tff(156,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ k3(d,d,b)
| ~ k2(e,b)
| ~ q0(e,d)
| k3(e,e,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(157,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ q0(e,d)
| ~ k2(e,b)
| ~ k3(d,d,b)
| k3(e,e,d) ),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
k3(e,e,d),
inference(unit_resolution,[status(thm)],[157,151,148,138,97]) ).
tff(159,plain,
( q0(b,e)
<=> q0(b,e) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,axiom,
q0(b,e),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',axiom_21) ).
tff(161,plain,
q0(b,e),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ q0(b,e)
| ~ k2(d,d)
| ~ k3(e,e,d)
| k3(d,d,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ q0(b,e)
| ~ k2(d,d)
| ~ k3(e,e,d)
| k3(d,d,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,plain,
( ( ~ k3(e,e,d)
| ~ k2(d,d)
| ~ q0(b,e)
| k3(d,d,e) )
<=> ( ~ q0(b,e)
| ~ k2(d,d)
| ~ k3(e,e,d)
| k3(d,d,e) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ k3(e,e,d)
| ~ k2(d,d)
| ~ q0(b,e)
| k3(d,d,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ q0(b,e)
| ~ k2(d,d)
| ~ k3(e,e,d)
| k3(d,d,e) ) ),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
( ( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ k3(e,e,d)
| ~ k2(d,d)
| ~ q0(b,e)
| k3(d,d,e) )
<=> ( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ q0(b,e)
| ~ k2(d,d)
| ~ k3(e,e,d)
| k3(d,d,e) ) ),
inference(transitivity,[status(thm)],[164,162]) ).
tff(166,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ k3(e,e,d)
| ~ k2(d,d)
| ~ q0(b,e)
| k3(d,d,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
( ~ ! [I: $i,A: $i,J: $i,H: $i,G: $i] :
( ~ k3(H,A,J)
| ~ k2(G,J)
| ~ q0(I,H)
| k3(G,G,H) )
| ~ q0(b,e)
| ~ k2(d,d)
| ~ k3(e,e,d)
| k3(d,d,e) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
k3(d,d,e),
inference(unit_resolution,[status(thm)],[167,161,148,32,158]) ).
tff(169,plain,
^ [B: $i,C: $i] :
refl(( ( p4(B,C,B)
| ~ k3(B,B,C) )
<=> ( p4(B,C,B)
| ~ k3(B,B,C) ) )),
inference(bind,[status(th)],[]) ).
tff(170,plain,
( ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
<=> ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) ) ),
inference(quant_intro,[status(thm)],[169]) ).
tff(171,plain,
( ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
<=> ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,axiom,
! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN001-0.ax',rule_287) ).
tff(173,plain,
! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) ),
inference(skolemize,[status(sab)],[173]) ).
tff(175,plain,
! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) ),
inference(modus_ponens,[status(thm)],[174,170]) ).
tff(176,plain,
( ( ~ ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
| ~ k3(d,d,e)
| p4(d,e,d) )
<=> ( ~ ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
| ~ k3(d,d,e)
| p4(d,e,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(177,plain,
( ( p4(d,e,d)
| ~ k3(d,d,e) )
<=> ( ~ k3(d,d,e)
| p4(d,e,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,plain,
( ( ~ ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
| p4(d,e,d)
| ~ k3(d,d,e) )
<=> ( ~ ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
| ~ k3(d,d,e)
| p4(d,e,d) ) ),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( ( ~ ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
| p4(d,e,d)
| ~ k3(d,d,e) )
<=> ( ~ ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
| ~ k3(d,d,e)
| p4(d,e,d) ) ),
inference(transitivity,[status(thm)],[178,176]) ).
tff(180,plain,
( ~ ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
| p4(d,e,d)
| ~ k3(d,d,e) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
( ~ ! [B: $i,C: $i] :
( p4(B,C,B)
| ~ k3(B,B,C) )
| ~ k3(d,d,e)
| p4(d,e,d) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
p4(d,e,d),
inference(unit_resolution,[status(thm)],[181,175,168]) ).
tff(183,plain,
^ [X: $i] :
refl(( ~ p4(d,e,X)
<=> ~ p4(d,e,X) )),
inference(bind,[status(th)],[]) ).
tff(184,plain,
( ! [X: $i] : ~ p4(d,e,X)
<=> ! [X: $i] : ~ p4(d,e,X) ),
inference(quant_intro,[status(thm)],[183]) ).
tff(185,plain,
( ! [X: $i] : ~ p4(d,e,X)
<=> ! [X: $i] : ~ p4(d,e,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,axiom,
! [X: $i] : ~ p4(d,e,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(187,plain,
! [X: $i] : ~ p4(d,e,X),
inference(modus_ponens,[status(thm)],[186,185]) ).
tff(188,plain,
! [X: $i] : ~ p4(d,e,X),
inference(skolemize,[status(sab)],[187]) ).
tff(189,plain,
! [X: $i] : ~ p4(d,e,X),
inference(modus_ponens,[status(thm)],[188,184]) ).
tff(190,plain,
( ~ ! [X: $i] : ~ p4(d,e,X)
| ~ p4(d,e,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(191,plain,
$false,
inference(unit_resolution,[status(thm)],[190,189,182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN272-1 : TPTP v9.0.0. Released v1.1.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.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
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:31:57 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.46 % SZS status Unsatisfiable
% 0.19/0.46 % SZS output start Proof
% See solution above
% 0.19/0.50 % E exiting
%------------------------------------------------------------------------------