TSTP Solution File: SYN562-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN562-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 0.13s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 30
% Syntax : Number of formulae : 57 ( 16 unt; 8 typ; 0 def)
% Number of atoms : 316 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 468 ( 224 ~; 212 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 19 ( 8 avg)
% Number of FOOLs : 23 ( 23 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 6 >; 2 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-1 aty)
% Number of variables : 157 ( 142 !; 0 ?; 157 :)
% Comments :
%------------------------------------------------------------------------------
tff(p10_type,type,
p10: ( $i * $i ) > $o ).
tff(f3_type,type,
f3: $i > $i ).
tff(f4_type,type,
f4: $i > $i ).
tff(f5_type,type,
f5: $i > $i ).
tff(c12_type,type,
c12: $i ).
tff(p2_type,type,
p2: ( $i * $i ) > $o ).
tff(f7_type,type,
f7: $i > $i ).
tff(c11_type,type,
c11: $i ).
tff(1,plain,
( p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
<=> p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_15) ).
tff(3,plain,
p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X6: $i,X4: $i,X5: $i] :
refl(
( ( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) )
<=> ( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) )
<=> ! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) )
<=> ! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [X6: $i,X4: $i,X5: $i] :
trans(
monotonicity(
rewrite(
( ( p2(X5,X6)
| ~ p2(X4,X5) )
<=> ( ~ p2(X4,X5)
| p2(X5,X6) ) )),
( ( p2(X5,X6)
| ~ p2(X4,X5)
| ~ p2(X4,X6) )
<=> ( ~ p2(X4,X5)
| p2(X5,X6)
| ~ p2(X4,X6) ) )),
rewrite(
( ( ~ p2(X4,X5)
| p2(X5,X6)
| ~ p2(X4,X6) )
<=> ( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) ) )),
( ( p2(X5,X6)
| ~ p2(X4,X5)
| ~ p2(X4,X6) )
<=> ( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [X6: $i,X4: $i,X5: $i] :
( p2(X5,X6)
| ~ p2(X4,X5)
| ~ p2(X4,X6) )
<=> ! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [X6: $i,X4: $i,X5: $i] :
( p2(X5,X6)
| ~ p2(X4,X5)
| ~ p2(X4,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_12) ).
tff(10,plain,
! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) )
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) )
<=> ( ~ ! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) )
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ( ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) )
<=> ( ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ( ~ ! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) )
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) )
<=> ( ~ ! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) )
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( ~ ! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) )
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) )
<=> ( ~ ! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) )
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ) ),
inference(transitivity,[status(thm)],[16,14]) ).
tff(18,plain,
( ~ ! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) )
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [X6: $i,X4: $i,X5: $i] :
( ~ p2(X4,X5)
| ~ p2(X4,X6)
| p2(X5,X6) )
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))),
inference(unit_resolution,[status(thm)],[19,13,3]) ).
tff(21,plain,
( p10(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
<=> p10(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
p10(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_16) ).
tff(23,plain,
p10(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [X0: $i,X3: $i,X2: $i,X1: $i] :
refl(
( ( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) )
<=> ( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) )
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) )
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,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) )
<=> ( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ) )),
( ( p10(X0,X1)
| ~ p2(X2,X0)
| ~ p2(X3,X1)
| ~ p10(X2,X3) )
<=> ( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ) )),
inference(bind,[status(th)],]) ).
tff(28,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] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,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(30,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) )
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p10(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) )
<=> ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) )
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p10(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( ~ p10(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) )
<=> ( ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p10(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) )
| ~ p10(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) )
<=> ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) )
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p10(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) )
| ~ p10(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) )
<=> ( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) )
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p10(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) )
| ~ p10(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) )
| ~ p2(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p10(f7(c11),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| ~ p2(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))))
| p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))),
inference(unit_resolution,[status(thm)],[39,33,3,23,20]) ).
tff(41,plain,
^ [X22: $i] :
refl(
( ~ p10(X22,X22)
<=> ~ p10(X22,X22) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [X22: $i] : ~ p10(X22,X22)
<=> ! [X22: $i] : ~ p10(X22,X22) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [X22: $i] : ~ p10(X22,X22)
<=> ! [X22: $i] : ~ p10(X22,X22) ),
inference(rewrite,[status(thm)],]) ).
tff(44,axiom,
! [X22: $i] : ~ p10(X22,X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p10_3) ).
tff(45,plain,
! [X22: $i] : ~ p10(X22,X22),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [X22: $i] : ~ p10(X22,X22),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [X22: $i] : ~ p10(X22,X22),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [X22: $i] : ~ p10(X22,X22)
| ~ p10(f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12)))))))))))))))))),f3(f4(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(f5(c12))))))))))))))))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,47,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN562-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.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 05:47:20 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.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------