%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN557-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:34 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 32
% Syntax : Number of formulae : 68 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 276 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 372 ( 175 ~; 170 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 192 ( 178 !; 0 ?; 192 :)
% 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(c7_type,type,
c7: $i ).
tff(c9_type,type,
c9: $i ).
tff(c8_type,type,
c8: $i ).
tff(c6_type,type,
c6: $i ).
tff(1,plain,
^ [X0: $i,X2: $i,X1: $i] :
refl(( ( p2(X0,X1)
| ~ p2(f3(X0,X2),f3(X1,X2)) )
<=> ( p2(X0,X1)
| ~ p2(f3(X0,X2),f3(X1,X2)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( p2(X0,X1)
| ~ p2(f3(X0,X2),f3(X1,X2)) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( p2(X0,X1)
| ~ p2(f3(X0,X2),f3(X1,X2)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( p2(X0,X1)
| ~ p2(f3(X0,X2),f3(X1,X2)) )
<=> ! [X0: $i,X2: $i,X1: $i] :
( p2(X0,X1)
| ~ p2(f3(X0,X2),f3(X1,X2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X0: $i,X2: $i,X1: $i] :
( p2(X0,X1)
| ~ p2(f3(X0,X2),f3(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_8) ).
tff(5,plain,
! [X0: $i,X2: $i,X1: $i] :
( p2(X0,X1)
| ~ p2(f3(X0,X2),f3(X1,X2)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X0: $i,X2: $i,X1: $i] :
( p2(X0,X1)
| ~ p2(f3(X0,X2),f3(X1,X2)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X0: $i,X2: $i,X1: $i] :
( p2(X0,X1)
| ~ p2(f3(X0,X2),f3(X1,X2)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ p2(c6,f3(c8,f5(c9)))
<=> ~ p2(c6,f3(c8,f5(c9))) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
~ p2(c6,f3(c8,f5(c9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p2_3) ).
tff(10,plain,
~ p2(c6,f3(c8,f5(c9))),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( ~ ! [X0: $i,X2: $i,X1: $i] :
( p2(X0,X1)
| ~ p2(f3(X0,X2),f3(X1,X2)) )
| p2(c6,f3(c8,f5(c9)))
| ~ p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7))) )
<=> ( ~ ! [X0: $i,X2: $i,X1: $i] :
( p2(X0,X1)
| ~ p2(f3(X0,X2),f3(X1,X2)) )
| p2(c6,f3(c8,f5(c9)))
| ~ p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( p2(X0,X1)
| ~ p2(f3(X0,X2),f3(X1,X2)) )
| p2(c6,f3(c8,f5(c9)))
| ~ p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [X0: $i,X2: $i,X1: $i] :
( p2(X0,X1)
| ~ p2(f3(X0,X2),f3(X1,X2)) )
| p2(c6,f3(c8,f5(c9)))
| ~ p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7))) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7))),
inference(unit_resolution,[status(thm)],[13,10,7]) ).
tff(15,plain,
^ [X11: $i,X10: $i] :
refl(( p2(f3(X10,X11),f3(X11,X10))
<=> p2(f3(X10,X11),f3(X11,X10)) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [X11: $i,X10: $i] : p2(f3(X10,X11),f3(X11,X10))
<=> ! [X11: $i,X10: $i] : p2(f3(X10,X11),f3(X11,X10)) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X11: $i,X10: $i] : p2(f3(X10,X11),f3(X11,X10))
<=> ! [X11: $i,X10: $i] : p2(f3(X10,X11),f3(X11,X10)) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [X11: $i,X10: $i] : p2(f3(X10,X11),f3(X11,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_4) ).
tff(19,plain,
! [X11: $i,X10: $i] : p2(f3(X10,X11),f3(X11,X10)),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X11: $i,X10: $i] : p2(f3(X10,X11),f3(X11,X10)),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [X11: $i,X10: $i] : p2(f3(X10,X11),f3(X11,X10)),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [X11: $i,X10: $i] : p2(f3(X10,X11),f3(X11,X10))
| p2(f3(f5(c7),f3(c8,f5(c9))),f3(f3(c8,f5(c9)),f5(c7))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
p2(f3(f5(c7),f3(c8,f5(c9))),f3(f3(c8,f5(c9)),f5(c7))),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
^ [X14: $i,X12: $i,X13: $i] :
refl(( p2(f3(X12,f3(X13,X14)),f3(X13,f3(X12,X14)))
<=> p2(f3(X12,f3(X13,X14)),f3(X13,f3(X12,X14))) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [X14: $i,X12: $i,X13: $i] : p2(f3(X12,f3(X13,X14)),f3(X13,f3(X12,X14)))
<=> ! [X14: $i,X12: $i,X13: $i] : p2(f3(X12,f3(X13,X14)),f3(X13,f3(X12,X14))) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X14: $i,X12: $i,X13: $i] : p2(f3(X12,f3(X13,X14)),f3(X13,f3(X12,X14)))
<=> ! [X14: $i,X12: $i,X13: $i] : p2(f3(X12,f3(X13,X14)),f3(X13,f3(X12,X14))) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
! [X14: $i,X12: $i,X13: $i] : p2(f3(X12,f3(X13,X14)),f3(X13,f3(X12,X14))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_10) ).
tff(28,plain,
! [X14: $i,X12: $i,X13: $i] : p2(f3(X12,f3(X13,X14)),f3(X13,f3(X12,X14))),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [X14: $i,X12: $i,X13: $i] : p2(f3(X12,f3(X13,X14)),f3(X13,f3(X12,X14))),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [X14: $i,X12: $i,X13: $i] : p2(f3(X12,f3(X13,X14)),f3(X13,f3(X12,X14))),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [X14: $i,X12: $i,X13: $i] : p2(f3(X12,f3(X13,X14)),f3(X13,f3(X12,X14)))
| p2(f3(f5(c7),f3(c8,f5(c9))),f3(c8,f3(f5(c7),f5(c9)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
p2(f3(f5(c7),f3(c8,f5(c9))),f3(c8,f3(f5(c7),f5(c9)))),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
^ [X4: $i,X3: $i,X5: $i] :
refl(( ( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
<=> ( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
<=> ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
<=> ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
^ [X4: $i,X3: $i,X5: $i] :
trans(monotonicity(rewrite(( ( p2(X4,X5)
| ~ p2(X3,X4) )
<=> ( ~ p2(X3,X4)
| p2(X4,X5) ) )),
( ( p2(X4,X5)
| ~ p2(X3,X4)
| ~ p2(X3,X5) )
<=> ( ~ p2(X3,X4)
| p2(X4,X5)
| ~ p2(X3,X5) ) )),
rewrite(( ( ~ p2(X3,X4)
| p2(X4,X5)
| ~ p2(X3,X5) )
<=> ( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) ) )),
( ( p2(X4,X5)
| ~ p2(X3,X4)
| ~ p2(X3,X5) )
<=> ( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [X4: $i,X3: $i,X5: $i] :
( p2(X4,X5)
| ~ p2(X3,X4)
| ~ p2(X3,X5) )
<=> ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [X4: $i,X3: $i,X5: $i] :
( p2(X4,X5)
| ~ p2(X3,X4)
| ~ p2(X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_6) ).
tff(39,plain,
! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(f5(c7),f3(c8,f5(c9))),f3(f3(c8,f5(c9)),f5(c7)))
| ~ p2(f3(f5(c7),f3(c8,f5(c9))),f3(c8,f3(f5(c7),f5(c9))))
| p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7))) )
<=> ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(f5(c7),f3(c8,f5(c9))),f3(f3(c8,f5(c9)),f5(c7)))
| ~ p2(f3(f5(c7),f3(c8,f5(c9))),f3(c8,f3(f5(c7),f5(c9))))
| p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(f5(c7),f3(c8,f5(c9))),f3(f3(c8,f5(c9)),f5(c7)))
| ~ p2(f3(f5(c7),f3(c8,f5(c9))),f3(c8,f3(f5(c7),f5(c9))))
| p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(f5(c7),f3(c8,f5(c9))),f3(f3(c8,f5(c9)),f5(c7)))
| ~ p2(f3(f5(c7),f3(c8,f5(c9))),f3(c8,f3(f5(c7),f5(c9))))
| p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7))) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7))),
inference(unit_resolution,[status(thm)],[45,42,32,23]) ).
tff(47,plain,
( ~ ! [X11: $i,X10: $i] : p2(f3(X10,X11),f3(X11,X10))
| p2(f3(c6,f5(c7)),f3(f5(c7),c6)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
p2(f3(c6,f5(c7)),f3(f5(c7),c6)),
inference(unit_resolution,[status(thm)],[47,21]) ).
tff(49,plain,
( p2(f3(c6,f5(c7)),f3(c8,f3(f5(c7),f5(c9))))
<=> p2(f3(c6,f5(c7)),f3(c8,f3(f5(c7),f5(c9)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
p2(f3(c6,f5(c7)),f3(c8,f3(f5(c7),f5(c9)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_12) ).
tff(51,plain,
p2(f3(c6,f5(c7)),f3(c8,f3(f5(c7),f5(c9)))),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(c6,f5(c7)),f3(c8,f3(f5(c7),f5(c9))))
| ~ p2(f3(c6,f5(c7)),f3(f5(c7),c6))
| p2(f3(f5(c7),c6),f3(c8,f3(f5(c7),f5(c9)))) )
<=> ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(c6,f5(c7)),f3(c8,f3(f5(c7),f5(c9))))
| ~ p2(f3(c6,f5(c7)),f3(f5(c7),c6))
| p2(f3(f5(c7),c6),f3(c8,f3(f5(c7),f5(c9)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(c6,f5(c7)),f3(c8,f3(f5(c7),f5(c9))))
| ~ p2(f3(c6,f5(c7)),f3(f5(c7),c6))
| p2(f3(f5(c7),c6),f3(c8,f3(f5(c7),f5(c9)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(c6,f5(c7)),f3(c8,f3(f5(c7),f5(c9))))
| ~ p2(f3(c6,f5(c7)),f3(f5(c7),c6))
| p2(f3(f5(c7),c6),f3(c8,f3(f5(c7),f5(c9)))) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
p2(f3(f5(c7),c6),f3(c8,f3(f5(c7),f5(c9)))),
inference(unit_resolution,[status(thm)],[54,42,51,48]) ).
tff(56,plain,
( ~ ! [X11: $i,X10: $i] : p2(f3(X10,X11),f3(X11,X10))
| p2(f3(f5(c7),c6),f3(c6,f5(c7))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
p2(f3(f5(c7),c6),f3(c6,f5(c7))),
inference(unit_resolution,[status(thm)],[56,21]) ).
tff(58,plain,
( ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(f5(c7),c6),f3(c6,f5(c7)))
| ~ p2(f3(f5(c7),c6),f3(c8,f3(f5(c7),f5(c9))))
| p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7))) )
<=> ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(f5(c7),c6),f3(c6,f5(c7)))
| ~ p2(f3(f5(c7),c6),f3(c8,f3(f5(c7),f5(c9))))
| p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(f5(c7),c6),f3(c6,f5(c7)))
| ~ p2(f3(f5(c7),c6),f3(c8,f3(f5(c7),f5(c9))))
| p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(f5(c7),c6),f3(c6,f5(c7)))
| ~ p2(f3(f5(c7),c6),f3(c8,f3(f5(c7),f5(c9))))
| p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7))) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7))),
inference(unit_resolution,[status(thm)],[60,42,57,55]) ).
tff(62,plain,
( ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7))) )
<=> ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7)))
| p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7))) )
<=> ( p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7)))
| p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7))) )
<=> ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7))) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7)))
| p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7))) )
<=> ( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7))) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7)))
| p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [X4: $i,X3: $i,X5: $i] :
( ~ p2(X3,X5)
| ~ p2(X3,X4)
| p2(X4,X5) )
| p2(f3(c6,f5(c7)),f3(f3(c8,f5(c9)),f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(c6,f5(c7)))
| ~ p2(f3(c8,f3(f5(c7),f5(c9))),f3(f3(c8,f5(c9)),f5(c7))) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
$false,
inference(unit_resolution,[status(thm)],[67,42,61,46,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN557-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:40:20 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% See solution above
% 0.17/0.38 % E exiting
%------------------------------------------------------------------------------