%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN193-10 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:27 AM UTC 2025
% Result : Unsatisfiable 0.58s 0.75s
% Output : Proof 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 74
% Syntax : Number of formulae : 222 ( 168 unt; 0 typ; 0 def)
% Number of atoms : 298 ( 286 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 92 ( 27 ~; 23 |; 0 &)
% ( 42 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of FOOLs : 11 ( 11 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 : 22 ( 22 usr; 6 con; 0-4 aty)
% Number of variables : 286 ( 261 !; 0 ?; 286 :)
% Comments :
%------------------------------------------------------------------------------
tff(true_type,type,
true: $i ).
tff(r4_type,type,
r4: $i > $i ).
tff(b_type,type,
b: $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(p0_type,type,
p0: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(n3_type,type,
n3: $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(d_type,type,
d: $i ).
tff(e_type,type,
e: $i ).
tff(k0_type,type,
k0: $i > $i ).
tff(r1_type,type,
r1: $i > $i ).
tff(s0_type,type,
s0: $i > $i ).
tff(q0_type,type,
q0: ( $i * $i ) > $i ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $i ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $i ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $i ).
tff(r0_type,type,
r0: $i > $i ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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/sandbox2/benchmark/theBenchmark.p',rule_298) ).
tff(5,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)],[4,3]) ).
tff(6,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)],[5]) ).
tff(7,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)],[6,2]) ).
tff(8,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(b),true,ifeq(p0(c,b),true,r4(b),true),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq(q3(b,a),true,ifeq(n3(b),true,ifeq(p0(c,b),true,r4(b),true),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/sandbox2/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,q3(b,a),true) = q3(b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ifeq(true,true,q3(b,a),true) = q3(b,a),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ( n0(a,b) = true )
<=> ( n0(a,b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
n0(a,b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).
tff(21,plain,
n0(a,b) = true,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
true = n0(a,b),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
ifeq(true,true,q3(b,a),true) = ifeq(n0(a,b),true,q3(b,a),true),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
ifeq(n0(a,b),true,q3(b,a),true) = ifeq(true,true,q3(b,a),true),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
q3(b,a) = ifeq(true,true,q3(b,a),true),
inference(symmetry,[status(thm)],[18]) ).
tff(26,plain,
q3(b,a) = ifeq(n0(a,b),true,q3(b,a),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,q2(a,b,a),true) = q2(a,b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
ifeq(true,true,q2(a,b,a),true) = q2(a,b,a),
inference(unit_resolution,[status(thm)],[27,16]) ).
tff(29,plain,
( ( m0(e,d,a) = true )
<=> ( m0(e,d,a) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
m0(e,d,a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
tff(31,plain,
m0(e,d,a) = true,
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
true = m0(e,d,a),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
ifeq(true,true,q2(a,b,a),true) = ifeq(m0(e,d,a),true,q2(a,b,a),true),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
ifeq(m0(e,d,a),true,q2(a,b,a),true) = ifeq(true,true,q2(a,b,a),true),
inference(symmetry,[status(thm)],[33]) ).
tff(35,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(36,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)],[35,16]) ).
tff(37,plain,
( ( k0(b) = true )
<=> ( k0(b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
k0(b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).
tff(39,plain,
k0(b) = true,
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
true = k0(b),
inference(symmetry,[status(thm)],[39]) ).
tff(41,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)],[40]) ).
tff(42,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)],[41]) ).
tff(43,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)],[42,36]) ).
tff(44,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(45,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)],[44]) ).
tff(46,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(47,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/sandbox2/benchmark/theBenchmark.p',rule_124) ).
tff(48,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)],[47,46]) ).
tff(49,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)],[48]) ).
tff(50,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)],[49,45]) ).
tff(51,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(52,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)],[51,50]) ).
tff(53,plain,
( ( q0(b,b) = true )
<=> ( q0(b,b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,axiom,
q0(b,b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
tff(55,plain,
q0(b,b) = true,
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
true = q0(b,b),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
^ [X: $i] :
refl(( ( q0(X,d) = true )
<=> ( q0(X,d) = true ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [X: $i] : ( q0(X,d) = true )
<=> ! [X: $i] : ( q0(X,d) = true ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [X: $i] : ( q0(X,d) = true )
<=> ! [X: $i] : ( q0(X,d) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
! [X: $i] : ( q0(X,d) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
tff(61,plain,
! [X: $i] : ( q0(X,d) = true ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [X: $i] : ( q0(X,d) = true ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [X: $i] : ( q0(X,d) = true ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [X: $i] : ( q0(X,d) = true )
| ( q0(b,d) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
q0(b,d) = true,
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
q0(b,d) = q0(b,b),
inference(transitivity,[status(thm)],[65,56]) ).
tff(67,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)],[66]) ).
tff(68,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)],[67]) ).
tff(69,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)],[56]) ).
tff(70,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(71,plain,
ifeq(true,true,ifeq(s0(d),true,r1(b),true),true) = ifeq(s0(d),true,r1(b),true),
inference(unit_resolution,[status(thm)],[70,16]) ).
tff(72,plain,
ifeq(s0(d),true,r1(b),true) = ifeq(true,true,ifeq(s0(d),true,r1(b),true),true),
inference(symmetry,[status(thm)],[71]) ).
tff(73,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)],[72,69,68]) ).
tff(74,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(75,plain,
ifeq(true,true,q1(d,d,d),true) = q1(d,d,d),
inference(unit_resolution,[status(thm)],[74,16]) ).
tff(76,plain,
( ( s0(d) = true )
<=> ( s0(d) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,axiom,
s0(d) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
tff(78,plain,
s0(d) = true,
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
true = s0(d),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
ifeq(true,true,q1(d,d,d),true) = ifeq(s0(d),true,q1(d,d,d),true),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
ifeq(s0(d),true,q1(d,d,d),true) = ifeq(true,true,q1(d,d,d),true),
inference(symmetry,[status(thm)],[80]) ).
tff(82,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(83,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)],[82]) ).
tff(84,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(85,axiom,
! [B: $i] : ( ifeq(s0(B),true,q1(B,B,B),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_106) ).
tff(86,plain,
! [B: $i] : ( ifeq(s0(B),true,q1(B,B,B),true) = true ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [B: $i] : ( ifeq(s0(B),true,q1(B,B,B),true) = true ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [B: $i] : ( ifeq(s0(B),true,q1(B,B,B),true) = true ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,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(90,plain,
ifeq(s0(d),true,q1(d,d,d),true) = true,
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
true = ifeq(s0(d),true,q1(d,d,d),true),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
q0(b,b) = q1(d,d,d),
inference(transitivity,[status(thm)],[55,91,81,75]) ).
tff(93,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)],[92,73]) ).
tff(94,plain,
ifeq(true,true,r1(b),true) = ifeq(s0(d),true,r1(b),true),
inference(monotonicity,[status(thm)],[79]) ).
tff(95,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(96,plain,
ifeq(true,true,r1(b),true) = r1(b),
inference(unit_resolution,[status(thm)],[95,16]) ).
tff(97,plain,
r1(b) = ifeq(true,true,r1(b),true),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
r1(b) = k0(b),
inference(transitivity,[status(thm)],[97,94,72,69,93,52,40]) ).
tff(99,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)],[98,43]) ).
tff(100,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)],[99]) ).
tff(101,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)],[36]) ).
tff(102,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)],[101,41,100]) ).
tff(103,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(104,plain,
ifeq(true,true,q2(b,b,b),true) = q2(b,b,b),
inference(unit_resolution,[status(thm)],[103,16]) ).
tff(105,plain,
ifeq(true,true,q2(b,b,b),true) = ifeq(q0(b,b),true,q2(b,b,b),true),
inference(monotonicity,[status(thm)],[56]) ).
tff(106,plain,
ifeq(q0(b,b),true,q2(b,b,b),true) = ifeq(true,true,q2(b,b,b),true),
inference(symmetry,[status(thm)],[105]) ).
tff(107,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(108,plain,
ifeq(true,true,p1(b,b,b),true) = p1(b,b,b),
inference(unit_resolution,[status(thm)],[107,16]) ).
tff(109,plain,
( ( p0(c,b) = true )
<=> ( p0(c,b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,axiom,
p0(c,b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_18) ).
tff(111,plain,
p0(c,b) = true,
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
true = p0(c,b),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
ifeq(true,true,p1(b,b,b),true) = ifeq(p0(c,b),true,p1(b,b,b),true),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
ifeq(p0(c,b),true,p1(b,b,b),true) = ifeq(true,true,p1(b,b,b),true),
inference(symmetry,[status(thm)],[113]) ).
tff(115,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(116,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)],[115]) ).
tff(117,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(118,axiom,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_085) ).
tff(119,plain,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
inference(skolemize,[status(sab)],[119]) ).
tff(121,plain,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,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(123,plain,
ifeq(p0(c,b),true,p1(b,b,b),true) = true,
inference(unit_resolution,[status(thm)],[122,121]) ).
tff(124,plain,
true = ifeq(p0(c,b),true,p1(b,b,b),true),
inference(symmetry,[status(thm)],[123]) ).
tff(125,plain,
q0(b,b) = p1(b,b,b),
inference(transitivity,[status(thm)],[55,124,114,108]) ).
tff(126,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)],[125]) ).
tff(127,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)],[126]) ).
tff(128,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(129,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)],[128]) ).
tff(130,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(131,axiom,
! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_181) ).
tff(132,plain,
! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [I: $i] : ( ifeq(p1(I,I,I),true,q2(I,I,I),true) = true ),
inference(modus_ponens,[status(thm)],[133,129]) ).
tff(135,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(136,plain,
ifeq(p1(b,b,b),true,q2(b,b,b),true) = true,
inference(unit_resolution,[status(thm)],[135,134]) ).
tff(137,plain,
true = ifeq(p1(b,b,b),true,q2(b,b,b),true),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
k0(b) = q2(b,b,b),
inference(transitivity,[status(thm)],[39,137,127,106,104]) ).
tff(139,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)],[138,102]) ).
tff(140,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)],[139]) ).
tff(141,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(142,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)],[141]) ).
tff(143,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(144,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/sandbox2/benchmark/theBenchmark.p',rule_187) ).
tff(145,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)],[144,143]) ).
tff(146,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)],[145]) ).
tff(147,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)],[146,142]) ).
tff(148,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(149,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)],[148,147]) ).
tff(150,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)],[149]) ).
tff(151,plain,
n0(a,b) = q2(a,b,a),
inference(transitivity,[status(thm)],[21,150,140,42,36,34,28]) ).
tff(152,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)],[151,26]) ).
tff(153,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)],[152]) ).
tff(154,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(155,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)],[154]) ).
tff(156,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(157,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/sandbox2/benchmark/theBenchmark.p',rule_255) ).
tff(158,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)],[157,156]) ).
tff(159,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)],[158]) ).
tff(160,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)],[159,155]) ).
tff(161,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(162,plain,
ifeq(q2(a,b,a),true,ifeq(n0(a,b),true,q3(b,a),true),true) = true,
inference(unit_resolution,[status(thm)],[161,160]) ).
tff(163,plain,
true = ifeq(q2(a,b,a),true,ifeq(n0(a,b),true,q3(b,a),true),true),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
true = q3(b,a),
inference(transitivity,[status(thm)],[163,153,24,18]) ).
tff(165,plain,
ifeq(true,true,ifeq(n3(b),true,ifeq(p0(c,b),true,r4(b),true),true),true) = ifeq(q3(b,a),true,ifeq(n3(b),true,ifeq(p0(c,b),true,r4(b),true),true),true),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,ifeq(n3(b),true,ifeq(p0(c,b),true,r4(b),true),true),true) = ifeq(n3(b),true,ifeq(p0(c,b),true,r4(b),true),true) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(167,plain,
ifeq(true,true,ifeq(n3(b),true,ifeq(p0(c,b),true,r4(b),true),true),true) = ifeq(n3(b),true,ifeq(p0(c,b),true,r4(b),true),true),
inference(unit_resolution,[status(thm)],[166,16]) ).
tff(168,plain,
ifeq(n3(b),true,ifeq(p0(c,b),true,r4(b),true),true) = ifeq(true,true,ifeq(n3(b),true,ifeq(p0(c,b),true,r4(b),true),true),true),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
ifeq(true,true,r4(b),true) = ifeq(p0(c,b),true,r4(b),true),
inference(monotonicity,[status(thm)],[112]) ).
tff(170,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,r4(b),true) = r4(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(171,plain,
ifeq(true,true,r4(b),true) = r4(b),
inference(unit_resolution,[status(thm)],[170,16]) ).
tff(172,plain,
r4(b) = ifeq(true,true,r4(b),true),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
r4(b) = ifeq(p0(c,b),true,r4(b),true),
inference(transitivity,[status(thm)],[172,169]) ).
tff(174,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,n3(b),true) = n3(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
ifeq(true,true,n3(b),true) = n3(b),
inference(unit_resolution,[status(thm)],[174,16]) ).
tff(176,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,p2(b,b,b),true) = p2(b,b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
ifeq(true,true,p2(b,b,b),true) = p2(b,b,b),
inference(unit_resolution,[status(thm)],[176,16]) ).
tff(178,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(179,plain,
ifeq(true,true,q1(b,b,b),true) = q1(b,b,b),
inference(unit_resolution,[status(thm)],[178,16]) ).
tff(180,plain,
( ( r0(b) = true )
<=> ( r0(b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(181,axiom,
r0(b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
tff(182,plain,
r0(b) = true,
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
true = r0(b),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
ifeq(true,true,q1(b,b,b),true) = ifeq(r0(b),true,q1(b,b,b),true),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
ifeq(r0(b),true,q1(b,b,b),true) = ifeq(true,true,q1(b,b,b),true),
inference(symmetry,[status(thm)],[184]) ).
tff(186,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(187,axiom,
ifeq(r0(b),true,q1(b,b,b),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_120) ).
tff(188,plain,
ifeq(r0(b),true,q1(b,b,b),true) = true,
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
true = ifeq(r0(b),true,q1(b,b,b),true),
inference(symmetry,[status(thm)],[188]) ).
tff(190,plain,
true = q1(b,b,b),
inference(transitivity,[status(thm)],[189,185,179]) ).
tff(191,plain,
ifeq(true,true,p2(b,b,b),true) = ifeq(q1(b,b,b),true,p2(b,b,b),true),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
ifeq(q1(b,b,b),true,p2(b,b,b),true) = ifeq(true,true,p2(b,b,b),true),
inference(symmetry,[status(thm)],[191]) ).
tff(193,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(194,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)],[193]) ).
tff(195,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(196,axiom,
! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_154) ).
tff(197,plain,
! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true ),
inference(modus_ponens,[status(thm)],[196,195]) ).
tff(198,plain,
! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true ),
inference(skolemize,[status(sab)],[197]) ).
tff(199,plain,
! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true ),
inference(modus_ponens,[status(thm)],[198,194]) ).
tff(200,plain,
( ~ ! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true )
| ( ifeq(q1(b,b,b),true,p2(b,b,b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(201,plain,
ifeq(q1(b,b,b),true,p2(b,b,b),true) = true,
inference(unit_resolution,[status(thm)],[200,199]) ).
tff(202,plain,
true = ifeq(q1(b,b,b),true,p2(b,b,b),true),
inference(symmetry,[status(thm)],[201]) ).
tff(203,plain,
true = p2(b,b,b),
inference(transitivity,[status(thm)],[202,192,177]) ).
tff(204,plain,
ifeq(true,true,n3(b),true) = ifeq(p2(b,b,b),true,n3(b),true),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
ifeq(p2(b,b,b),true,n3(b),true) = ifeq(true,true,n3(b),true),
inference(symmetry,[status(thm)],[204]) ).
tff(206,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(207,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)],[206]) ).
tff(208,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(209,axiom,
! [D: $i,E: $i,F: $i] : ( ifeq(p2(E,F,D),true,n3(D),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_240) ).
tff(210,plain,
! [D: $i,E: $i,F: $i] : ( ifeq(p2(E,F,D),true,n3(D),true) = true ),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
! [D: $i,E: $i,F: $i] : ( ifeq(p2(E,F,D),true,n3(D),true) = true ),
inference(skolemize,[status(sab)],[210]) ).
tff(212,plain,
! [D: $i,E: $i,F: $i] : ( ifeq(p2(E,F,D),true,n3(D),true) = true ),
inference(modus_ponens,[status(thm)],[211,207]) ).
tff(213,plain,
( ~ ! [D: $i,E: $i,F: $i] : ( ifeq(p2(E,F,D),true,n3(D),true) = true )
| ( ifeq(p2(b,b,b),true,n3(b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(214,plain,
ifeq(p2(b,b,b),true,n3(b),true) = true,
inference(unit_resolution,[status(thm)],[213,212]) ).
tff(215,plain,
true = ifeq(p2(b,b,b),true,n3(b),true),
inference(symmetry,[status(thm)],[214]) ).
tff(216,plain,
p0(c,b) = n3(b),
inference(transitivity,[status(thm)],[111,215,205,175]) ).
tff(217,plain,
ifeq(p0(c,b),true,r4(b),true) = ifeq(n3(b),true,ifeq(p0(c,b),true,r4(b),true),true),
inference(monotonicity,[status(thm)],[216,173]) ).
tff(218,plain,
r4(b) = true,
inference(transitivity,[status(thm)],[172,169,217,168,165,9]) ).
tff(219,plain,
( ( r4(b) != true )
<=> ( r4(b) != true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(220,axiom,
r4(b) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(221,plain,
r4(b) != true,
inference(modus_ponens,[status(thm)],[220,219]) ).
tff(222,plain,
$false,
inference(unit_resolution,[status(thm)],[221,218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN193-10 : TPTP v9.0.0. Released v7.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 12:29:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.58/0.75 % SZS status Unsatisfiable
% 0.58/0.75 % SZS output start Proof
% See solution above
% 0.61/0.79 % E exiting
%------------------------------------------------------------------------------