%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN116-10 : TPTP v9.0.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:38:16 AM UTC 2025
% Result : Unsatisfiable 0.61s 0.79s
% Output : Proof 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 63
% Syntax : Number of formulae : 192 ( 146 unt; 0 typ; 0 def)
% Number of atoms : 256 ( 246 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 79 ( 24 ~; 20 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 9 ( 9 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 : 20 ( 20 usr; 5 con; 0-4 aty)
% Number of variables : 242 ( 221 !; 0 ?; 242 :)
% Comments :
%------------------------------------------------------------------------------
tff(true_type,type,
true: $i ).
tff(k5_type,type,
k5: $i > $i ).
tff(b_type,type,
b: $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(r3_type,type,
r3: ( $i * $i * $i ) > $i ).
tff(s4_type,type,
s4: $i > $i ).
tff(a_type,type,
a: $i ).
tff(n1_type,type,
n1: ( $i * $i * $i ) > $i ).
tff(q0_type,type,
q0: ( $i * $i ) > $i ).
tff(d_type,type,
d: $i ).
tff(e_type,type,
e: $i ).
tff(r0_type,type,
r0: $i > $i ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $i ).
tff(q1_type,type,
q1: ( $i * $i * $i ) > $i ).
tff(l1_type,type,
l1: ( $i * $i ) > $i ).
tff(n0_type,type,
n0: ( $i * $i ) > $i ).
tff(p3_type,type,
p3: ( $i * $i * $i ) > $i ).
tff(n2_type,type,
n2: $i > $i ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $i ).
tff(l0_type,type,
l0: $i > $i ).
tff(1,plain,
^ [E: $i,F: $i,G: $i] :
refl(( ( ifeq(s4(F),true,ifeq(r3(G,E,E),true,k5(E),true),true) = true )
<=> ( ifeq(s4(F),true,ifeq(r3(G,E,E),true,k5(E),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [E: $i,F: $i,G: $i] : ( ifeq(s4(F),true,ifeq(r3(G,E,E),true,k5(E),true),true) = true )
<=> ! [E: $i,F: $i,G: $i] : ( ifeq(s4(F),true,ifeq(r3(G,E,E),true,k5(E),true),true) = true ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [E: $i,F: $i,G: $i] : ( ifeq(s4(F),true,ifeq(r3(G,E,E),true,k5(E),true),true) = true )
<=> ! [E: $i,F: $i,G: $i] : ( ifeq(s4(F),true,ifeq(r3(G,E,E),true,k5(E),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [E: $i,F: $i,G: $i] : ( ifeq(s4(F),true,ifeq(r3(G,E,E),true,k5(E),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_300) ).
tff(5,plain,
! [E: $i,F: $i,G: $i] : ( ifeq(s4(F),true,ifeq(r3(G,E,E),true,k5(E),true),true) = true ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [E: $i,F: $i,G: $i] : ( ifeq(s4(F),true,ifeq(r3(G,E,E),true,k5(E),true),true) = true ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [E: $i,F: $i,G: $i] : ( ifeq(s4(F),true,ifeq(r3(G,E,E),true,k5(E),true),true) = true ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [E: $i,F: $i,G: $i] : ( ifeq(s4(F),true,ifeq(r3(G,E,E),true,k5(E),true),true) = true )
| ( ifeq(s4(a),true,ifeq(r3(b,b,b),true,k5(b),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq(s4(a),true,ifeq(r3(b,b,b),true,k5(b),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,n1(b,b,b),true) = n1(b,b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ifeq(true,true,n1(b,b,b),true) = n1(b,b,b),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ( q0(e,d) = true )
<=> ( q0(e,d) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
q0(e,d) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(21,plain,
q0(e,d) = true,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
true = q0(e,d),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
ifeq(true,true,n1(b,b,b),true) = ifeq(q0(e,d),true,n1(b,b,b),true),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
ifeq(q0(e,d),true,n1(b,b,b),true) = ifeq(true,true,n1(b,b,b),true),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( ( r0(b) = true )
<=> ( r0(b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
r0(b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
tff(27,plain,
r0(b) = true,
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
true = r0(b),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
q0(e,d) = r0(b),
inference(transitivity,[status(thm)],[21,28]) ).
tff(30,plain,
ifeq(q0(e,d),true,n1(b,b,b),true) = ifeq(r0(b),true,n1(b,b,b),true),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
ifeq(r0(b),true,n1(b,b,b),true) = ifeq(q0(e,d),true,n1(b,b,b),true),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
^ [D: $i] :
refl(( ( ifeq(r0(D),true,n1(D,D,D),true) = true )
<=> ( ifeq(r0(D),true,n1(D,D,D),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [D: $i] : ( ifeq(r0(D),true,n1(D,D,D),true) = true )
<=> ! [D: $i] : ( ifeq(r0(D),true,n1(D,D,D),true) = true ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [D: $i] : ( ifeq(r0(D),true,n1(D,D,D),true) = true )
<=> ! [D: $i] : ( ifeq(r0(D),true,n1(D,D,D),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
! [D: $i] : ( ifeq(r0(D),true,n1(D,D,D),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_057) ).
tff(36,plain,
! [D: $i] : ( ifeq(r0(D),true,n1(D,D,D),true) = true ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [D: $i] : ( ifeq(r0(D),true,n1(D,D,D),true) = true ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [D: $i] : ( ifeq(r0(D),true,n1(D,D,D),true) = true ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [D: $i] : ( ifeq(r0(D),true,n1(D,D,D),true) = true )
| ( ifeq(r0(b),true,n1(b,b,b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
ifeq(r0(b),true,n1(b,b,b),true) = true,
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
true = ifeq(r0(b),true,n1(b,b,b),true),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
^ [B: $i,D: $i,C: $i] :
refl(( ( ifeq(p2(B,D,C),true,r3(B,C,B),true) = true )
<=> ( ifeq(p2(B,D,C),true,r3(B,C,B),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [B: $i,D: $i,C: $i] : ( ifeq(p2(B,D,C),true,r3(B,C,B),true) = true )
<=> ! [B: $i,D: $i,C: $i] : ( ifeq(p2(B,D,C),true,r3(B,C,B),true) = true ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [B: $i,D: $i,C: $i] : ( ifeq(p2(B,D,C),true,r3(B,C,B),true) = true )
<=> ! [B: $i,D: $i,C: $i] : ( ifeq(p2(B,D,C),true,r3(B,C,B),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
! [B: $i,D: $i,C: $i] : ( ifeq(p2(B,D,C),true,r3(B,C,B),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_267) ).
tff(46,plain,
! [B: $i,D: $i,C: $i] : ( ifeq(p2(B,D,C),true,r3(B,C,B),true) = true ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [B: $i,D: $i,C: $i] : ( ifeq(p2(B,D,C),true,r3(B,C,B),true) = true ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [B: $i,D: $i,C: $i] : ( ifeq(p2(B,D,C),true,r3(B,C,B),true) = true ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ~ ! [B: $i,D: $i,C: $i] : ( ifeq(p2(B,D,C),true,r3(B,C,B),true) = true )
| ( ifeq(p2(b,b,b),true,r3(b,b,b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
ifeq(p2(b,b,b),true,r3(b,b,b),true) = true,
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,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(52,plain,
ifeq(true,true,p2(b,b,b),true) = p2(b,b,b),
inference(unit_resolution,[status(thm)],[51,16]) ).
tff(53,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(54,plain,
ifeq(true,true,q1(b,b,b),true) = q1(b,b,b),
inference(unit_resolution,[status(thm)],[53,16]) ).
tff(55,plain,
ifeq(true,true,q1(b,b,b),true) = ifeq(r0(b),true,q1(b,b,b),true),
inference(monotonicity,[status(thm)],[28]) ).
tff(56,plain,
ifeq(r0(b),true,q1(b,b,b),true) = ifeq(true,true,q1(b,b,b),true),
inference(symmetry,[status(thm)],[55]) ).
tff(57,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(58,axiom,
ifeq(r0(b),true,q1(b,b,b),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_120) ).
tff(59,plain,
ifeq(r0(b),true,q1(b,b,b),true) = true,
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
true = ifeq(r0(b),true,q1(b,b,b),true),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
true = q1(b,b,b),
inference(transitivity,[status(thm)],[60,56,54]) ).
tff(62,plain,
ifeq(true,true,p2(b,b,b),true) = ifeq(q1(b,b,b),true,p2(b,b,b),true),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
ifeq(q1(b,b,b),true,p2(b,b,b),true) = ifeq(true,true,p2(b,b,b),true),
inference(symmetry,[status(thm)],[62]) ).
tff(64,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(65,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)],[64]) ).
tff(66,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(67,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(68,plain,
! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [A: $i] : ( ifeq(q1(A,A,A),true,p2(A,A,A),true) = true ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,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(72,plain,
ifeq(q1(b,b,b),true,p2(b,b,b),true) = true,
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
true = ifeq(q1(b,b,b),true,p2(b,b,b),true),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
r0(b) = p2(b,b,b),
inference(transitivity,[status(thm)],[27,73,63,52]) ).
tff(75,plain,
ifeq(r0(b),true,r3(b,b,b),true) = ifeq(p2(b,b,b),true,r3(b,b,b),true),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
ifeq(true,true,r3(b,b,b),true) = ifeq(r0(b),true,r3(b,b,b),true),
inference(monotonicity,[status(thm)],[28]) ).
tff(77,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,r3(b,b,b),true) = r3(b,b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
ifeq(true,true,r3(b,b,b),true) = r3(b,b,b),
inference(unit_resolution,[status(thm)],[77,16]) ).
tff(79,plain,
r3(b,b,b) = ifeq(true,true,r3(b,b,b),true),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
r3(b,b,b) = n1(b,b,b),
inference(transitivity,[status(thm)],[79,76,75,50,41,31,24,18]) ).
tff(81,plain,
ifeq(r3(b,b,b),true,k5(b),true) = ifeq(n1(b,b,b),true,k5(b),true),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
ifeq(n1(b,b,b),true,k5(b),true) = ifeq(r3(b,b,b),true,k5(b),true),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
true = n1(b,b,b),
inference(transitivity,[status(thm)],[41,31,24,18]) ).
tff(84,plain,
ifeq(true,true,k5(b),true) = ifeq(n1(b,b,b),true,k5(b),true),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,k5(b),true) = k5(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
ifeq(true,true,k5(b),true) = k5(b),
inference(unit_resolution,[status(thm)],[85,16]) ).
tff(87,plain,
k5(b) = ifeq(true,true,k5(b),true),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
k5(b) = ifeq(r3(b,b,b),true,k5(b),true),
inference(transitivity,[status(thm)],[87,84,82]) ).
tff(89,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,s4(a),true) = s4(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(90,plain,
ifeq(true,true,s4(a),true) = s4(a),
inference(unit_resolution,[status(thm)],[89,16]) ).
tff(91,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,l1(a,a),true) = l1(a,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
ifeq(true,true,l1(a,a),true) = l1(a,a),
inference(unit_resolution,[status(thm)],[91,16]) ).
tff(93,plain,
( ( n0(b,a) = true )
<=> ( n0(b,a) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,axiom,
n0(b,a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
tff(95,plain,
n0(b,a) = true,
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
true = n0(b,a),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
ifeq(true,true,l1(a,a),true) = ifeq(n0(b,a),true,l1(a,a),true),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
ifeq(n0(b,a),true,l1(a,a),true) = ifeq(true,true,l1(a,a),true),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
^ [H: $i,G: $i] :
refl(( ( ifeq(n0(H,G),true,l1(G,G),true) = true )
<=> ( ifeq(n0(H,G),true,l1(G,G),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true )
<=> ! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true )
<=> ! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,axiom,
! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_002) ).
tff(103,plain,
! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
( ~ ! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true )
| ( ifeq(n0(b,a),true,l1(a,a),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
ifeq(n0(b,a),true,l1(a,a),true) = true,
inference(unit_resolution,[status(thm)],[106,105]) ).
tff(108,plain,
true = ifeq(n0(b,a),true,l1(a,a),true),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
true = l1(a,a),
inference(transitivity,[status(thm)],[108,98,92]) ).
tff(110,plain,
ifeq(true,true,s4(a),true) = ifeq(l1(a,a),true,s4(a),true),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
ifeq(l1(a,a),true,s4(a),true) = ifeq(true,true,s4(a),true),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
s4(a) = ifeq(true,true,s4(a),true),
inference(symmetry,[status(thm)],[90]) ).
tff(113,plain,
s4(a) = ifeq(l1(a,a),true,s4(a),true),
inference(transitivity,[status(thm)],[112,110]) ).
tff(114,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,p3(a,a,a),true) = p3(a,a,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
ifeq(true,true,p3(a,a,a),true) = p3(a,a,a),
inference(unit_resolution,[status(thm)],[114,16]) ).
tff(116,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,l1(b,b),true) = l1(b,b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
ifeq(true,true,l1(b,b),true) = l1(b,b),
inference(unit_resolution,[status(thm)],[116,16]) ).
tff(118,plain,
( ( n0(d,b) = true )
<=> ( n0(d,b) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,axiom,
n0(d,b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
tff(120,plain,
n0(d,b) = true,
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
true = n0(d,b),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
ifeq(true,true,l1(b,b),true) = ifeq(n0(d,b),true,l1(b,b),true),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
ifeq(n0(d,b),true,l1(b,b),true) = ifeq(true,true,l1(b,b),true),
inference(symmetry,[status(thm)],[122]) ).
tff(124,plain,
( ~ ! [H: $i,G: $i] : ( ifeq(n0(H,G),true,l1(G,G),true) = true )
| ( ifeq(n0(d,b),true,l1(b,b),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
ifeq(n0(d,b),true,l1(b,b),true) = true,
inference(unit_resolution,[status(thm)],[124,105]) ).
tff(126,plain,
true = ifeq(n0(d,b),true,l1(b,b),true),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
true = l1(b,b),
inference(transitivity,[status(thm)],[126,123,117]) ).
tff(128,plain,
ifeq(true,true,p3(a,a,a),true) = ifeq(l1(b,b),true,p3(a,a,a),true),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
ifeq(l1(b,b),true,p3(a,a,a),true) = ifeq(true,true,p3(a,a,a),true),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,n2(a),true) = n2(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
ifeq(true,true,n2(a),true) = n2(a),
inference(unit_resolution,[status(thm)],[130,16]) ).
tff(132,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,p1(a,a,a),true) = p1(a,a,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
ifeq(true,true,p1(a,a,a),true) = p1(a,a,a),
inference(unit_resolution,[status(thm)],[132,16]) ).
tff(134,plain,
( ( l0(a) = true )
<=> ( l0(a) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,axiom,
l0(a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
tff(136,plain,
l0(a) = true,
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
true = l0(a),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
ifeq(true,true,p1(a,a,a),true) = ifeq(l0(a),true,p1(a,a,a),true),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
ifeq(l0(a),true,p1(a,a,a),true) = ifeq(true,true,p1(a,a,a),true),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ( ifeq(l0(a),true,p1(a,a,a),true) = true )
<=> ( ifeq(l0(a),true,p1(a,a,a),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,axiom,
ifeq(l0(a),true,p1(a,a,a),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_088) ).
tff(142,plain,
ifeq(l0(a),true,p1(a,a,a),true) = true,
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
true = ifeq(l0(a),true,p1(a,a,a),true),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
true = p1(a,a,a),
inference(transitivity,[status(thm)],[143,139,133]) ).
tff(145,plain,
ifeq(true,true,n2(a),true) = ifeq(p1(a,a,a),true,n2(a),true),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
ifeq(p1(a,a,a),true,n2(a),true) = ifeq(true,true,n2(a),true),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ifeq(p1(B,C,A),true,n2(A),true) = true )
<=> ( ifeq(p1(B,C,A),true,n2(A),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(148,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(p1(B,C,A),true,n2(A),true) = true )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(p1(B,C,A),true,n2(A),true) = true ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(p1(B,C,A),true,n2(A),true) = true )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(p1(B,C,A),true,n2(A),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(p1(B,C,A),true,n2(A),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_137) ).
tff(151,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(p1(B,C,A),true,n2(A),true) = true ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(p1(B,C,A),true,n2(A),true) = true ),
inference(skolemize,[status(sab)],[151]) ).
tff(153,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(p1(B,C,A),true,n2(A),true) = true ),
inference(modus_ponens,[status(thm)],[152,148]) ).
tff(154,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(p1(B,C,A),true,n2(A),true) = true )
| ( ifeq(p1(a,a,a),true,n2(a),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
ifeq(p1(a,a,a),true,n2(a),true) = true,
inference(unit_resolution,[status(thm)],[154,153]) ).
tff(156,plain,
true = ifeq(p1(a,a,a),true,n2(a),true),
inference(symmetry,[status(thm)],[155]) ).
tff(157,plain,
l1(b,b) = ifeq(true,true,l1(b,b),true),
inference(symmetry,[status(thm)],[117]) ).
tff(158,plain,
l1(b,b) = n2(a),
inference(transitivity,[status(thm)],[157,122,125,156,146,131]) ).
tff(159,plain,
ifeq(l1(b,b),true,p3(a,a,a),true) = ifeq(n2(a),true,p3(a,a,a),true),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
ifeq(n2(a),true,p3(a,a,a),true) = ifeq(l1(b,b),true,p3(a,a,a),true),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
^ [H: $i] :
refl(( ( ifeq(n2(H),true,p3(H,H,H),true) = true )
<=> ( ifeq(n2(H),true,p3(H,H,H),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(162,plain,
( ! [H: $i] : ( ifeq(n2(H),true,p3(H,H,H),true) = true )
<=> ! [H: $i] : ( ifeq(n2(H),true,p3(H,H,H),true) = true ) ),
inference(quant_intro,[status(thm)],[161]) ).
tff(163,plain,
( ! [H: $i] : ( ifeq(n2(H),true,p3(H,H,H),true) = true )
<=> ! [H: $i] : ( ifeq(n2(H),true,p3(H,H,H),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,axiom,
! [H: $i] : ( ifeq(n2(H),true,p3(H,H,H),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_244) ).
tff(165,plain,
! [H: $i] : ( ifeq(n2(H),true,p3(H,H,H),true) = true ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
! [H: $i] : ( ifeq(n2(H),true,p3(H,H,H),true) = true ),
inference(skolemize,[status(sab)],[165]) ).
tff(167,plain,
! [H: $i] : ( ifeq(n2(H),true,p3(H,H,H),true) = true ),
inference(modus_ponens,[status(thm)],[166,162]) ).
tff(168,plain,
( ~ ! [H: $i] : ( ifeq(n2(H),true,p3(H,H,H),true) = true )
| ( ifeq(n2(a),true,p3(a,a,a),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(169,plain,
ifeq(n2(a),true,p3(a,a,a),true) = true,
inference(unit_resolution,[status(thm)],[168,167]) ).
tff(170,plain,
true = ifeq(n2(a),true,p3(a,a,a),true),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
l1(a,a) = ifeq(true,true,l1(a,a),true),
inference(symmetry,[status(thm)],[92]) ).
tff(172,plain,
l1(a,a) = p3(a,a,a),
inference(transitivity,[status(thm)],[171,97,107,170,160,129,115]) ).
tff(173,plain,
ifeq(l1(a,a),true,s4(a),true) = ifeq(p3(a,a,a),true,ifeq(l1(a,a),true,s4(a),true),true),
inference(monotonicity,[status(thm)],[172,113]) ).
tff(174,plain,
ifeq(p3(a,a,a),true,ifeq(l1(a,a),true,s4(a),true),true) = ifeq(l1(a,a),true,s4(a),true),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true )
<=> ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(176,plain,
( ! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true )
<=> ! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ) ),
inference(quant_intro,[status(thm)],[175]) ).
tff(177,plain,
( ! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true )
<=> ! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,axiom,
! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_299) ).
tff(179,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ),
inference(skolemize,[status(sab)],[179]) ).
tff(181,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ),
inference(modus_ponens,[status(thm)],[180,176]) ).
tff(182,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true )
| ( ifeq(p3(a,a,a),true,ifeq(l1(a,a),true,s4(a),true),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(183,plain,
ifeq(p3(a,a,a),true,ifeq(l1(a,a),true,s4(a),true),true) = true,
inference(unit_resolution,[status(thm)],[182,181]) ).
tff(184,plain,
true = ifeq(p3(a,a,a),true,ifeq(l1(a,a),true,s4(a),true),true),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
n1(b,b,b) = ifeq(true,true,n1(b,b,b),true),
inference(symmetry,[status(thm)],[18]) ).
tff(186,plain,
n1(b,b,b) = s4(a),
inference(transitivity,[status(thm)],[185,23,30,40,184,174,111,90]) ).
tff(187,plain,
ifeq(n1(b,b,b),true,k5(b),true) = ifeq(s4(a),true,ifeq(r3(b,b,b),true,k5(b),true),true),
inference(monotonicity,[status(thm)],[186,88]) ).
tff(188,plain,
k5(b) = true,
inference(transitivity,[status(thm)],[87,84,187,9]) ).
tff(189,plain,
( ( k5(b) != true )
<=> ( k5(b) != true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(190,axiom,
k5(b) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(191,plain,
k5(b) != true,
inference(modus_ponens,[status(thm)],[190,189]) ).
tff(192,plain,
$false,
inference(unit_resolution,[status(thm)],[191,188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN116-10 : TPTP v9.0.0. Released v7.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.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 12:28:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.61/0.79 % SZS status Unsatisfiable
% 0.61/0.79 % SZS output start Proof
% See solution above
% 0.66/0.82 % E exiting
%------------------------------------------------------------------------------