%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN214-10 : TPTP v9.0.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 0.64s 0.82s
% Output : Proof 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 100
% Syntax : Number of formulae : 301 ( 227 unt; 0 typ; 0 def)
% Number of atoms : 405 ( 389 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 126 ( 37 ~; 33 |; 0 &)
% ( 56 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 6 con; 0-4 aty)
% Number of variables : 404 ( 369 !; 0 ?; 404 :)
% Comments :
%------------------------------------------------------------------------------
tff(true_type,type,
true: $i ).
tff(s5_type,type,
s5: $i > $i ).
tff(c_type,type,
c: $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(l4_type,type,
l4: $i > $i ).
tff(r4_type,type,
r4: $i > $i ).
tff(d_type,type,
d: $i ).
tff(p0_type,type,
p0: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(n3_type,type,
n3: $i > $i ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $i ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $i ).
tff(s0_type,type,
s0: $i > $i ).
tff(q3_type,type,
q3: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(n0_type,type,
n0: ( $i * $i ) > $i ).
tff(q2_type,type,
q2: ( $i * $i * $i ) > $i ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $i ).
tff(e_type,type,
e: $i ).
tff(k0_type,type,
k0: $i > $i ).
tff(r1_type,type,
r1: $i > $i ).
tff(q0_type,type,
q0: ( $i * $i ) > $i ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $i ).
tff(p3_type,type,
p3: ( $i * $i * $i ) > $i ).
tff(k2_type,type,
k2: ( $i * $i ) > $i ).
tff(r0_type,type,
r0: $i > $i ).
tff(1,plain,
^ [I: $i,H: $i] :
refl(( ( ifeq(r4(I),true,ifeq(l4(H),true,s5(H),true),true) = true )
<=> ( ifeq(r4(I),true,ifeq(l4(H),true,s5(H),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [I: $i,H: $i] : ( ifeq(r4(I),true,ifeq(l4(H),true,s5(H),true),true) = true )
<=> ! [I: $i,H: $i] : ( ifeq(r4(I),true,ifeq(l4(H),true,s5(H),true),true) = true ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [I: $i,H: $i] : ( ifeq(r4(I),true,ifeq(l4(H),true,s5(H),true),true) = true )
<=> ! [I: $i,H: $i] : ( ifeq(r4(I),true,ifeq(l4(H),true,s5(H),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [I: $i,H: $i] : ( ifeq(r4(I),true,ifeq(l4(H),true,s5(H),true),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_329) ).
tff(5,plain,
! [I: $i,H: $i] : ( ifeq(r4(I),true,ifeq(l4(H),true,s5(H),true),true) = true ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [I: $i,H: $i] : ( ifeq(r4(I),true,ifeq(l4(H),true,s5(H),true),true) = true ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [I: $i,H: $i] : ( ifeq(r4(I),true,ifeq(l4(H),true,s5(H),true),true) = true ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [I: $i,H: $i] : ( ifeq(r4(I),true,ifeq(l4(H),true,s5(H),true),true) = true )
| ( ifeq(r4(d),true,ifeq(l4(c),true,s5(c),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq(r4(d),true,ifeq(l4(c),true,s5(c),true),true) = true,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq(A,A,B,C) = B )
<=> ( ifeq(A,A,B,C) = B ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,r4(d),true) = r4(d) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ifeq(true,true,r4(d),true) = r4(d),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ( p0(b,d) = true )
<=> ( p0(b,d) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
p0(b,d) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
tff(21,plain,
p0(b,d) = true,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
true = p0(b,d),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
ifeq(true,true,r4(d),true) = ifeq(p0(b,d),true,r4(d),true),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
ifeq(p0(b,d),true,r4(d),true) = ifeq(true,true,r4(d),true),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
r4(d) = ifeq(true,true,r4(d),true),
inference(symmetry,[status(thm)],[18]) ).
tff(26,plain,
r4(d) = ifeq(p0(b,d),true,r4(d),true),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,n3(d),true) = n3(d) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
ifeq(true,true,n3(d),true) = n3(d),
inference(unit_resolution,[status(thm)],[27,16]) ).
tff(29,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,p2(d,d,d),true) = p2(d,d,d) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
ifeq(true,true,p2(d,d,d),true) = p2(d,d,d),
inference(unit_resolution,[status(thm)],[29,16]) ).
tff(31,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,q1(d,d,d),true) = q1(d,d,d) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
ifeq(true,true,q1(d,d,d),true) = q1(d,d,d),
inference(unit_resolution,[status(thm)],[31,16]) ).
tff(33,plain,
( ( s0(d) = true )
<=> ( s0(d) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
s0(d) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
tff(35,plain,
s0(d) = true,
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
true = s0(d),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
ifeq(true,true,q1(d,d,d),true) = ifeq(s0(d),true,q1(d,d,d),true),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
ifeq(s0(d),true,q1(d,d,d),true) = ifeq(true,true,q1(d,d,d),true),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
^ [B: $i] :
refl(( ( ifeq(s0(B),true,q1(B,B,B),true) = true )
<=> ( ifeq(s0(B),true,q1(B,B,B),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [B: $i] : ( ifeq(s0(B),true,q1(B,B,B),true) = true )
<=> ! [B: $i] : ( ifeq(s0(B),true,q1(B,B,B),true) = true ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [B: $i] : ( ifeq(s0(B),true,q1(B,B,B),true) = true )
<=> ! [B: $i] : ( ifeq(s0(B),true,q1(B,B,B),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
! [B: $i] : ( ifeq(s0(B),true,q1(B,B,B),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_106) ).
tff(43,plain,
! [B: $i] : ( ifeq(s0(B),true,q1(B,B,B),true) = true ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [B: $i] : ( ifeq(s0(B),true,q1(B,B,B),true) = true ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [B: $i] : ( ifeq(s0(B),true,q1(B,B,B),true) = true ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ~ ! [B: $i] : ( ifeq(s0(B),true,q1(B,B,B),true) = true )
| ( ifeq(s0(d),true,q1(d,d,d),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
ifeq(s0(d),true,q1(d,d,d),true) = true,
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
true = ifeq(s0(d),true,q1(d,d,d),true),
inference(symmetry,[status(thm)],[47]) ).
tff(49,plain,
true = q1(d,d,d),
inference(transitivity,[status(thm)],[48,38,32]) ).
tff(50,plain,
ifeq(true,true,p2(d,d,d),true) = ifeq(q1(d,d,d),true,p2(d,d,d),true),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
ifeq(q1(d,d,d),true,p2(d,d,d),true) = ifeq(true,true,p2(d,d,d),true),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
^ [A: $i] :
refl(( ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true )
<=> ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true )
<=> ! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true )
<=> ! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_154) ).
tff(56,plain,
! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ~ ! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true )
| ( ifeq(q1(d,d,d),true,p2(d,d,d),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
ifeq(q1(d,d,d),true,p2(d,d,d),true) = true,
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
true = ifeq(q1(d,d,d),true,p2(d,d,d),true),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
true = p2(d,d,d),
inference(transitivity,[status(thm)],[61,51,30]) ).
tff(63,plain,
ifeq(true,true,n3(d),true) = ifeq(p2(d,d,d),true,n3(d),true),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
ifeq(p2(d,d,d),true,n3(d),true) = ifeq(true,true,n3(d),true),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
^ [D: $i,E: $i,F: $i] :
refl(( ( ifeq(p2(E,F,D),true,n3(D),true) = true )
<=> ( ifeq(p2(E,F,D),true,n3(D),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [D: $i,E: $i,F: $i] : ( ifeq(p2(E,F,D),true,n3(D),true) = true )
<=> ! [D: $i,E: $i,F: $i] : ( ifeq(p2(E,F,D),true,n3(D),true) = true ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [D: $i,E: $i,F: $i] : ( ifeq(p2(E,F,D),true,n3(D),true) = true )
<=> ! [D: $i,E: $i,F: $i] : ( ifeq(p2(E,F,D),true,n3(D),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,axiom,
! [D: $i,E: $i,F: $i] : ( ifeq(p2(E,F,D),true,n3(D),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_240) ).
tff(69,plain,
! [D: $i,E: $i,F: $i] : ( ifeq(p2(E,F,D),true,n3(D),true) = true ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [D: $i,E: $i,F: $i] : ( ifeq(p2(E,F,D),true,n3(D),true) = true ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [D: $i,E: $i,F: $i] : ( ifeq(p2(E,F,D),true,n3(D),true) = true ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( ~ ! [D: $i,E: $i,F: $i] : ( ifeq(p2(E,F,D),true,n3(D),true) = true )
| ( ifeq(p2(d,d,d),true,n3(d),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
ifeq(p2(d,d,d),true,n3(d),true) = true,
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
true = ifeq(p2(d,d,d),true,n3(d),true),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
p0(b,d) = n3(d),
inference(transitivity,[status(thm)],[21,74,64,28]) ).
tff(76,plain,
ifeq(p0(b,d),true,r4(d),true) = ifeq(n3(d),true,ifeq(p0(b,d),true,r4(d),true),true),
inference(monotonicity,[status(thm)],[75,26]) ).
tff(77,plain,
ifeq(n3(d),true,ifeq(p0(b,d),true,r4(d),true),true) = ifeq(p0(b,d),true,r4(d),true),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(n3(d),true,ifeq(p0(b,d),true,r4(d),true),true),true) = ifeq(n3(d),true,ifeq(p0(b,d),true,r4(d),true),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
ifeq(true,true,ifeq(n3(d),true,ifeq(p0(b,d),true,r4(d),true),true),true) = ifeq(n3(d),true,ifeq(p0(b,d),true,r4(d),true),true),
inference(unit_resolution,[status(thm)],[78,16]) ).
tff(80,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,q3(b,a),true) = q3(b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
ifeq(true,true,q3(b,a),true) = q3(b,a),
inference(unit_resolution,[status(thm)],[80,16]) ).
tff(82,plain,
( ( n0(a,b) = true )
<=> ( n0(a,b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
n0(a,b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
tff(84,plain,
n0(a,b) = true,
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
true = n0(a,b),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
ifeq(true,true,q3(b,a),true) = ifeq(n0(a,b),true,q3(b,a),true),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
ifeq(n0(a,b),true,q3(b,a),true) = ifeq(true,true,q3(b,a),true),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
q3(b,a) = ifeq(true,true,q3(b,a),true),
inference(symmetry,[status(thm)],[81]) ).
tff(89,plain,
q3(b,a) = ifeq(n0(a,b),true,q3(b,a),true),
inference(transitivity,[status(thm)],[88,86]) ).
tff(90,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,q2(a,b,a),true) = q2(a,b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
ifeq(true,true,q2(a,b,a),true) = q2(a,b,a),
inference(unit_resolution,[status(thm)],[90,16]) ).
tff(92,plain,
( ( m0(e,d,a) = true )
<=> ( m0(e,d,a) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,axiom,
m0(e,d,a) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(94,plain,
m0(e,d,a) = true,
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
true = m0(e,d,a),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
ifeq(true,true,q2(a,b,a),true) = ifeq(m0(e,d,a),true,q2(a,b,a),true),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
ifeq(m0(e,d,a),true,q2(a,b,a),true) = ifeq(true,true,q2(a,b,a),true),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true) = ifeq(m0(e,d,a),true,q2(a,b,a),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
ifeq(true,true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true) = ifeq(m0(e,d,a),true,q2(a,b,a),true),
inference(unit_resolution,[status(thm)],[98,16]) ).
tff(100,plain,
( ( k0(b) = true )
<=> ( k0(b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,axiom,
k0(b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
tff(102,plain,
k0(b) = true,
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
true = k0(b),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
ifeq(true,true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true) = ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true) = ifeq(true,true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true) = ifeq(m0(e,d,a),true,q2(a,b,a),true),
inference(transitivity,[status(thm)],[105,99]) ).
tff(107,plain,
^ [D: $i,E: $i] :
refl(( ( ifeq(q1(d,E,d),true,ifeq(q0(D,E),true,ifeq(s0(d),true,r1(D),true),true),true) = true )
<=> ( ifeq(q1(d,E,d),true,ifeq(q0(D,E),true,ifeq(s0(d),true,r1(D),true),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(108,plain,
( ! [D: $i,E: $i] : ( ifeq(q1(d,E,d),true,ifeq(q0(D,E),true,ifeq(s0(d),true,r1(D),true),true),true) = true )
<=> ! [D: $i,E: $i] : ( ifeq(q1(d,E,d),true,ifeq(q0(D,E),true,ifeq(s0(d),true,r1(D),true),true),true) = true ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,plain,
( ! [D: $i,E: $i] : ( ifeq(q1(d,E,d),true,ifeq(q0(D,E),true,ifeq(s0(d),true,r1(D),true),true),true) = true )
<=> ! [D: $i,E: $i] : ( ifeq(q1(d,E,d),true,ifeq(q0(D,E),true,ifeq(s0(d),true,r1(D),true),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,axiom,
! [D: $i,E: $i] : ( ifeq(q1(d,E,d),true,ifeq(q0(D,E),true,ifeq(s0(d),true,r1(D),true),true),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_124) ).
tff(111,plain,
! [D: $i,E: $i] : ( ifeq(q1(d,E,d),true,ifeq(q0(D,E),true,ifeq(s0(d),true,r1(D),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [D: $i,E: $i] : ( ifeq(q1(d,E,d),true,ifeq(q0(D,E),true,ifeq(s0(d),true,r1(D),true),true),true) = true ),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [D: $i,E: $i] : ( ifeq(q1(d,E,d),true,ifeq(q0(D,E),true,ifeq(s0(d),true,r1(D),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
( ~ ! [D: $i,E: $i] : ( ifeq(q1(d,E,d),true,ifeq(q0(D,E),true,ifeq(s0(d),true,r1(D),true),true),true) = true )
| ( ifeq(q1(d,d,d),true,ifeq(q0(b,d),true,ifeq(s0(d),true,r1(b),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
ifeq(q1(d,d,d),true,ifeq(q0(b,d),true,ifeq(s0(d),true,r1(b),true),true),true) = true,
inference(unit_resolution,[status(thm)],[114,113]) ).
tff(116,plain,
( ( q0(b,b) = true )
<=> ( q0(b,b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,axiom,
q0(b,b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(118,plain,
q0(b,b) = true,
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
true = q0(b,b),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
^ [X: $i] :
refl(( ( q0(X,d) = true )
<=> ( q0(X,d) = true ) )),
inference(bind,[status(th)],[]) ).
tff(121,plain,
( ! [X: $i] : ( q0(X,d) = true )
<=> ! [X: $i] : ( q0(X,d) = true ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
( ! [X: $i] : ( q0(X,d) = true )
<=> ! [X: $i] : ( q0(X,d) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,axiom,
! [X: $i] : ( q0(X,d) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
tff(124,plain,
! [X: $i] : ( q0(X,d) = true ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [X: $i] : ( q0(X,d) = true ),
inference(skolemize,[status(sab)],[124]) ).
tff(126,plain,
! [X: $i] : ( q0(X,d) = true ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
( ~ ! [X: $i] : ( q0(X,d) = true )
| ( q0(b,d) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
q0(b,d) = true,
inference(unit_resolution,[status(thm)],[127,126]) ).
tff(129,plain,
q0(b,d) = q0(b,b),
inference(transitivity,[status(thm)],[128,119]) ).
tff(130,plain,
ifeq(q0(b,d),true,ifeq(s0(d),true,r1(b),true),true) = ifeq(q0(b,b),true,ifeq(s0(d),true,r1(b),true),true),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
ifeq(q0(b,b),true,ifeq(s0(d),true,r1(b),true),true) = ifeq(q0(b,d),true,ifeq(s0(d),true,r1(b),true),true),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
ifeq(true,true,ifeq(s0(d),true,r1(b),true),true) = ifeq(q0(b,b),true,ifeq(s0(d),true,r1(b),true),true),
inference(monotonicity,[status(thm)],[119]) ).
tff(133,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(s0(d),true,r1(b),true),true) = ifeq(s0(d),true,r1(b),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
ifeq(true,true,ifeq(s0(d),true,r1(b),true),true) = ifeq(s0(d),true,r1(b),true),
inference(unit_resolution,[status(thm)],[133,16]) ).
tff(135,plain,
ifeq(s0(d),true,r1(b),true) = ifeq(true,true,ifeq(s0(d),true,r1(b),true),true),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
ifeq(s0(d),true,r1(b),true) = ifeq(q0(b,d),true,ifeq(s0(d),true,r1(b),true),true),
inference(transitivity,[status(thm)],[135,132,131]) ).
tff(137,plain,
q0(b,b) = q1(d,d,d),
inference(transitivity,[status(thm)],[118,48,38,32]) ).
tff(138,plain,
ifeq(q0(b,b),true,ifeq(s0(d),true,r1(b),true),true) = ifeq(q1(d,d,d),true,ifeq(q0(b,d),true,ifeq(s0(d),true,r1(b),true),true),true),
inference(monotonicity,[status(thm)],[137,136]) ).
tff(139,plain,
ifeq(true,true,r1(b),true) = ifeq(s0(d),true,r1(b),true),
inference(monotonicity,[status(thm)],[36]) ).
tff(140,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,r1(b),true) = r1(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
ifeq(true,true,r1(b),true) = r1(b),
inference(unit_resolution,[status(thm)],[140,16]) ).
tff(142,plain,
r1(b) = ifeq(true,true,r1(b),true),
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
r1(b) = k0(b),
inference(transitivity,[status(thm)],[142,139,135,132,138,115,103]) ).
tff(144,plain,
ifeq(r1(b),true,ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true),true) = ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true),
inference(monotonicity,[status(thm)],[143,106]) ).
tff(145,plain,
ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true) = ifeq(r1(b),true,ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true),true),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
ifeq(m0(e,d,a),true,q2(a,b,a),true) = ifeq(true,true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true),
inference(symmetry,[status(thm)],[99]) ).
tff(147,plain,
ifeq(m0(e,d,a),true,q2(a,b,a),true) = ifeq(r1(b),true,ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true),true),
inference(transitivity,[status(thm)],[146,104,145]) ).
tff(148,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,q2(b,b,b),true) = q2(b,b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(149,plain,
ifeq(true,true,q2(b,b,b),true) = q2(b,b,b),
inference(unit_resolution,[status(thm)],[148,16]) ).
tff(150,plain,
ifeq(true,true,q2(b,b,b),true) = ifeq(q0(b,b),true,q2(b,b,b),true),
inference(monotonicity,[status(thm)],[119]) ).
tff(151,plain,
ifeq(q0(b,b),true,q2(b,b,b),true) = ifeq(true,true,q2(b,b,b),true),
inference(symmetry,[status(thm)],[150]) ).
tff(152,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,p1(b,b,b),true) = p1(b,b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
ifeq(true,true,p1(b,b,b),true) = p1(b,b,b),
inference(unit_resolution,[status(thm)],[152,16]) ).
tff(154,plain,
( ( p0(c,b) = true )
<=> ( p0(c,b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,axiom,
p0(c,b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).
tff(156,plain,
p0(c,b) = true,
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
true = p0(c,b),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
ifeq(true,true,p1(b,b,b),true) = ifeq(p0(c,b),true,p1(b,b,b),true),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
ifeq(p0(c,b),true,p1(b,b,b),true) = ifeq(true,true,p1(b,b,b),true),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
^ [B: $i,C: $i] :
refl(( ( ifeq(p0(C,B),true,p1(B,B,B),true) = true )
<=> ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(161,plain,
( ! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true )
<=> ! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ) ),
inference(quant_intro,[status(thm)],[160]) ).
tff(162,plain,
( ! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true )
<=> ! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,axiom,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_085) ).
tff(164,plain,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
inference(skolemize,[status(sab)],[164]) ).
tff(166,plain,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
inference(modus_ponens,[status(thm)],[165,161]) ).
tff(167,plain,
( ~ ! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true )
| ( ifeq(p0(c,b),true,p1(b,b,b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
ifeq(p0(c,b),true,p1(b,b,b),true) = true,
inference(unit_resolution,[status(thm)],[167,166]) ).
tff(169,plain,
true = ifeq(p0(c,b),true,p1(b,b,b),true),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
q0(b,b) = p1(b,b,b),
inference(transitivity,[status(thm)],[118,169,159,153]) ).
tff(171,plain,
ifeq(q0(b,b),true,q2(b,b,b),true) = ifeq(p1(b,b,b),true,q2(b,b,b),true),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
ifeq(p1(b,b,b),true,q2(b,b,b),true) = ifeq(q0(b,b),true,q2(b,b,b),true),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
^ [I: $i] :
refl(( ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true )
<=> ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(174,plain,
( ! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true )
<=> ! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ) ),
inference(quant_intro,[status(thm)],[173]) ).
tff(175,plain,
( ! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true )
<=> ! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,axiom,
! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_181) ).
tff(177,plain,
! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ),
inference(modus_ponens,[status(thm)],[176,175]) ).
tff(178,plain,
! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ),
inference(skolemize,[status(sab)],[177]) ).
tff(179,plain,
! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ),
inference(modus_ponens,[status(thm)],[178,174]) ).
tff(180,plain,
( ~ ! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true )
| ( ifeq(p1(b,b,b),true,q2(b,b,b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
ifeq(p1(b,b,b),true,q2(b,b,b),true) = true,
inference(unit_resolution,[status(thm)],[180,179]) ).
tff(182,plain,
true = ifeq(p1(b,b,b),true,q2(b,b,b),true),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
k0(b) = q2(b,b,b),
inference(transitivity,[status(thm)],[102,182,172,151,149]) ).
tff(184,plain,
ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true) = ifeq(q2(b,b,b),true,ifeq(r1(b),true,ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true),true),true),
inference(monotonicity,[status(thm)],[183,147]) ).
tff(185,plain,
ifeq(q2(b,b,b),true,ifeq(r1(b),true,ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true),true),true) = ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
^ [D: $i,E: $i,F: $i,C: $i] :
refl(( ( ifeq(q2(D,D,D),true,ifeq(r1(D),true,ifeq(k0(D),true,ifeq(m0(E,F,C),true,q2(C,D,C),true),true),true),true) = true )
<=> ( ifeq(q2(D,D,D),true,ifeq(r1(D),true,ifeq(k0(D),true,ifeq(m0(E,F,C),true,q2(C,D,C),true),true),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(187,plain,
( ! [D: $i,E: $i,F: $i,C: $i] : ( ifeq(q2(D,D,D),true,ifeq(r1(D),true,ifeq(k0(D),true,ifeq(m0(E,F,C),true,q2(C,D,C),true),true),true),true) = true )
<=> ! [D: $i,E: $i,F: $i,C: $i] : ( ifeq(q2(D,D,D),true,ifeq(r1(D),true,ifeq(k0(D),true,ifeq(m0(E,F,C),true,q2(C,D,C),true),true),true),true) = true ) ),
inference(quant_intro,[status(thm)],[186]) ).
tff(188,plain,
( ! [D: $i,E: $i,F: $i,C: $i] : ( ifeq(q2(D,D,D),true,ifeq(r1(D),true,ifeq(k0(D),true,ifeq(m0(E,F,C),true,q2(C,D,C),true),true),true),true) = true )
<=> ! [D: $i,E: $i,F: $i,C: $i] : ( ifeq(q2(D,D,D),true,ifeq(r1(D),true,ifeq(k0(D),true,ifeq(m0(E,F,C),true,q2(C,D,C),true),true),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(189,axiom,
! [D: $i,E: $i,F: $i,C: $i] : ( ifeq(q2(D,D,D),true,ifeq(r1(D),true,ifeq(k0(D),true,ifeq(m0(E,F,C),true,q2(C,D,C),true),true),true),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_187) ).
tff(190,plain,
! [D: $i,E: $i,F: $i,C: $i] : ( ifeq(q2(D,D,D),true,ifeq(r1(D),true,ifeq(k0(D),true,ifeq(m0(E,F,C),true,q2(C,D,C),true),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,plain,
! [D: $i,E: $i,F: $i,C: $i] : ( ifeq(q2(D,D,D),true,ifeq(r1(D),true,ifeq(k0(D),true,ifeq(m0(E,F,C),true,q2(C,D,C),true),true),true),true) = true ),
inference(skolemize,[status(sab)],[190]) ).
tff(192,plain,
! [D: $i,E: $i,F: $i,C: $i] : ( ifeq(q2(D,D,D),true,ifeq(r1(D),true,ifeq(k0(D),true,ifeq(m0(E,F,C),true,q2(C,D,C),true),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[191,187]) ).
tff(193,plain,
( ~ ! [D: $i,E: $i,F: $i,C: $i] : ( ifeq(q2(D,D,D),true,ifeq(r1(D),true,ifeq(k0(D),true,ifeq(m0(E,F,C),true,q2(C,D,C),true),true),true),true) = true )
| ( ifeq(q2(b,b,b),true,ifeq(r1(b),true,ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(194,plain,
ifeq(q2(b,b,b),true,ifeq(r1(b),true,ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true),true),true) = true,
inference(unit_resolution,[status(thm)],[193,192]) ).
tff(195,plain,
true = ifeq(q2(b,b,b),true,ifeq(r1(b),true,ifeq(k0(b),true,ifeq(m0(e,d,a),true,q2(a,b,a),true),true),true),true),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
n0(a,b) = q2(a,b,a),
inference(transitivity,[status(thm)],[84,195,185,105,99,97,91]) ).
tff(197,plain,
ifeq(n0(a,b),true,q3(b,a),true) = ifeq(q2(a,b,a),true,ifeq(n0(a,b),true,q3(b,a),true),true),
inference(monotonicity,[status(thm)],[196,89]) ).
tff(198,plain,
ifeq(q2(a,b,a),true,ifeq(n0(a,b),true,q3(b,a),true),true) = ifeq(n0(a,b),true,q3(b,a),true),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
^ [I: $i,H: $i,G: $i] :
refl(( ( ifeq(q2(I,G,H),true,ifeq(n0(I,G),true,q3(G,H),true),true) = true )
<=> ( ifeq(q2(I,G,H),true,ifeq(n0(I,G),true,q3(G,H),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(200,plain,
( ! [I: $i,H: $i,G: $i] : ( ifeq(q2(I,G,H),true,ifeq(n0(I,G),true,q3(G,H),true),true) = true )
<=> ! [I: $i,H: $i,G: $i] : ( ifeq(q2(I,G,H),true,ifeq(n0(I,G),true,q3(G,H),true),true) = true ) ),
inference(quant_intro,[status(thm)],[199]) ).
tff(201,plain,
( ! [I: $i,H: $i,G: $i] : ( ifeq(q2(I,G,H),true,ifeq(n0(I,G),true,q3(G,H),true),true) = true )
<=> ! [I: $i,H: $i,G: $i] : ( ifeq(q2(I,G,H),true,ifeq(n0(I,G),true,q3(G,H),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(202,axiom,
! [I: $i,H: $i,G: $i] : ( ifeq(q2(I,G,H),true,ifeq(n0(I,G),true,q3(G,H),true),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_255) ).
tff(203,plain,
! [I: $i,H: $i,G: $i] : ( ifeq(q2(I,G,H),true,ifeq(n0(I,G),true,q3(G,H),true),true) = true ),
inference(modus_ponens,[status(thm)],[202,201]) ).
tff(204,plain,
! [I: $i,H: $i,G: $i] : ( ifeq(q2(I,G,H),true,ifeq(n0(I,G),true,q3(G,H),true),true) = true ),
inference(skolemize,[status(sab)],[203]) ).
tff(205,plain,
! [I: $i,H: $i,G: $i] : ( ifeq(q2(I,G,H),true,ifeq(n0(I,G),true,q3(G,H),true),true) = true ),
inference(modus_ponens,[status(thm)],[204,200]) ).
tff(206,plain,
( ~ ! [I: $i,H: $i,G: $i] : ( ifeq(q2(I,G,H),true,ifeq(n0(I,G),true,q3(G,H),true),true) = true )
| ( ifeq(q2(a,b,a),true,ifeq(n0(a,b),true,q3(b,a),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(207,plain,
ifeq(q2(a,b,a),true,ifeq(n0(a,b),true,q3(b,a),true),true) = true,
inference(unit_resolution,[status(thm)],[206,205]) ).
tff(208,plain,
true = ifeq(q2(a,b,a),true,ifeq(n0(a,b),true,q3(b,a),true),true),
inference(symmetry,[status(thm)],[207]) ).
tff(209,plain,
true = q3(b,a),
inference(transitivity,[status(thm)],[208,198,87,81]) ).
tff(210,plain,
ifeq(true,true,ifeq(n3(d),true,ifeq(p0(b,d),true,r4(d),true),true),true) = ifeq(q3(b,a),true,ifeq(n3(d),true,ifeq(p0(b,d),true,r4(d),true),true),true),
inference(monotonicity,[status(thm)],[209]) ).
tff(211,plain,
ifeq(q3(b,a),true,ifeq(n3(d),true,ifeq(p0(b,d),true,r4(d),true),true),true) = ifeq(true,true,ifeq(n3(d),true,ifeq(p0(b,d),true,r4(d),true),true),true),
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
^ [I: $i,J: $i,H: $i,G: $i] :
refl(( ( ifeq(q3(H,I),true,ifeq(n3(G),true,ifeq(p0(J,G),true,r4(G),true),true),true) = true )
<=> ( ifeq(q3(H,I),true,ifeq(n3(G),true,ifeq(p0(J,G),true,r4(G),true),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(213,plain,
( ! [I: $i,J: $i,H: $i,G: $i] : ( ifeq(q3(H,I),true,ifeq(n3(G),true,ifeq(p0(J,G),true,r4(G),true),true),true) = true )
<=> ! [I: $i,J: $i,H: $i,G: $i] : ( ifeq(q3(H,I),true,ifeq(n3(G),true,ifeq(p0(J,G),true,r4(G),true),true),true) = true ) ),
inference(quant_intro,[status(thm)],[212]) ).
tff(214,plain,
( ! [I: $i,J: $i,H: $i,G: $i] : ( ifeq(q3(H,I),true,ifeq(n3(G),true,ifeq(p0(J,G),true,r4(G),true),true),true) = true )
<=> ! [I: $i,J: $i,H: $i,G: $i] : ( ifeq(q3(H,I),true,ifeq(n3(G),true,ifeq(p0(J,G),true,r4(G),true),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(215,axiom,
! [I: $i,J: $i,H: $i,G: $i] : ( ifeq(q3(H,I),true,ifeq(n3(G),true,ifeq(p0(J,G),true,r4(G),true),true),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_298) ).
tff(216,plain,
! [I: $i,J: $i,H: $i,G: $i] : ( ifeq(q3(H,I),true,ifeq(n3(G),true,ifeq(p0(J,G),true,r4(G),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[215,214]) ).
tff(217,plain,
! [I: $i,J: $i,H: $i,G: $i] : ( ifeq(q3(H,I),true,ifeq(n3(G),true,ifeq(p0(J,G),true,r4(G),true),true),true) = true ),
inference(skolemize,[status(sab)],[216]) ).
tff(218,plain,
! [I: $i,J: $i,H: $i,G: $i] : ( ifeq(q3(H,I),true,ifeq(n3(G),true,ifeq(p0(J,G),true,r4(G),true),true),true) = true ),
inference(modus_ponens,[status(thm)],[217,213]) ).
tff(219,plain,
( ~ ! [I: $i,J: $i,H: $i,G: $i] : ( ifeq(q3(H,I),true,ifeq(n3(G),true,ifeq(p0(J,G),true,r4(G),true),true),true) = true )
| ( ifeq(q3(b,a),true,ifeq(n3(d),true,ifeq(p0(b,d),true,r4(d),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(220,plain,
ifeq(q3(b,a),true,ifeq(n3(d),true,ifeq(p0(b,d),true,r4(d),true),true),true) = true,
inference(unit_resolution,[status(thm)],[219,218]) ).
tff(221,plain,
true = ifeq(q3(b,a),true,ifeq(n3(d),true,ifeq(p0(b,d),true,r4(d),true),true),true),
inference(symmetry,[status(thm)],[220]) ).
tff(222,plain,
true = r4(d),
inference(transitivity,[status(thm)],[221,211,79,77,24,18]) ).
tff(223,plain,
ifeq(true,true,ifeq(l4(c),true,s5(c),true),true) = ifeq(r4(d),true,ifeq(l4(c),true,s5(c),true),true),
inference(monotonicity,[status(thm)],[222]) ).
tff(224,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(l4(c),true,s5(c),true),true) = ifeq(l4(c),true,s5(c),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(225,plain,
ifeq(true,true,ifeq(l4(c),true,s5(c),true),true) = ifeq(l4(c),true,s5(c),true),
inference(unit_resolution,[status(thm)],[224,16]) ).
tff(226,plain,
ifeq(l4(c),true,s5(c),true) = ifeq(true,true,ifeq(l4(c),true,s5(c),true),true),
inference(symmetry,[status(thm)],[225]) ).
tff(227,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,l4(c),true) = l4(c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(228,plain,
ifeq(true,true,l4(c),true) = l4(c),
inference(unit_resolution,[status(thm)],[227,16]) ).
tff(229,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,p3(c,c,c),true) = p3(c,c,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(230,plain,
ifeq(true,true,p3(c,c,c),true) = p3(c,c,c),
inference(unit_resolution,[status(thm)],[229,16]) ).
tff(231,plain,
( ( q0(d,c) = true )
<=> ( q0(d,c) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(232,axiom,
q0(d,c) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
tff(233,plain,
q0(d,c) = true,
inference(modus_ponens,[status(thm)],[232,231]) ).
tff(234,plain,
true = q0(d,c),
inference(symmetry,[status(thm)],[233]) ).
tff(235,plain,
ifeq(true,true,p3(c,c,c),true) = ifeq(q0(d,c),true,p3(c,c,c),true),
inference(monotonicity,[status(thm)],[234]) ).
tff(236,plain,
ifeq(q0(d,c),true,p3(c,c,c),true) = ifeq(true,true,p3(c,c,c),true),
inference(symmetry,[status(thm)],[235]) ).
tff(237,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(q0(d,c),true,p3(c,c,c),true),true) = ifeq(q0(d,c),true,p3(c,c,c),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(238,plain,
ifeq(true,true,ifeq(q0(d,c),true,p3(c,c,c),true),true) = ifeq(q0(d,c),true,p3(c,c,c),true),
inference(unit_resolution,[status(thm)],[237,16]) ).
tff(239,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,k2(b,b),true) = k2(b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(240,plain,
ifeq(true,true,k2(b,b),true) = k2(b,b),
inference(unit_resolution,[status(thm)],[239,16]) ).
tff(241,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,q1(b,b,b),true) = q1(b,b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(242,plain,
ifeq(true,true,q1(b,b,b),true) = q1(b,b,b),
inference(unit_resolution,[status(thm)],[241,16]) ).
tff(243,plain,
( ( r0(b) = true )
<=> ( r0(b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(244,axiom,
r0(b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
tff(245,plain,
r0(b) = true,
inference(modus_ponens,[status(thm)],[244,243]) ).
tff(246,plain,
true = r0(b),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
ifeq(true,true,q1(b,b,b),true) = ifeq(r0(b),true,q1(b,b,b),true),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
ifeq(r0(b),true,q1(b,b,b),true) = ifeq(true,true,q1(b,b,b),true),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
( ( ifeq(r0(b),true,q1(b,b,b),true) = true )
<=> ( ifeq(r0(b),true,q1(b,b,b),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(250,axiom,
ifeq(r0(b),true,q1(b,b,b),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_120) ).
tff(251,plain,
ifeq(r0(b),true,q1(b,b,b),true) = true,
inference(modus_ponens,[status(thm)],[250,249]) ).
tff(252,plain,
true = ifeq(r0(b),true,q1(b,b,b),true),
inference(symmetry,[status(thm)],[251]) ).
tff(253,plain,
true = q1(b,b,b),
inference(transitivity,[status(thm)],[252,248,242]) ).
tff(254,plain,
ifeq(true,true,k2(b,b),true) = ifeq(q1(b,b,b),true,k2(b,b),true),
inference(monotonicity,[status(thm)],[253]) ).
tff(255,plain,
ifeq(q1(b,b,b),true,k2(b,b),true) = ifeq(true,true,k2(b,b),true),
inference(symmetry,[status(thm)],[254]) ).
tff(256,plain,
^ [A: $i,J: $i] :
refl(( ( ifeq(q1(A,J,J),true,k2(J,J),true) = true )
<=> ( ifeq(q1(A,J,J),true,k2(J,J),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(257,plain,
( ! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true )
<=> ! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true ) ),
inference(quant_intro,[status(thm)],[256]) ).
tff(258,plain,
( ! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true )
<=> ! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(259,axiom,
! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_129) ).
tff(260,plain,
! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true ),
inference(modus_ponens,[status(thm)],[259,258]) ).
tff(261,plain,
! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true ),
inference(skolemize,[status(sab)],[260]) ).
tff(262,plain,
! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true ),
inference(modus_ponens,[status(thm)],[261,257]) ).
tff(263,plain,
( ~ ! [A: $i,J: $i] : ( ifeq(q1(A,J,J),true,k2(J,J),true) = true )
| ( ifeq(q1(b,b,b),true,k2(b,b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(264,plain,
ifeq(q1(b,b,b),true,k2(b,b),true) = true,
inference(unit_resolution,[status(thm)],[263,262]) ).
tff(265,plain,
true = ifeq(q1(b,b,b),true,k2(b,b),true),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
true = k2(b,b),
inference(transitivity,[status(thm)],[265,255,240]) ).
tff(267,plain,
ifeq(true,true,ifeq(q0(d,c),true,p3(c,c,c),true),true) = ifeq(k2(b,b),true,ifeq(q0(d,c),true,p3(c,c,c),true),true),
inference(monotonicity,[status(thm)],[266]) ).
tff(268,plain,
ifeq(k2(b,b),true,ifeq(q0(d,c),true,p3(c,c,c),true),true) = ifeq(true,true,ifeq(q0(d,c),true,p3(c,c,c),true),true),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
^ [I: $i,J: $i,H: $i] :
refl(( ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true )
<=> ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(270,plain,
( ! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true )
<=> ! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true ) ),
inference(quant_intro,[status(thm)],[269]) ).
tff(271,plain,
( ! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true )
<=> ! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(272,axiom,
! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_252) ).
tff(273,plain,
! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true ),
inference(modus_ponens,[status(thm)],[272,271]) ).
tff(274,plain,
! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true ),
inference(skolemize,[status(sab)],[273]) ).
tff(275,plain,
! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true ),
inference(modus_ponens,[status(thm)],[274,270]) ).
tff(276,plain,
( ~ ! [I: $i,J: $i,H: $i] : ( ifeq(k2(J,J),true,ifeq(q0(I,H),true,p3(H,H,H),true),true) = true )
| ( ifeq(k2(b,b),true,ifeq(q0(d,c),true,p3(c,c,c),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(277,plain,
ifeq(k2(b,b),true,ifeq(q0(d,c),true,p3(c,c,c),true),true) = true,
inference(unit_resolution,[status(thm)],[276,275]) ).
tff(278,plain,
true = ifeq(k2(b,b),true,ifeq(q0(d,c),true,p3(c,c,c),true),true),
inference(symmetry,[status(thm)],[277]) ).
tff(279,plain,
true = p3(c,c,c),
inference(transitivity,[status(thm)],[278,268,238,236,230]) ).
tff(280,plain,
ifeq(true,true,l4(c),true) = ifeq(p3(c,c,c),true,l4(c),true),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
ifeq(p3(c,c,c),true,l4(c),true) = ifeq(true,true,l4(c),true),
inference(symmetry,[status(thm)],[280]) ).
tff(282,plain,
^ [B: $i,A: $i,J: $i] :
refl(( ( ifeq(p3(A,B,J),true,l4(J),true) = true )
<=> ( ifeq(p3(A,B,J),true,l4(J),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(283,plain,
( ! [B: $i,A: $i,J: $i] : ( ifeq(p3(A,B,J),true,l4(J),true) = true )
<=> ! [B: $i,A: $i,J: $i] : ( ifeq(p3(A,B,J),true,l4(J),true) = true ) ),
inference(quant_intro,[status(thm)],[282]) ).
tff(284,plain,
( ! [B: $i,A: $i,J: $i] : ( ifeq(p3(A,B,J),true,l4(J),true) = true )
<=> ! [B: $i,A: $i,J: $i] : ( ifeq(p3(A,B,J),true,l4(J),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(285,axiom,
! [B: $i,A: $i,J: $i] : ( ifeq(p3(A,B,J),true,l4(J),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_277) ).
tff(286,plain,
! [B: $i,A: $i,J: $i] : ( ifeq(p3(A,B,J),true,l4(J),true) = true ),
inference(modus_ponens,[status(thm)],[285,284]) ).
tff(287,plain,
! [B: $i,A: $i,J: $i] : ( ifeq(p3(A,B,J),true,l4(J),true) = true ),
inference(skolemize,[status(sab)],[286]) ).
tff(288,plain,
! [B: $i,A: $i,J: $i] : ( ifeq(p3(A,B,J),true,l4(J),true) = true ),
inference(modus_ponens,[status(thm)],[287,283]) ).
tff(289,plain,
( ~ ! [B: $i,A: $i,J: $i] : ( ifeq(p3(A,B,J),true,l4(J),true) = true )
| ( ifeq(p3(c,c,c),true,l4(c),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(290,plain,
ifeq(p3(c,c,c),true,l4(c),true) = true,
inference(unit_resolution,[status(thm)],[289,288]) ).
tff(291,plain,
true = ifeq(p3(c,c,c),true,l4(c),true),
inference(symmetry,[status(thm)],[290]) ).
tff(292,plain,
true = l4(c),
inference(transitivity,[status(thm)],[291,281,228]) ).
tff(293,plain,
ifeq(true,true,s5(c),true) = ifeq(l4(c),true,s5(c),true),
inference(monotonicity,[status(thm)],[292]) ).
tff(294,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,s5(c),true) = s5(c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(295,plain,
ifeq(true,true,s5(c),true) = s5(c),
inference(unit_resolution,[status(thm)],[294,16]) ).
tff(296,plain,
s5(c) = ifeq(true,true,s5(c),true),
inference(symmetry,[status(thm)],[295]) ).
tff(297,plain,
s5(c) = true,
inference(transitivity,[status(thm)],[296,293,226,223,9]) ).
tff(298,plain,
( ( s5(c) != true )
<=> ( s5(c) != true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(299,axiom,
s5(c) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(300,plain,
s5(c) != true,
inference(modus_ponens,[status(thm)],[299,298]) ).
tff(301,plain,
$false,
inference(unit_resolution,[status(thm)],[300,297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN214-10 : TPTP v9.0.0. Released v7.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 12:30:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.64/0.82 % SZS status Unsatisfiable
% 0.64/0.82 % SZS output start Proof
% See solution above
% 0.67/0.85 % E exiting
%------------------------------------------------------------------------------