%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN170-10 : TPTP v9.0.0. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:38:24 AM UTC 2025
% Result : Unsatisfiable 0.61s 0.80s
% Output : Proof 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 38
% Syntax : Number of formulae : 108 ( 81 unt; 0 typ; 0 def)
% Number of atoms : 147 ( 140 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 56 ( 23 ~; 10 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 6 ( 6 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 : 14 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 142 ( 129 !; 0 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
tff(true_type,type,
true: $i ).
tff(p4_type,type,
p4: ( $i * $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(k3_type,type,
k3: ( $i * $i * $i ) > $i ).
tff(p1_type,type,
p1: ( $i * $i * $i ) > $i ).
tff(r0_type,type,
r0: $i > $i ).
tff(e_type,type,
e: $i ).
tff(p2_type,type,
p2: ( $i * $i * $i ) > $i ).
tff(m1_type,type,
m1: ( $i * $i * $i ) > $i ).
tff(l0_type,type,
l0: $i > $i ).
tff(p0_type,type,
p0: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(m0_type,type,
m0: ( $i * $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,C: $i] :
refl(( ( ifeq(k3(B,B,C),true,p4(B,C,B),true) = true )
<=> ( ifeq(k3(B,B,C),true,p4(B,C,B),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,C: $i] : ( ifeq(k3(B,B,C),true,p4(B,C,B),true) = true )
<=> ! [B: $i,C: $i] : ( ifeq(k3(B,B,C),true,p4(B,C,B),true) = true ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,C: $i] : ( ifeq(k3(B,B,C),true,p4(B,C,B),true) = true )
<=> ! [B: $i,C: $i] : ( ifeq(k3(B,B,C),true,p4(B,C,B),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,C: $i] : ( ifeq(k3(B,B,C),true,p4(B,C,B),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_287) ).
tff(5,plain,
! [B: $i,C: $i] : ( ifeq(k3(B,B,C),true,p4(B,C,B),true) = true ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,C: $i] : ( ifeq(k3(B,B,C),true,p4(B,C,B),true) = true ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,C: $i] : ( ifeq(k3(B,B,C),true,p4(B,C,B),true) = true ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,C: $i] : ( ifeq(k3(B,B,C),true,p4(B,C,B),true) = true )
| ( ifeq(k3(c,c,c),true,p4(c,c,c),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
ifeq(k3(c,c,c),true,p4(c,c,c),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,k3(c,c,c),true) = k3(c,c,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
ifeq(true,true,k3(c,c,c),true) = k3(c,c,c),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ( r0(e) = true )
<=> ( r0(e) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
r0(e) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
tff(21,plain,
r0(e) = true,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
true = r0(e),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
ifeq(true,true,k3(c,c,c),true) = ifeq(r0(e),true,k3(c,c,c),true),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
ifeq(r0(e),true,k3(c,c,c),true) = ifeq(true,true,k3(c,c,c),true),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,p2(c,c,c),true) = p2(c,c,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
ifeq(true,true,p2(c,c,c),true) = p2(c,c,c),
inference(unit_resolution,[status(thm)],[25,16]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,m1(c,c,c),true) = m1(c,c,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
ifeq(true,true,m1(c,c,c),true) = m1(c,c,c),
inference(unit_resolution,[status(thm)],[27,16]) ).
tff(29,plain,
( ( l0(c) = true )
<=> ( l0(c) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
l0(c) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
tff(31,plain,
l0(c) = true,
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
true = l0(c),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
ifeq(true,true,m1(c,c,c),true) = ifeq(l0(c),true,m1(c,c,c),true),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
ifeq(l0(c),true,m1(c,c,c),true) = ifeq(true,true,m1(c,c,c),true),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
( ( ifeq(l0(c),true,m1(c,c,c),true) = true )
<=> ( ifeq(l0(c),true,m1(c,c,c),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
ifeq(l0(c),true,m1(c,c,c),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_020) ).
tff(37,plain,
ifeq(l0(c),true,m1(c,c,c),true) = true,
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
true = ifeq(l0(c),true,m1(c,c,c),true),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
true = m1(c,c,c),
inference(transitivity,[status(thm)],[38,34,28]) ).
tff(40,plain,
ifeq(true,true,p2(c,c,c),true) = ifeq(m1(c,c,c),true,p2(c,c,c),true),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
ifeq(m1(c,c,c),true,p2(c,c,c),true) = ifeq(true,true,p2(c,c,c),true),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
^ [D: $i,E: $i] :
refl(( ( ifeq(m1(E,D,E),true,p2(D,E,D),true) = true )
<=> ( ifeq(m1(E,D,E),true,p2(D,E,D),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [D: $i,E: $i] : ( ifeq(m1(E,D,E),true,p2(D,E,D),true) = true )
<=> ! [D: $i,E: $i] : ( ifeq(m1(E,D,E),true,p2(D,E,D),true) = true ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [D: $i,E: $i] : ( ifeq(m1(E,D,E),true,p2(D,E,D),true) = true )
<=> ! [D: $i,E: $i] : ( ifeq(m1(E,D,E),true,p2(D,E,D),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
! [D: $i,E: $i] : ( ifeq(m1(E,D,E),true,p2(D,E,D),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_176) ).
tff(46,plain,
! [D: $i,E: $i] : ( ifeq(m1(E,D,E),true,p2(D,E,D),true) = true ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [D: $i,E: $i] : ( ifeq(m1(E,D,E),true,p2(D,E,D),true) = true ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [D: $i,E: $i] : ( ifeq(m1(E,D,E),true,p2(D,E,D),true) = true ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ~ ! [D: $i,E: $i] : ( ifeq(m1(E,D,E),true,p2(D,E,D),true) = true )
| ( ifeq(m1(c,c,c),true,p2(c,c,c),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
ifeq(m1(c,c,c),true,p2(c,c,c),true) = true,
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
true = ifeq(m1(c,c,c),true,p2(c,c,c),true),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
r0(e) = p2(c,c,c),
inference(transitivity,[status(thm)],[21,51,41,26]) ).
tff(53,plain,
ifeq(r0(e),true,k3(c,c,c),true) = ifeq(p2(c,c,c),true,k3(c,c,c),true),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
ifeq(p2(c,c,c),true,k3(c,c,c),true) = ifeq(r0(e),true,k3(c,c,c),true),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
^ [D: $i,C: $i] :
refl(( ( ifeq(p2(D,C,C),true,k3(C,D,C),true) = true )
<=> ( ifeq(p2(D,C,C),true,k3(C,D,C),true) = true ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [D: $i,C: $i] : ( ifeq(p2(D,C,C),true,k3(C,D,C),true) = true )
<=> ! [D: $i,C: $i] : ( ifeq(p2(D,C,C),true,k3(C,D,C),true) = true ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [D: $i,C: $i] : ( ifeq(p2(D,C,C),true,k3(C,D,C),true) = true )
<=> ! [D: $i,C: $i] : ( ifeq(p2(D,C,C),true,k3(C,D,C),true) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
! [D: $i,C: $i] : ( ifeq(p2(D,C,C),true,k3(C,D,C),true) = true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_206) ).
tff(59,plain,
! [D: $i,C: $i] : ( ifeq(p2(D,C,C),true,k3(C,D,C),true) = true ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [D: $i,C: $i] : ( ifeq(p2(D,C,C),true,k3(C,D,C),true) = true ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [D: $i,C: $i] : ( ifeq(p2(D,C,C),true,k3(C,D,C),true) = true ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [D: $i,C: $i] : ( ifeq(p2(D,C,C),true,k3(C,D,C),true) = true )
| ( ifeq(p2(c,c,c),true,k3(c,c,c),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
ifeq(p2(c,c,c),true,k3(c,c,c),true) = true,
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
true = ifeq(p2(c,c,c),true,k3(c,c,c),true),
inference(symmetry,[status(thm)],[63]) ).
tff(65,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(66,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)],[65]) ).
tff(67,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(68,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(69,plain,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( ~ ! [B: $i,C: $i] : ( ifeq(p0(C,B),true,p1(B,B,B),true) = true )
| ( ifeq(p0(b,c),true,p1(c,c,c),true) = true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
ifeq(p0(b,c),true,p1(c,c,c),true) = true,
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
( ( p0(b,c) = true )
<=> ( p0(b,c) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
p0(b,c) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
tff(76,plain,
p0(b,c) = true,
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
true = p0(b,c),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
( ( m0(e,b,c) = true )
<=> ( m0(e,b,c) = true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,axiom,
m0(e,b,c) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).
tff(80,plain,
m0(e,b,c) = true,
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
m0(e,b,c) = p0(b,c),
inference(transitivity,[status(thm)],[80,77]) ).
tff(82,plain,
ifeq(m0(e,b,c),true,p1(c,c,c),true) = ifeq(p0(b,c),true,p1(c,c,c),true),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
true = m0(e,b,c),
inference(symmetry,[status(thm)],[80]) ).
tff(84,plain,
ifeq(true,true,p1(c,c,c),true) = ifeq(m0(e,b,c),true,p1(c,c,c),true),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,p1(c,c,c),true) = p1(c,c,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
ifeq(true,true,p1(c,c,c),true) = p1(c,c,c),
inference(unit_resolution,[status(thm)],[85,16]) ).
tff(87,plain,
p1(c,c,c) = ifeq(true,true,p1(c,c,c),true),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
p1(c,c,c) = k3(c,c,c),
inference(transitivity,[status(thm)],[87,84,82,73,64,54,24,18]) ).
tff(89,plain,
ifeq(p1(c,c,c),true,p4(c,c,c),true) = ifeq(k3(c,c,c),true,p4(c,c,c),true),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
ifeq(m0(e,b,c),true,p1(c,c,c),true) = ifeq(true,true,p1(c,c,c),true),
inference(symmetry,[status(thm)],[84]) ).
tff(91,plain,
ifeq(p0(b,c),true,p1(c,c,c),true) = ifeq(m0(e,b,c),true,p1(c,c,c),true),
inference(symmetry,[status(thm)],[82]) ).
tff(92,plain,
true = ifeq(p0(b,c),true,p1(c,c,c),true),
inference(symmetry,[status(thm)],[73]) ).
tff(93,plain,
true = p1(c,c,c),
inference(transitivity,[status(thm)],[92,91,90,86]) ).
tff(94,plain,
ifeq(true,true,p4(c,c,c),true) = ifeq(p1(c,c,c),true,p4(c,c,c),true),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,p4(c,c,c),true) = p4(c,c,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
ifeq(true,true,p4(c,c,c),true) = p4(c,c,c),
inference(unit_resolution,[status(thm)],[95,16]) ).
tff(97,plain,
p4(c,c,c) = ifeq(true,true,p4(c,c,c),true),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
p4(c,c,c) = true,
inference(transitivity,[status(thm)],[97,94,89,9]) ).
tff(99,plain,
^ [Y: $i,X: $i] :
refl(( ( p4(X,c,Y) != true )
<=> ( p4(X,c,Y) != true ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [Y: $i,X: $i] : ( p4(X,c,Y) != true )
<=> ! [Y: $i,X: $i] : ( p4(X,c,Y) != true ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [Y: $i,X: $i] : ( p4(X,c,Y) != true )
<=> ! [Y: $i,X: $i] : ( p4(X,c,Y) != true ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,axiom,
! [Y: $i,X: $i] : ( p4(X,c,Y) != true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
tff(103,plain,
! [Y: $i,X: $i] : ( p4(X,c,Y) != true ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [Y: $i,X: $i] : ( p4(X,c,Y) != true ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [Y: $i,X: $i] : ( p4(X,c,Y) != true ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
( ~ ! [Y: $i,X: $i] : ( p4(X,c,Y) != true )
| ( p4(c,c,c) != true ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
p4(c,c,c) != true,
inference(unit_resolution,[status(thm)],[106,105]) ).
tff(108,plain,
$false,
inference(unit_resolution,[status(thm)],[107,98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYN170-10 : TPTP v9.0.0. Released v7.5.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:30:31 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.61/0.80 % SZS status Unsatisfiable
% 0.61/0.80 % SZS output start Proof
% See solution above
% 0.67/0.83 % E exiting
%------------------------------------------------------------------------------