TSTP Solution File: SYN565-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN565-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 : Thu Sep 29 23:56:26 EDT 2022
% Result : Unsatisfiable 0.57s 0.62s
% Output : Proof 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 69
% Syntax : Number of formulae : 142 ( 45 unt; 11 typ; 0 def)
% Number of atoms : 635 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 874 ( 407 ~; 402 |; 0 &)
% ( 65 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 37 ( 37 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 404 ( 368 !; 0 ?; 404 :)
% Comments :
%------------------------------------------------------------------------------
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(f3_type,type,
f3: ( $i * $i ) > $i ).
tff(f5_type,type,
f5: $i > $i ).
tff(c12_type,type,
c12: $i ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(c11_type,type,
c11: $i ).
tff(f7_type,type,
f7: $i > $i ).
tff(f6_type,type,
f6: ( $i * $i ) > $i ).
tff(p4_type,type,
p4: ( $i * $i ) > $o ).
tff(p10_type,type,
p10: ( $i * $i ) > $o ).
tff(f9_type,type,
f9: ( $i * $i ) > $i ).
tff(1,plain,
^ [X18: $i] :
refl(
( p2(f5(f7(X18)),f5(X18))
<=> p2(f5(f7(X18)),f5(X18)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X18: $i] : p2(f5(f7(X18)),f5(X18))
<=> ! [X18: $i] : p2(f5(f7(X18)),f5(X18)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X18: $i] : p2(f5(f7(X18)),f5(X18))
<=> ! [X18: $i] : p2(f5(f7(X18)),f5(X18)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X18: $i] : p2(f5(f7(X18)),f5(X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_3) ).
tff(5,plain,
! [X18: $i] : p2(f5(f7(X18)),f5(X18)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X18: $i] : p2(f5(f7(X18)),f5(X18)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X18: $i] : p2(f5(f7(X18)),f5(X18)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X18: $i] : p2(f5(f7(X18)),f5(X18))
| p2(f5(f7(f8(c11,c12))),f5(f8(c11,c12))) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p2(f5(f7(f8(c11,c12))),f5(f8(c11,c12))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X32: $i,X33: $i] :
refl(
( p4(f7(f8(X32,X33)),f8(X33,X32))
<=> p4(f7(f8(X32,X33)),f8(X33,X32)) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X32: $i,X33: $i] : p4(f7(f8(X32,X33)),f8(X33,X32))
<=> ! [X32: $i,X33: $i] : p4(f7(f8(X32,X33)),f8(X33,X32)) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X32: $i,X33: $i] : p4(f7(f8(X32,X33)),f8(X33,X32))
<=> ! [X32: $i,X33: $i] : p4(f7(f8(X32,X33)),f8(X33,X32)) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X32: $i,X33: $i] : p4(f7(f8(X32,X33)),f8(X33,X32)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_5) ).
tff(14,plain,
! [X32: $i,X33: $i] : p4(f7(f8(X32,X33)),f8(X33,X32)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X32: $i,X33: $i] : p4(f7(f8(X32,X33)),f8(X33,X32)),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X32: $i,X33: $i] : p4(f7(f8(X32,X33)),f8(X33,X32)),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X32: $i,X33: $i] : p4(f7(f8(X32,X33)),f8(X33,X32))
| p4(f7(f8(c11,c12)),f8(c12,c11)) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
p4(f7(f8(c11,c12)),f8(c12,c11)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
^ [X17: $i,X16: $i] :
refl(
( ( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) )
<=> ( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) )
<=> ! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) )
<=> ! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [X17: $i,X16: $i] :
rewrite(
( ( p2(f5(X16),f5(X17))
| ~ p4(X16,X17) )
<=> ( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [X17: $i,X16: $i] :
( p2(f5(X16),f5(X17))
| ~ p4(X16,X17) )
<=> ! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [X17: $i,X16: $i] :
( p2(f5(X16),f5(X17))
| ~ p4(X16,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_6) ).
tff(25,plain,
! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( ~ ! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) )
| ~ p4(f7(f8(c11,c12)),f8(c12,c11))
| p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11))) )
<=> ( ~ ! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) )
| ~ p4(f7(f8(c11,c12)),f8(c12,c11))
| p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ~ ! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) )
| ~ p4(f7(f8(c11,c12)),f8(c12,c11))
| p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11))) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) )
| ~ p4(f7(f8(c11,c12)),f8(c12,c11))
| p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11))) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11))),
inference(unit_resolution,[status(thm)],[31,28,18]) ).
tff(33,plain,
^ [X9: $i,X11: $i,X10: $i] :
refl(
( ( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
<=> ( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
<=> ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
<=> ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
^ [X9: $i,X11: $i,X10: $i] :
trans(
monotonicity(
rewrite(
( ( p2(X10,X11)
| ~ p2(X9,X10) )
<=> ( ~ p2(X9,X10)
| p2(X10,X11) ) )),
( ( p2(X10,X11)
| ~ p2(X9,X10)
| ~ p2(X9,X11) )
<=> ( ~ p2(X9,X10)
| p2(X10,X11)
| ~ p2(X9,X11) ) )),
rewrite(
( ( ~ p2(X9,X10)
| p2(X10,X11)
| ~ p2(X9,X11) )
<=> ( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) ) )),
( ( p2(X10,X11)
| ~ p2(X9,X10)
| ~ p2(X9,X11) )
<=> ( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [X9: $i,X11: $i,X10: $i] :
( p2(X10,X11)
| ~ p2(X9,X10)
| ~ p2(X9,X11) )
<=> ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [X9: $i,X11: $i,X10: $i] :
( p2(X10,X11)
| ~ p2(X9,X10)
| ~ p2(X9,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_8) ).
tff(39,plain,
! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c11,c12)))
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11)))
| p2(f5(f8(c11,c12)),f5(f8(c12,c11))) )
<=> ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c11,c12)))
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11)))
| p2(f5(f8(c11,c12)),f5(f8(c12,c11))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( ~ p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11)))
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c11,c12)))
| p2(f5(f8(c11,c12)),f5(f8(c12,c11))) )
<=> ( ~ p2(f5(f7(f8(c11,c12))),f5(f8(c11,c12)))
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11)))
| p2(f5(f8(c11,c12)),f5(f8(c12,c11))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11)))
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c11,c12)))
| p2(f5(f8(c11,c12)),f5(f8(c12,c11))) )
<=> ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c11,c12)))
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11)))
| p2(f5(f8(c11,c12)),f5(f8(c12,c11))) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11)))
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c11,c12)))
| p2(f5(f8(c11,c12)),f5(f8(c12,c11))) )
<=> ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c11,c12)))
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11)))
| p2(f5(f8(c11,c12)),f5(f8(c12,c11))) ) ),
inference(transitivity,[status(thm)],[45,43]) ).
tff(47,plain,
( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11)))
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c11,c12)))
| p2(f5(f8(c11,c12)),f5(f8(c12,c11))) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c11,c12)))
| ~ p2(f5(f7(f8(c11,c12))),f5(f8(c12,c11)))
| p2(f5(f8(c11,c12)),f5(f8(c12,c11))) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
p2(f5(f8(c11,c12)),f5(f8(c12,c11))),
inference(unit_resolution,[status(thm)],[48,42,32,9]) ).
tff(50,plain,
^ [X39: $i,X38: $i] :
refl(
( p4(f8(X38,X39),f6(X38,f7(X39)))
<=> p4(f8(X38,X39),f6(X38,f7(X39))) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [X39: $i,X38: $i] : p4(f8(X38,X39),f6(X38,f7(X39)))
<=> ! [X39: $i,X38: $i] : p4(f8(X38,X39),f6(X38,f7(X39))) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [X39: $i,X38: $i] : p4(f8(X38,X39),f6(X38,f7(X39)))
<=> ! [X39: $i,X38: $i] : p4(f8(X38,X39),f6(X38,f7(X39))) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
! [X39: $i,X38: $i] : p4(f8(X38,X39),f6(X38,f7(X39))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_4) ).
tff(54,plain,
! [X39: $i,X38: $i] : p4(f8(X38,X39),f6(X38,f7(X39))),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [X39: $i,X38: $i] : p4(f8(X38,X39),f6(X38,f7(X39))),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [X39: $i,X38: $i] : p4(f8(X38,X39),f6(X38,f7(X39))),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [X39: $i,X38: $i] : p4(f8(X38,X39),f6(X38,f7(X39)))
| p4(f8(c11,c12),f6(c11,f7(c12))) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
p4(f8(c11,c12),f6(c11,f7(c12))),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
( ( ~ ! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) )
| ~ p4(f8(c11,c12),f6(c11,f7(c12)))
| p2(f5(f8(c11,c12)),f5(f6(c11,f7(c12)))) )
<=> ( ~ ! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) )
| ~ p4(f8(c11,c12),f6(c11,f7(c12)))
| p2(f5(f8(c11,c12)),f5(f6(c11,f7(c12)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) )
| ~ p4(f8(c11,c12),f6(c11,f7(c12)))
| p2(f5(f8(c11,c12)),f5(f6(c11,f7(c12)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [X17: $i,X16: $i] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) )
| ~ p4(f8(c11,c12),f6(c11,f7(c12)))
| p2(f5(f8(c11,c12)),f5(f6(c11,f7(c12)))) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
p2(f5(f8(c11,c12)),f5(f6(c11,f7(c12)))),
inference(unit_resolution,[status(thm)],[61,28,58]) ).
tff(63,plain,
( ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f8(c11,c12)),f5(f8(c12,c11)))
| ~ p2(f5(f8(c11,c12)),f5(f6(c11,f7(c12))))
| p2(f5(f6(c11,f7(c12))),f5(f8(c12,c11))) )
<=> ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f8(c11,c12)),f5(f8(c12,c11)))
| ~ p2(f5(f8(c11,c12)),f5(f6(c11,f7(c12))))
| p2(f5(f6(c11,f7(c12))),f5(f8(c12,c11))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f8(c11,c12)),f5(f8(c12,c11)))
| ~ p2(f5(f8(c11,c12)),f5(f6(c11,f7(c12))))
| p2(f5(f6(c11,f7(c12))),f5(f8(c12,c11))) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f8(c11,c12)),f5(f8(c12,c11)))
| ~ p2(f5(f8(c11,c12)),f5(f6(c11,f7(c12))))
| p2(f5(f6(c11,f7(c12))),f5(f8(c12,c11))) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
p2(f5(f6(c11,f7(c12))),f5(f8(c12,c11))),
inference(unit_resolution,[status(thm)],[65,42,62,49]) ).
tff(67,plain,
( ~ ! [X18: $i] : p2(f5(f7(X18)),f5(X18))
| p2(f5(f7(c12)),f5(c12)) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
p2(f5(f7(c12)),f5(c12)),
inference(unit_resolution,[status(thm)],[67,7]) ).
tff(69,plain,
^ [X14: $i,X12: $i,X13: $i,X15: $i] :
refl(
( ( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) )
<=> ( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) )
<=> ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) )
<=> ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
^ [X14: $i,X12: $i,X13: $i,X15: $i] :
trans(
monotonicity(
rewrite(
( ( p2(f3(X12,X13),f3(X14,X15))
| ~ p2(X12,X14) )
<=> ( ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) ) )),
( ( p2(f3(X12,X13),f3(X14,X15))
| ~ p2(X12,X14)
| ~ p2(X13,X15) )
<=> ( ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15))
| ~ p2(X13,X15) ) )),
rewrite(
( ( ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15))
| ~ p2(X13,X15) )
<=> ( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) ) )),
( ( p2(f3(X12,X13),f3(X14,X15))
| ~ p2(X12,X14)
| ~ p2(X13,X15) )
<=> ( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( p2(f3(X12,X13),f3(X14,X15))
| ~ p2(X12,X14)
| ~ p2(X13,X15) )
<=> ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,axiom,
! [X14: $i,X12: $i,X13: $i,X15: $i] :
( p2(f3(X12,X13),f3(X14,X15))
| ~ p2(X12,X14)
| ~ p2(X13,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_16) ).
tff(75,plain,
! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
( ( ~ ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) )
| ~ p2(f5(f7(c12)),f5(c12))
| ~ p2(f5(f6(c11,f7(c12))),f5(f8(c12,c11)))
| p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12))) )
<=> ( ~ ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) )
| ~ p2(f5(f7(c12)),f5(c12))
| ~ p2(f5(f6(c11,f7(c12))),f5(f8(c12,c11)))
| p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ~ ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) )
| ~ p2(f5(f7(c12)),f5(c12))
| ~ p2(f5(f6(c11,f7(c12))),f5(f8(c12,c11)))
| p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12))) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [X14: $i,X12: $i,X13: $i,X15: $i] :
( ~ p2(X13,X15)
| ~ p2(X12,X14)
| p2(f3(X12,X13),f3(X14,X15)) )
| ~ p2(f5(f7(c12)),f5(c12))
| ~ p2(f5(f6(c11,f7(c12))),f5(f8(c12,c11)))
| p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12))) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12))),
inference(unit_resolution,[status(thm)],[81,78,68,66]) ).
tff(83,plain,
^ [X7: $i,X8: $i] :
refl(
( p10(f5(X7),f3(f5(f6(X7,X8)),f5(X8)))
<=> p10(f5(X7),f3(f5(f6(X7,X8)),f5(X8))) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [X7: $i,X8: $i] : p10(f5(X7),f3(f5(f6(X7,X8)),f5(X8)))
<=> ! [X7: $i,X8: $i] : p10(f5(X7),f3(f5(f6(X7,X8)),f5(X8))) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [X7: $i,X8: $i] : p10(f5(X7),f3(f5(f6(X7,X8)),f5(X8)))
<=> ! [X7: $i,X8: $i] : p10(f5(X7),f3(f5(f6(X7,X8)),f5(X8))) ),
inference(rewrite,[status(thm)],]) ).
tff(86,axiom,
! [X7: $i,X8: $i] : p10(f5(X7),f3(f5(f6(X7,X8)),f5(X8))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_10) ).
tff(87,plain,
! [X7: $i,X8: $i] : p10(f5(X7),f3(f5(f6(X7,X8)),f5(X8))),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [X7: $i,X8: $i] : p10(f5(X7),f3(f5(f6(X7,X8)),f5(X8))),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [X7: $i,X8: $i] : p10(f5(X7),f3(f5(f6(X7,X8)),f5(X8))),
inference(modus_ponens,[status(thm)],[88,84]) ).
tff(90,plain,
( ~ ! [X7: $i,X8: $i] : p10(f5(X7),f3(f5(f6(X7,X8)),f5(X8)))
| p10(f5(c11),f3(f5(f6(c11,f7(c12))),f5(f7(c12)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
p10(f5(c11),f3(f5(f6(c11,f7(c12))),f5(f7(c12)))),
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
( ~ ! [X18: $i] : p2(f5(f7(X18)),f5(X18))
| p2(f5(f7(c11)),f5(c11)) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
p2(f5(f7(c11)),f5(c11)),
inference(unit_resolution,[status(thm)],[92,7]) ).
tff(94,plain,
( ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(c11)),f5(c11))
| p2(f5(c11),f5(c11)) )
<=> ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(c11)),f5(c11))
| p2(f5(c11),f5(c11)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ( ~ p2(f5(f7(c11)),f5(c11))
| ~ p2(f5(f7(c11)),f5(c11))
| p2(f5(c11),f5(c11)) )
<=> ( ~ p2(f5(f7(c11)),f5(c11))
| p2(f5(c11),f5(c11)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(c11)),f5(c11))
| ~ p2(f5(f7(c11)),f5(c11))
| p2(f5(c11),f5(c11)) )
<=> ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(c11)),f5(c11))
| p2(f5(c11),f5(c11)) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(c11)),f5(c11))
| ~ p2(f5(f7(c11)),f5(c11))
| p2(f5(c11),f5(c11)) )
<=> ( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(c11)),f5(c11))
| p2(f5(c11),f5(c11)) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(c11)),f5(c11))
| ~ p2(f5(f7(c11)),f5(c11))
| p2(f5(c11),f5(c11)) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [X9: $i,X11: $i,X10: $i] :
( ~ p2(X9,X11)
| ~ p2(X9,X10)
| p2(X10,X11) )
| ~ p2(f5(f7(c11)),f5(c11))
| p2(f5(c11),f5(c11)) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
p2(f5(c11),f5(c11)),
inference(unit_resolution,[status(thm)],[99,42,93]) ).
tff(101,plain,
^ [X6: $i,X4: $i,X5: $i] :
refl(
( ( p10(f9(X4,X6),X5)
| ~ p10(X4,f3(X5,X6)) )
<=> ( p10(f9(X4,X6),X5)
| ~ p10(X4,f3(X5,X6)) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [X6: $i,X4: $i,X5: $i] :
( p10(f9(X4,X6),X5)
| ~ p10(X4,f3(X5,X6)) )
<=> ! [X6: $i,X4: $i,X5: $i] :
( p10(f9(X4,X6),X5)
| ~ p10(X4,f3(X5,X6)) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [X6: $i,X4: $i,X5: $i] :
( p10(f9(X4,X6),X5)
| ~ p10(X4,f3(X5,X6)) )
<=> ! [X6: $i,X4: $i,X5: $i] :
( p10(f9(X4,X6),X5)
| ~ p10(X4,f3(X5,X6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,axiom,
! [X6: $i,X4: $i,X5: $i] :
( p10(f9(X4,X6),X5)
| ~ p10(X4,f3(X5,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_13) ).
tff(105,plain,
! [X6: $i,X4: $i,X5: $i] :
( p10(f9(X4,X6),X5)
| ~ p10(X4,f3(X5,X6)) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [X6: $i,X4: $i,X5: $i] :
( p10(f9(X4,X6),X5)
| ~ p10(X4,f3(X5,X6)) ),
inference(skolemize,[status(sab)],[105]) ).
tff(107,plain,
! [X6: $i,X4: $i,X5: $i] :
( p10(f9(X4,X6),X5)
| ~ p10(X4,f3(X5,X6)) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
( ~ p10(f9(f5(c11),f5(c12)),f5(f8(c12,c11)))
<=> ~ p10(f9(f5(c11),f5(c12)),f5(f8(c12,c11))) ),
inference(rewrite,[status(thm)],]) ).
tff(109,axiom,
~ p10(f9(f5(c11),f5(c12)),f5(f8(c12,c11))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p10_11) ).
tff(110,plain,
~ p10(f9(f5(c11),f5(c12)),f5(f8(c12,c11))),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
( ( ~ ! [X6: $i,X4: $i,X5: $i] :
( p10(f9(X4,X6),X5)
| ~ p10(X4,f3(X5,X6)) )
| p10(f9(f5(c11),f5(c12)),f5(f8(c12,c11)))
| ~ p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12))) )
<=> ( ~ ! [X6: $i,X4: $i,X5: $i] :
( p10(f9(X4,X6),X5)
| ~ p10(X4,f3(X5,X6)) )
| p10(f9(f5(c11),f5(c12)),f5(f8(c12,c11)))
| ~ p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ~ ! [X6: $i,X4: $i,X5: $i] :
( p10(f9(X4,X6),X5)
| ~ p10(X4,f3(X5,X6)) )
| p10(f9(f5(c11),f5(c12)),f5(f8(c12,c11)))
| ~ p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12))) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
( ~ ! [X6: $i,X4: $i,X5: $i] :
( p10(f9(X4,X6),X5)
| ~ p10(X4,f3(X5,X6)) )
| p10(f9(f5(c11),f5(c12)),f5(f8(c12,c11)))
| ~ p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12))) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
~ p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12))),
inference(unit_resolution,[status(thm)],[113,110,107]) ).
tff(115,plain,
^ [X0: $i,X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) )
<=> ( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) ) )),
inference(bind,[status(th)],]) ).
tff(116,plain,
( ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) )
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) )
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
^ [X0: $i,X3: $i,X2: $i,X1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p10(X0,X1)
| ~ p2(X2,X0) )
<=> ( ~ p2(X2,X0)
| p10(X0,X1) ) )),
( ( p10(X0,X1)
| ~ p2(X2,X0)
| ~ p2(X3,X1) )
<=> ( ~ p2(X2,X0)
| p10(X0,X1)
| ~ p2(X3,X1) ) )),
rewrite(
( ( ~ p2(X2,X0)
| p10(X0,X1)
| ~ p2(X3,X1) )
<=> ( ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ) )),
( ( p10(X0,X1)
| ~ p2(X2,X0)
| ~ p2(X3,X1) )
<=> ( ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ) )),
( ( p10(X0,X1)
| ~ p2(X2,X0)
| ~ p2(X3,X1)
| ~ p10(X2,X3) )
<=> ( ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1)
| ~ p10(X2,X3) ) )),
rewrite(
( ( ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1)
| ~ p10(X2,X3) )
<=> ( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) ) )),
( ( p10(X0,X1)
| ~ p2(X2,X0)
| ~ p2(X3,X1)
| ~ p10(X2,X3) )
<=> ( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) ) )),
inference(bind,[status(th)],]) ).
tff(119,plain,
( ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( p10(X0,X1)
| ~ p2(X2,X0)
| ~ p2(X3,X1)
| ~ p10(X2,X3) )
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,axiom,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( p10(X0,X1)
| ~ p2(X2,X0)
| ~ p2(X3,X1)
| ~ p10(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_14) ).
tff(121,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) ),
inference(modus_ponens,[status(thm)],[121,117]) ).
tff(123,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) ),
inference(modus_ponens,[status(thm)],[123,116]) ).
tff(125,plain,
( ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) )
| p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12)))
| ~ p10(f5(c11),f3(f5(f6(c11,f7(c12))),f5(f7(c12))))
| ~ p2(f5(c11),f5(c11))
| ~ p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12))) )
<=> ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) )
| p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12)))
| ~ p10(f5(c11),f3(f5(f6(c11,f7(c12))),f5(f7(c12))))
| ~ p2(f5(c11),f5(c11))
| ~ p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ( ~ p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12)))
| ~ p10(f5(c11),f3(f5(f6(c11,f7(c12))),f5(f7(c12))))
| ~ p2(f5(c11),f5(c11))
| p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12))) )
<=> ( p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12)))
| ~ p10(f5(c11),f3(f5(f6(c11,f7(c12))),f5(f7(c12))))
| ~ p2(f5(c11),f5(c11))
| ~ p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
( ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) )
| ~ p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12)))
| ~ p10(f5(c11),f3(f5(f6(c11,f7(c12))),f5(f7(c12))))
| ~ p2(f5(c11),f5(c11))
| p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12))) )
<=> ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) )
| p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12)))
| ~ p10(f5(c11),f3(f5(f6(c11,f7(c12))),f5(f7(c12))))
| ~ p2(f5(c11),f5(c11))
| ~ p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12))) ) ),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
( ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) )
| ~ p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12)))
| ~ p10(f5(c11),f3(f5(f6(c11,f7(c12))),f5(f7(c12))))
| ~ p2(f5(c11),f5(c11))
| p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12))) )
<=> ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) )
| p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12)))
| ~ p10(f5(c11),f3(f5(f6(c11,f7(c12))),f5(f7(c12))))
| ~ p2(f5(c11),f5(c11))
| ~ p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12))) ) ),
inference(transitivity,[status(thm)],[127,125]) ).
tff(129,plain,
( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) )
| ~ p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12)))
| ~ p10(f5(c11),f3(f5(f6(c11,f7(c12))),f5(f7(c12))))
| ~ p2(f5(c11),f5(c11))
| p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12))) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p2(X3,X1)
| ~ p10(X2,X3)
| ~ p2(X2,X0)
| p10(X0,X1) )
| p10(f5(c11),f3(f5(f8(c12,c11)),f5(c12)))
| ~ p10(f5(c11),f3(f5(f6(c11,f7(c12))),f5(f7(c12))))
| ~ p2(f5(c11),f5(c11))
| ~ p2(f3(f5(f6(c11,f7(c12))),f5(f7(c12))),f3(f5(f8(c12,c11)),f5(c12))) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
$false,
inference(unit_resolution,[status(thm)],[130,124,114,100,91,82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN565-1 : TPTP v8.1.0. Released v2.5.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n013.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 : Mon Sep 5 05:42:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.57/0.62 % SZS status Unsatisfiable
% 0.57/0.62 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------