TSTP Solution File: SYN561-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN561-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 23:56:25 EDT 2022
% Result : Unsatisfiable 1.27s 1.03s
% Output : Proof 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 50
% Syntax : Number of formulae : 89 ( 25 unt; 15 typ; 0 def)
% Number of atoms : 447 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 703 ( 353 ~; 307 |; 0 &)
% ( 43 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 164 ( 153 !; 0 ?; 164 :)
% Comments :
%------------------------------------------------------------------------------
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(f6_type,type,
f6: ( $i * $i ) > $i ).
tff(c11_type,type,
c11: $i ).
tff(c15_type,type,
c15: $i ).
tff(c16_type,type,
c16: $i ).
tff(f3_type,type,
f3: ( $i * $i ) > $i ).
tff(c13_type,type,
c13: $i ).
tff(f4_type,type,
f4: $i > $i ).
tff(f5_type,type,
f5: $i > $i ).
tff(c12_type,type,
c12: $i ).
tff(p9_type,type,
p9: ( $i * $i ) > $o ).
tff(c10_type,type,
c10: $i ).
tff(p8_type,type,
p8: ( $i * $i ) > $o ).
tff(f7_type,type,
f7: ( $i * $i ) > $i ).
tff(c14_type,type,
c14: $i ).
tff(1,plain,
^ [X0: $i] :
refl(
( p2(X0,X0)
<=> p2(X0,X0) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X0: $i] : p2(X0,X0)
<=> ! [X0: $i] : p2(X0,X0) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X0: $i] : p2(X0,X0)
<=> ! [X0: $i] : p2(X0,X0) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X0: $i] : p2(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_1) ).
tff(5,plain,
! [X0: $i] : p2(X0,X0),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X0: $i] : p2(X0,X0),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X0: $i] : p2(X0,X0),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X0: $i] : p2(X0,X0)
| p2(f6(c15,c11),f6(c15,c11)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
p2(f6(c15,c11),f6(c15,c11)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X0: $i,X2: $i,X1: $i] :
refl(
( ( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
<=> ( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X0: $i,X2: $i,X1: $i] :
trans(
monotonicity(
rewrite(
( ( p2(X1,X2)
| ~ p2(X0,X1) )
<=> ( ~ p2(X0,X1)
| p2(X1,X2) ) )),
( ( p2(X1,X2)
| ~ p2(X0,X1)
| ~ p2(X0,X2) )
<=> ( ~ p2(X0,X1)
| p2(X1,X2)
| ~ p2(X0,X2) ) )),
rewrite(
( ( ~ p2(X0,X1)
| p2(X1,X2)
| ~ p2(X0,X2) )
<=> ( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ) )),
( ( p2(X1,X2)
| ~ p2(X0,X1)
| ~ p2(X0,X2) )
<=> ( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( p2(X1,X2)
| ~ p2(X0,X1)
| ~ p2(X0,X2) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X0: $i,X2: $i,X1: $i] :
( p2(X1,X2)
| ~ p2(X0,X1)
| ~ p2(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_9) ).
tff(16,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( p2(f6(c15,c11),c16)
<=> p2(f6(c15,c11),c16) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
p2(f6(c15,c11),c16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_5) ).
tff(22,plain,
p2(f6(c15,c11),c16),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f6(c15,c11),c16)
| p2(c16,f6(c15,c11))
| ~ p2(f6(c15,c11),f6(c15,c11)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f6(c15,c11),c16)
| p2(c16,f6(c15,c11))
| ~ p2(f6(c15,c11),f6(c15,c11)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ p2(f6(c15,c11),f6(c15,c11))
| ~ p2(f6(c15,c11),c16)
| p2(c16,f6(c15,c11)) )
<=> ( ~ p2(f6(c15,c11),c16)
| p2(c16,f6(c15,c11))
| ~ p2(f6(c15,c11),f6(c15,c11)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f6(c15,c11),f6(c15,c11))
| ~ p2(f6(c15,c11),c16)
| p2(c16,f6(c15,c11)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f6(c15,c11),c16)
| p2(c16,f6(c15,c11))
| ~ p2(f6(c15,c11),f6(c15,c11)) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f6(c15,c11),f6(c15,c11))
| ~ p2(f6(c15,c11),c16)
| p2(c16,f6(c15,c11)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f6(c15,c11),c16)
| p2(c16,f6(c15,c11))
| ~ p2(f6(c15,c11),f6(c15,c11)) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f6(c15,c11),f6(c15,c11))
| ~ p2(f6(c15,c11),c16)
| p2(c16,f6(c15,c11)) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f6(c15,c11),c16)
| p2(c16,f6(c15,c11))
| ~ p2(f6(c15,c11),f6(c15,c11)) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
p2(c16,f6(c15,c11)),
inference(unit_resolution,[status(thm)],[28,22,19,9]) ).
tff(30,plain,
( ~ ! [X0: $i] : p2(X0,X0)
| p2(f3(f4(f5(c12)),c13),f3(f4(f5(c12)),c13)) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
p2(f3(f4(f5(c12)),c13),f3(f4(f5(c12)),c13)),
inference(unit_resolution,[status(thm)],[30,7]) ).
tff(32,plain,
( p2(f3(f4(f5(c12)),c13),c16)
<=> p2(f3(f4(f5(c12)),c13),c16) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
p2(f3(f4(f5(c12)),c13),c16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_6) ).
tff(34,plain,
p2(f3(f4(f5(c12)),c13),c16),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(f4(f5(c12)),c13),c16)
| p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(f3(f4(f5(c12)),c13),f3(f4(f5(c12)),c13)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(f4(f5(c12)),c13),c16)
| p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(f3(f4(f5(c12)),c13),f3(f4(f5(c12)),c13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ~ p2(f3(f4(f5(c12)),c13),f3(f4(f5(c12)),c13))
| ~ p2(f3(f4(f5(c12)),c13),c16)
| p2(c16,f3(f4(f5(c12)),c13)) )
<=> ( ~ p2(f3(f4(f5(c12)),c13),c16)
| p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(f3(f4(f5(c12)),c13),f3(f4(f5(c12)),c13)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(f4(f5(c12)),c13),f3(f4(f5(c12)),c13))
| ~ p2(f3(f4(f5(c12)),c13),c16)
| p2(c16,f3(f4(f5(c12)),c13)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(f4(f5(c12)),c13),c16)
| p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(f3(f4(f5(c12)),c13),f3(f4(f5(c12)),c13)) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(f4(f5(c12)),c13),f3(f4(f5(c12)),c13))
| ~ p2(f3(f4(f5(c12)),c13),c16)
| p2(c16,f3(f4(f5(c12)),c13)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(f4(f5(c12)),c13),c16)
| p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(f3(f4(f5(c12)),c13),f3(f4(f5(c12)),c13)) ) ),
inference(transitivity,[status(thm)],[37,35]) ).
tff(39,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(f4(f5(c12)),c13),f3(f4(f5(c12)),c13))
| ~ p2(f3(f4(f5(c12)),c13),c16)
| p2(c16,f3(f4(f5(c12)),c13)) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(f3(f4(f5(c12)),c13),c16)
| p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(f3(f4(f5(c12)),c13),f3(f4(f5(c12)),c13)) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
p2(c16,f3(f4(f5(c12)),c13)),
inference(unit_resolution,[status(thm)],[40,34,19,31]) ).
tff(42,plain,
^ [X27: $i,X28: $i] :
refl(
( ( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) )
<=> ( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) )
<=> ! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) )
<=> ! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
^ [X27: $i,X28: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ p9(X28,c10)
| ~ p8(c11,X28) )
<=> ( ~ p8(c11,X28)
| ~ p9(X28,c10) ) )),
( ( ~ p9(X28,c10)
| ~ p8(c11,X28)
| ~ p2(f7(c10,X28),X27) )
<=> ( ~ p8(c11,X28)
| ~ p9(X28,c10)
| ~ p2(f7(c10,X28),X27) ) )),
rewrite(
( ( ~ p8(c11,X28)
| ~ p9(X28,c10)
| ~ p2(f7(c10,X28),X27) )
<=> ( ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ) )),
( ( ~ p9(X28,c10)
| ~ p8(c11,X28)
| ~ p2(f7(c10,X28),X27) )
<=> ( ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ) )),
( ( ~ p9(X28,c10)
| ~ p8(c11,X28)
| ~ p2(f7(c10,X28),X27)
| ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13)) )
<=> ( ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10)
| ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13)) ) )),
rewrite(
( ( ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10)
| ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13)) )
<=> ( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ) )),
( ( ~ p9(X28,c10)
| ~ p8(c11,X28)
| ~ p2(f7(c10,X28),X27)
| ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13)) )
<=> ( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [X27: $i,X28: $i] :
( ~ p9(X28,c10)
| ~ p8(c11,X28)
| ~ p2(f7(c10,X28),X27)
| ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13)) )
<=> ! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,axiom,
! [X27: $i,X28: $i] :
( ~ p9(X28,c10)
| ~ p8(c11,X28)
| ~ p2(f7(c10,X28),X27)
| ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p9_15) ).
tff(48,plain,
! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ),
inference(modus_ponens,[status(thm)],[50,43]) ).
tff(52,plain,
( p2(f7(c10,c14),c15)
<=> p2(f7(c10,c14),c15) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
p2(f7(c10,c14),c15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_4) ).
tff(54,plain,
p2(f7(c10,c14),c15),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( p8(c11,c14)
<=> p8(c11,c14) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
p8(c11,c14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_3) ).
tff(57,plain,
p8(c11,c14),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
( p9(c14,c10)
<=> p9(c14,c10) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
p9(c14,c10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_2) ).
tff(60,plain,
p9(c14,c10),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ( ~ ! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) )
| ~ p2(f7(c10,c14),c15)
| ~ p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p8(c11,c14)
| ~ p9(c14,c10) )
<=> ( ~ ! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) )
| ~ p2(f7(c10,c14),c15)
| ~ p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p8(c11,c14)
| ~ p9(c14,c10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ( ~ p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,c14),c15)
| ~ p8(c11,c14)
| ~ p9(c14,c10) )
<=> ( ~ p2(f7(c10,c14),c15)
| ~ p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p8(c11,c14)
| ~ p9(c14,c10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ( ~ ! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) )
| ~ p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,c14),c15)
| ~ p8(c11,c14)
| ~ p9(c14,c10) )
<=> ( ~ ! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) )
| ~ p2(f7(c10,c14),c15)
| ~ p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p8(c11,c14)
| ~ p9(c14,c10) ) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ( ~ ! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) )
| ~ p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,c14),c15)
| ~ p8(c11,c14)
| ~ p9(c14,c10) )
<=> ( ~ ! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) )
| ~ p2(f7(c10,c14),c15)
| ~ p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p8(c11,c14)
| ~ p9(c14,c10) ) ),
inference(transitivity,[status(thm)],[63,61]) ).
tff(65,plain,
( ~ ! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) )
| ~ p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,c14),c15)
| ~ p8(c11,c14)
| ~ p9(c14,c10) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [X27: $i,X28: $i] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) )
| ~ p2(f7(c10,c14),c15)
| ~ p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p8(c11,c14)
| ~ p9(c14,c10) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
~ p2(f6(c15,c11),f3(f4(f5(c12)),c13)),
inference(unit_resolution,[status(thm)],[66,60,57,54,51]) ).
tff(68,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(c16,f6(c15,c11)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(c16,f6(c15,c11)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( ~ p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(c16,f6(c15,c11))
| p2(f6(c15,c11),f3(f4(f5(c12)),c13)) )
<=> ( p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(c16,f6(c15,c11)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(c16,f6(c15,c11))
| p2(f6(c15,c11),f3(f4(f5(c12)),c13)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(c16,f6(c15,c11)) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(c16,f6(c15,c11))
| p2(f6(c15,c11),f3(f4(f5(c12)),c13)) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(c16,f6(c15,c11)) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| ~ p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(c16,f6(c15,c11))
| p2(f6(c15,c11),f3(f4(f5(c12)),c13)) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) )
| p2(f6(c15,c11),f3(f4(f5(c12)),c13))
| ~ p2(c16,f3(f4(f5(c12)),c13))
| ~ p2(c16,f6(c15,c11)) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,19,67,41,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN561-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n011.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 05:41:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.27/1.03 % SZS status Unsatisfiable
% 1.27/1.03 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------