TSTP Solution File: SYN578-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN578-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 23:56:30 EDT 2022
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 62
% Syntax : Number of formulae : 123 ( 33 unt; 13 typ; 0 def)
% Number of atoms : 706 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 1045 ( 490 ~; 490 |; 0 &)
% ( 65 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 41 ( 41 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 267 ( 244 !; 0 ?; 267 :)
% Comments :
%------------------------------------------------------------------------------
tff(p9_type,type,
p9: ( $i * $i ) > $o ).
tff(f4_type,type,
f4: $i > $i ).
tff(c14_type,type,
c14: $i ).
tff(f8_type,type,
f8: ( $i * $i ) > $i ).
tff(c12_type,type,
c12: $i ).
tff(f5_type,type,
f5: $i > $i ).
tff(p7_type,type,
p7: ( $i * $i ) > $o ).
tff(c16_type,type,
c16: $i ).
tff(c13_type,type,
c13: $i ).
tff(p3_type,type,
p3: ( $i * $i ) > $o ).
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(p11_type,type,
p11: ( $i * $i ) > $o ).
tff(c15_type,type,
c15: $i ).
tff(1,plain,
^ [X21: $i] :
refl(
( p7(X21,X21)
<=> p7(X21,X21) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X21: $i] : p7(X21,X21)
<=> ! [X21: $i] : p7(X21,X21) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X21: $i] : p7(X21,X21)
<=> ! [X21: $i] : p7(X21,X21) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X21: $i] : p7(X21,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_2) ).
tff(5,plain,
! [X21: $i] : p7(X21,X21),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X21: $i] : p7(X21,X21),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X21: $i] : p7(X21,X21),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X21: $i] : p7(X21,X21)
| p7(c12,c12) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p7(c12,c12),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X32: $i] :
refl(
( ( p9(X32,f4(c16))
| ~ p9(X32,c13) )
<=> ( p9(X32,f4(c16))
| ~ p9(X32,c13) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X32: $i] :
( p9(X32,f4(c16))
| ~ p9(X32,c13) )
<=> ! [X32: $i] :
( p9(X32,f4(c16))
| ~ p9(X32,c13) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X32: $i] :
( p9(X32,f4(c16))
| ~ p9(X32,c13) )
<=> ! [X32: $i] :
( p9(X32,f4(c16))
| ~ p9(X32,c13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [X32: $i] :
( p9(X32,f4(c16))
| ~ p9(X32,c13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_11) ).
tff(14,plain,
! [X32: $i] :
( p9(X32,f4(c16))
| ~ p9(X32,c13) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X32: $i] :
( p9(X32,f4(c16))
| ~ p9(X32,c13) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X32: $i] :
( p9(X32,f4(c16))
| ~ p9(X32,c13) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( p9(c12,c13)
<=> p9(c12,c13) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
p9(c12,c13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_5) ).
tff(19,plain,
p9(c12,c13),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ( ~ ! [X32: $i] :
( p9(X32,f4(c16))
| ~ p9(X32,c13) )
| p9(c12,f4(c16))
| ~ p9(c12,c13) )
<=> ( ~ ! [X32: $i] :
( p9(X32,f4(c16))
| ~ p9(X32,c13) )
| p9(c12,f4(c16))
| ~ p9(c12,c13) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ ! [X32: $i] :
( p9(X32,f4(c16))
| ~ p9(X32,c13) )
| p9(c12,f4(c16))
| ~ p9(c12,c13) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [X32: $i] :
( p9(X32,f4(c16))
| ~ p9(X32,c13) )
| p9(c12,f4(c16))
| ~ p9(c12,c13) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
p9(c12,f4(c16)),
inference(unit_resolution,[status(thm)],[22,19,16]) ).
tff(24,plain,
^ [X16: $i,X15: $i] :
refl(
( ( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
<=> ( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
<=> ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
<=> ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [X16: $i,X15: $i] :
rewrite(
( ( p3(f4(X15),f4(X16))
| ~ p2(X15,X16) )
<=> ( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [X16: $i,X15: $i] :
( p3(f4(X15),f4(X16))
| ~ p2(X15,X16) )
<=> ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [X16: $i,X15: $i] :
( p3(f4(X15),f4(X16))
| ~ p2(X15,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_14) ).
tff(30,plain,
! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( p2(c16,f5(c14))
<=> p2(c16,f5(c14)) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
p2(c16,f5(c14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_7) ).
tff(36,plain,
p2(c16,f5(c14)),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( ( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(c16,f5(c14))
| p3(f4(c16),f4(f5(c14))) )
<=> ( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(c16,f5(c14))
| p3(f4(c16),f4(f5(c14))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(c16,f5(c14))
| p3(f4(c16),f4(f5(c14))) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [X16: $i,X15: $i] :
( ~ p2(X15,X16)
| p3(f4(X15),f4(X16)) )
| ~ p2(c16,f5(c14))
| p3(f4(c16),f4(f5(c14))) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
p3(f4(c16),f4(f5(c14))),
inference(unit_resolution,[status(thm)],[39,36,33]) ).
tff(41,plain,
^ [X31: $i,X30: $i,X29: $i,X28: $i] :
refl(
( ( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
<=> ( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
<=> ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
<=> ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
^ [X31: $i,X30: $i,X29: $i,X28: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p9(X28,X29)
| ~ p7(X31,X28) )
<=> ( ~ p7(X31,X28)
| p9(X28,X29) ) )),
( ( p9(X28,X29)
| ~ p7(X31,X28)
| ~ p9(X31,X30) )
<=> ( ~ p7(X31,X28)
| p9(X28,X29)
| ~ p9(X31,X30) ) )),
rewrite(
( ( ~ p7(X31,X28)
| p9(X28,X29)
| ~ p9(X31,X30) )
<=> ( ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) ) )),
( ( p9(X28,X29)
| ~ p7(X31,X28)
| ~ p9(X31,X30) )
<=> ( ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) ) )),
( ( p9(X28,X29)
| ~ p7(X31,X28)
| ~ p9(X31,X30)
| ~ p3(X30,X29) )
<=> ( ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29)
| ~ p3(X30,X29) ) )),
rewrite(
( ( ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29)
| ~ p3(X30,X29) )
<=> ( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) ) )),
( ( p9(X28,X29)
| ~ p7(X31,X28)
| ~ p9(X31,X30)
| ~ p3(X30,X29) )
<=> ( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( p9(X28,X29)
| ~ p7(X31,X28)
| ~ p9(X31,X30)
| ~ p3(X30,X29) )
<=> ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [X31: $i,X30: $i,X29: $i,X28: $i] :
( p9(X28,X29)
| ~ p7(X31,X28)
| ~ p9(X31,X30)
| ~ p3(X30,X29) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_20) ).
tff(47,plain,
! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p7(c12,c12)
| ~ p9(c12,f4(c16))
| p9(c12,f4(f5(c14)))
| ~ p3(f4(c16),f4(f5(c14))) )
<=> ( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p7(c12,c12)
| ~ p9(c12,f4(c16))
| p9(c12,f4(f5(c14)))
| ~ p3(f4(c16),f4(f5(c14))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( ~ p3(f4(c16),f4(f5(c14)))
| ~ p9(c12,f4(c16))
| ~ p7(c12,c12)
| p9(c12,f4(f5(c14))) )
<=> ( ~ p7(c12,c12)
| ~ p9(c12,f4(c16))
| p9(c12,f4(f5(c14)))
| ~ p3(f4(c16),f4(f5(c14))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p3(f4(c16),f4(f5(c14)))
| ~ p9(c12,f4(c16))
| ~ p7(c12,c12)
| p9(c12,f4(f5(c14))) )
<=> ( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p7(c12,c12)
| ~ p9(c12,f4(c16))
| p9(c12,f4(f5(c14)))
| ~ p3(f4(c16),f4(f5(c14))) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p3(f4(c16),f4(f5(c14)))
| ~ p9(c12,f4(c16))
| ~ p7(c12,c12)
| p9(c12,f4(f5(c14))) )
<=> ( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p7(c12,c12)
| ~ p9(c12,f4(c16))
| p9(c12,f4(f5(c14)))
| ~ p3(f4(c16),f4(f5(c14))) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p3(f4(c16),f4(f5(c14)))
| ~ p9(c12,f4(c16))
| ~ p7(c12,c12)
| p9(c12,f4(f5(c14))) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p7(c12,c12)
| ~ p9(c12,f4(c16))
| p9(c12,f4(f5(c14)))
| ~ p3(f4(c16),f4(f5(c14))) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
p9(c12,f4(f5(c14))),
inference(unit_resolution,[status(thm)],[56,50,40,23,9]) ).
tff(58,plain,
^ [X17: $i] :
refl(
( p3(f4(f5(X17)),f4(X17))
<=> p3(f4(f5(X17)),f4(X17)) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [X17: $i] : p3(f4(f5(X17)),f4(X17))
<=> ! [X17: $i] : p3(f4(f5(X17)),f4(X17)) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [X17: $i] : p3(f4(f5(X17)),f4(X17))
<=> ! [X17: $i] : p3(f4(f5(X17)),f4(X17)) ),
inference(rewrite,[status(thm)],]) ).
tff(61,axiom,
! [X17: $i] : p3(f4(f5(X17)),f4(X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_8) ).
tff(62,plain,
! [X17: $i] : p3(f4(f5(X17)),f4(X17)),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [X17: $i] : p3(f4(f5(X17)),f4(X17)),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [X17: $i] : p3(f4(f5(X17)),f4(X17)),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( ~ ! [X17: $i] : p3(f4(f5(X17)),f4(X17))
| p3(f4(f5(c14)),f4(c14)) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
p3(f4(f5(c14)),f4(c14)),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
( ( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p3(f4(f5(c14)),f4(c14))
| ~ p7(c12,c12)
| ~ p9(c12,f4(f5(c14)))
| p9(c12,f4(c14)) )
<=> ( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p3(f4(f5(c14)),f4(c14))
| ~ p7(c12,c12)
| ~ p9(c12,f4(f5(c14)))
| p9(c12,f4(c14)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ~ p3(f4(f5(c14)),f4(c14))
| ~ p9(c12,f4(f5(c14)))
| ~ p7(c12,c12)
| p9(c12,f4(c14)) )
<=> ( ~ p3(f4(f5(c14)),f4(c14))
| ~ p7(c12,c12)
| ~ p9(c12,f4(f5(c14)))
| p9(c12,f4(c14)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p3(f4(f5(c14)),f4(c14))
| ~ p9(c12,f4(f5(c14)))
| ~ p7(c12,c12)
| p9(c12,f4(c14)) )
<=> ( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p3(f4(f5(c14)),f4(c14))
| ~ p7(c12,c12)
| ~ p9(c12,f4(f5(c14)))
| p9(c12,f4(c14)) ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p3(f4(f5(c14)),f4(c14))
| ~ p9(c12,f4(f5(c14)))
| ~ p7(c12,c12)
| p9(c12,f4(c14)) )
<=> ( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p3(f4(f5(c14)),f4(c14))
| ~ p7(c12,c12)
| ~ p9(c12,f4(f5(c14)))
| p9(c12,f4(c14)) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,plain,
( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p3(f4(f5(c14)),f4(c14))
| ~ p9(c12,f4(f5(c14)))
| ~ p7(c12,c12)
| p9(c12,f4(c14)) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
( ~ ! [X31: $i,X30: $i,X29: $i,X28: $i] :
( ~ p3(X30,X29)
| ~ p9(X31,X30)
| ~ p7(X31,X28)
| p9(X28,X29) )
| ~ p3(f4(f5(c14)),f4(c14))
| ~ p7(c12,c12)
| ~ p9(c12,f4(f5(c14)))
| p9(c12,f4(c14)) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
p9(c12,f4(c14)),
inference(unit_resolution,[status(thm)],[72,50,66,9,57]) ).
tff(74,plain,
^ [X34: $i,X33: $i] :
refl(
( ( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) )
<=> ( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) )
<=> ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) )
<=> ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
^ [X34: $i,X33: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( p9(f8(X33,X34),X33)
| p9(f8(X33,X34),f4(X34)) )
<=> ( p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) ) )),
( ( p9(f8(X33,X34),X33)
| p9(f8(X33,X34),f4(X34))
| ~ p11(X34,c15) )
<=> ( p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33)
| ~ p11(X34,c15) ) )),
rewrite(
( ( p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33)
| ~ p11(X34,c15) )
<=> ( ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) ) )),
( ( p9(f8(X33,X34),X33)
| p9(f8(X33,X34),f4(X34))
| ~ p11(X34,c15) )
<=> ( ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) ) )),
( ( p9(f8(X33,X34),X33)
| p9(f8(X33,X34),f4(X34))
| ~ p11(X34,c15)
| ~ p9(c12,X33) )
<=> ( ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33)
| ~ p9(c12,X33) ) )),
rewrite(
( ( ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33)
| ~ p9(c12,X33) )
<=> ( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) ) )),
( ( p9(f8(X33,X34),X33)
| p9(f8(X33,X34),f4(X34))
| ~ p11(X34,c15)
| ~ p9(c12,X33) )
<=> ( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) ) )),
inference(bind,[status(th)],]) ).
tff(78,plain,
( ! [X34: $i,X33: $i] :
( p9(f8(X33,X34),X33)
| p9(f8(X33,X34),f4(X34))
| ~ p11(X34,c15)
| ~ p9(c12,X33) )
<=> ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,axiom,
! [X34: $i,X33: $i] :
( p9(f8(X33,X34),X33)
| p9(f8(X33,X34),f4(X34))
| ~ p11(X34,c15)
| ~ p9(c12,X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_22) ).
tff(80,plain,
! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
( p11(c14,c15)
<=> p11(c14,c15) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
p11(c14,c15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_6) ).
tff(86,plain,
p11(c14,c15),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( ( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) )
| p9(f8(f4(c14),c14),f4(c14))
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15) )
<=> ( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) )
| p9(f8(f4(c14),c14),f4(c14))
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ( ~ p9(c12,f4(c14))
| ~ p11(c14,c15)
| p9(f8(f4(c14),c14),f4(c14))
| p9(f8(f4(c14),c14),f4(c14)) )
<=> ( p9(f8(f4(c14),c14),f4(c14))
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) )
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15)
| p9(f8(f4(c14),c14),f4(c14))
| p9(f8(f4(c14),c14),f4(c14)) )
<=> ( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) )
| p9(f8(f4(c14),c14),f4(c14))
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) )
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15)
| p9(f8(f4(c14),c14),f4(c14))
| p9(f8(f4(c14),c14),f4(c14)) )
<=> ( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) )
| p9(f8(f4(c14),c14),f4(c14))
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15) ) ),
inference(transitivity,[status(thm)],[89,87]) ).
tff(91,plain,
( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) )
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15)
| p9(f8(f4(c14),c14),f4(c14))
| p9(f8(f4(c14),c14),f4(c14)) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| p9(f8(X33,X34),f4(X34))
| p9(f8(X33,X34),X33) )
| p9(f8(f4(c14),c14),f4(c14))
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
p9(f8(f4(c14),c14),f4(c14)),
inference(unit_resolution,[status(thm)],[92,86,83,73]) ).
tff(94,plain,
^ [X34: $i,X33: $i] :
refl(
( ( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) )
<=> ( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) ) )),
inference(bind,[status(th)],]) ).
tff(95,plain,
( ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) )
<=> ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) )
<=> ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
^ [X34: $i,X33: $i] :
trans(
monotonicity(
rewrite(
( ( ~ p11(X34,c15)
| ~ p9(c12,X33)
| ~ p9(f8(X33,X34),X33) )
<=> ( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),X33) ) )),
( ( ~ p11(X34,c15)
| ~ p9(c12,X33)
| ~ p9(f8(X33,X34),X33)
| ~ p9(f8(X33,X34),f4(X34)) )
<=> ( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),X33)
| ~ p9(f8(X33,X34),f4(X34)) ) )),
rewrite(
( ( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),X33)
| ~ p9(f8(X33,X34),f4(X34)) )
<=> ( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) ) )),
( ( ~ p11(X34,c15)
| ~ p9(c12,X33)
| ~ p9(f8(X33,X34),X33)
| ~ p9(f8(X33,X34),f4(X34)) )
<=> ( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [X34: $i,X33: $i] :
( ~ p11(X34,c15)
| ~ p9(c12,X33)
| ~ p9(f8(X33,X34),X33)
| ~ p9(f8(X33,X34),f4(X34)) )
<=> ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,axiom,
! [X34: $i,X33: $i] :
( ~ p11(X34,c15)
| ~ p9(c12,X33)
| ~ p9(f8(X33,X34),X33)
| ~ p9(f8(X33,X34),f4(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p11_23) ).
tff(100,plain,
! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) ),
inference(modus_ponens,[status(thm)],[102,95]) ).
tff(104,plain,
( ( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) )
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15)
| ~ p9(f8(f4(c14),c14),f4(c14)) )
<=> ( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) )
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15)
| ~ p9(f8(f4(c14),c14),f4(c14)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( ~ p9(c12,f4(c14))
| ~ p11(c14,c15)
| ~ p9(f8(f4(c14),c14),f4(c14))
| ~ p9(f8(f4(c14),c14),f4(c14)) )
<=> ( ~ p9(c12,f4(c14))
| ~ p11(c14,c15)
| ~ p9(f8(f4(c14),c14),f4(c14)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) )
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15)
| ~ p9(f8(f4(c14),c14),f4(c14))
| ~ p9(f8(f4(c14),c14),f4(c14)) )
<=> ( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) )
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15)
| ~ p9(f8(f4(c14),c14),f4(c14)) ) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) )
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15)
| ~ p9(f8(f4(c14),c14),f4(c14))
| ~ p9(f8(f4(c14),c14),f4(c14)) )
<=> ( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) )
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15)
| ~ p9(f8(f4(c14),c14),f4(c14)) ) ),
inference(transitivity,[status(thm)],[106,104]) ).
tff(108,plain,
( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) )
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15)
| ~ p9(f8(f4(c14),c14),f4(c14))
| ~ p9(f8(f4(c14),c14),f4(c14)) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
( ~ ! [X34: $i,X33: $i] :
( ~ p9(c12,X33)
| ~ p11(X34,c15)
| ~ p9(f8(X33,X34),f4(X34))
| ~ p9(f8(X33,X34),X33) )
| ~ p9(c12,f4(c14))
| ~ p11(c14,c15)
| ~ p9(f8(f4(c14),c14),f4(c14)) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
$false,
inference(unit_resolution,[status(thm)],[109,86,103,73,93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN578-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 05:43:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------