TSTP Solution File: SEU975^5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU975^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %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 : Tue May 21 04:07:08 EDT 2024
% Result : Theorem 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 26
% Syntax : Number of formulae : 50 ( 9 unt; 21 typ; 0 def)
% Number of atoms : 1309 ( 288 equ; 0 cnn)
% Maximal formula atoms : 29 ( 45 avg)
% Number of connectives : 405 ( 109 ~; 95 |; 149 &; 0 @)
% ( 10 <=>; 40 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 67 ( 66 >; 1 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 5 con; 0-6 aty)
% Number of variables : 196 ( 0 ^ 141 !; 49 ?; 196 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cR: a > a ).
thf(func_def_2,type,
cP: a > a > a ).
thf(func_def_3,type,
cL: a > a ).
thf(func_def_4,type,
cZ: a ).
thf(func_def_8,type,
sK0: a ).
thf(func_def_9,type,
sK1: a ).
thf(func_def_10,type,
sK2: ( a > $o ) > a ).
thf(func_def_11,type,
sK3: ( a > $o ) > a ).
thf(func_def_12,type,
sK4: a > $o ).
thf(func_def_13,type,
sK5: ( a > $o ) > a ).
thf(func_def_14,type,
sK6: ( a > $o ) > a ).
thf(func_def_15,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_16,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_17,type,
vAND: $o > $o > $o ).
thf(func_def_18,type,
vOR: $o > $o > $o ).
thf(func_def_19,type,
vIMP: $o > $o > $o ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(func_def_21,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f521,plain,
$false,
inference(unit_resulting_resolution,[],[f334,f101,f242,f241,f31]) ).
thf(f31,plain,
! [X2: a > $o] :
( ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,vAPP(sTfun(a,$o),a,sK2,X2))),vAPP(a,a,cR,vAPP(sTfun(a,$o),a,sK3,X2)))) )
| ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,vAPP(sTfun(a,$o),a,sK2,X2))),vAPP(a,a,cL,vAPP(sTfun(a,$o),a,sK3,X2)))) )
| ( cZ != vAPP(sTfun(a,$o),a,sK2,X2) )
| ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,sK0)),vAPP(a,a,cL,sK1))) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f15,plain,
( ! [X2: a > $o] :
( ( ( ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,vAPP(sTfun(a,$o),a,sK2,X2))),vAPP(a,a,cR,vAPP(sTfun(a,$o),a,sK3,X2)))) )
| ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,vAPP(sTfun(a,$o),a,sK2,X2))),vAPP(a,a,cL,vAPP(sTfun(a,$o),a,sK3,X2)))) )
| ( ( cZ != vAPP(sTfun(a,$o),a,sK2,X2) )
& ( cZ = vAPP(sTfun(a,$o),a,sK3,X2) ) ) )
& ( $true = vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,$o),a,sK2,X2)),vAPP(sTfun(a,$o),a,sK3,X2))) ) )
| ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,sK0)),vAPP(a,a,cL,sK1))) ) )
& ! [X6: a,X7: a] :
( ( ( $true = vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X6)),vAPP(a,a,cR,X7))) )
& ( $true = vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X6)),vAPP(a,a,cL,X7))) )
& ( ( cZ = X6 )
| ( cZ != X7 ) ) )
| ( $true != vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)) ) )
& ( $true = vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,sK0),sK1)) )
& ! [X8: a > $o] :
( ! [X9: a,X10: a] :
( ( X9 = X10 )
| ( $true != vAPP(a,$o,X8,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X9),X10)) ) )
| ( ( ( $true != vAPP(a,$o,X8,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,vAPP(sTfun(a,$o),a,sK5,X8))),vAPP(a,a,cR,vAPP(sTfun(a,$o),a,sK6,X8)))) )
| ( $true != vAPP(a,$o,X8,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,vAPP(sTfun(a,$o),a,sK5,X8))),vAPP(a,a,cL,vAPP(sTfun(a,$o),a,sK6,X8)))) )
| ( ( ( cZ != vAPP(sTfun(a,$o),a,sK6,X8) )
| ( cZ != vAPP(sTfun(a,$o),a,sK5,X8) ) )
& ( ( cZ = vAPP(sTfun(a,$o),a,sK6,X8) )
| ( cZ = vAPP(sTfun(a,$o),a,sK5,X8) ) ) ) )
& ( $true = vAPP(a,$o,X8,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,$o),a,sK5,X8)),vAPP(sTfun(a,$o),a,sK6,X8))) ) ) )
& ! [X13: a] :
( ( ( cZ != X13 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X13)),vAPP(a,a,cR,X13)) != X13 ) )
& ( ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X13)),vAPP(a,a,cR,X13)) = X13 )
| ( cZ = X13 ) ) )
& ! [X14: a,X15: a] : ( vAPP(a,a,cR,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X14),X15)) = X15 )
& ! [X16: a,X17: a] : ( vAPP(a,a,cL,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17)) = X16 )
& ( cZ = vAPP(a,a,cR,cZ) )
& ( cZ = vAPP(a,a,cL,cZ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6])],[f10,f14,f13,f12,f11]) ).
thf(f11,plain,
( ? [X0: a,X1: a] :
( ! [X2: a > $o] :
( ? [X3: a,X4: a] :
( ( ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X3)),vAPP(a,a,cR,X4))) )
| ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X3)),vAPP(a,a,cL,X4))) )
| ( ( cZ != X3 )
& ( cZ = X4 ) ) )
& ( $true = vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4)) ) )
| ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X0)),vAPP(a,a,cL,X1))) ) )
& ? [X5: a > $o] :
( ! [X6: a,X7: a] :
( ( ( $true = vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X6)),vAPP(a,a,cR,X7))) )
& ( $true = vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X6)),vAPP(a,a,cL,X7))) )
& ( ( cZ = X6 )
| ( cZ != X7 ) ) )
| ( $true != vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)) ) )
& ( $true = vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1)) ) ) )
=> ( ! [X2: a > $o] :
( ? [X3: a,X4: a] :
( ( ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X3)),vAPP(a,a,cR,X4))) )
| ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X3)),vAPP(a,a,cL,X4))) )
| ( ( cZ != X3 )
& ( cZ = X4 ) ) )
& ( $true = vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4)) ) )
| ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,sK0)),vAPP(a,a,cL,sK1))) ) )
& ? [X5: a > $o] :
( ! [X6: a,X7: a] :
( ( ( $true = vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X6)),vAPP(a,a,cR,X7))) )
& ( $true = vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X6)),vAPP(a,a,cL,X7))) )
& ( ( cZ = X6 )
| ( cZ != X7 ) ) )
| ( $true != vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)) ) )
& ( $true = vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,sK0),sK1)) ) ) ) ),
introduced(choice_axiom,[]) ).
thf(f12,plain,
! [X2: a > $o] :
( ? [X3: a,X4: a] :
( ( ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X3)),vAPP(a,a,cR,X4))) )
| ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X3)),vAPP(a,a,cL,X4))) )
| ( ( cZ != X3 )
& ( cZ = X4 ) ) )
& ( $true = vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4)) ) )
=> ( ( ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,vAPP(sTfun(a,$o),a,sK2,X2))),vAPP(a,a,cR,vAPP(sTfun(a,$o),a,sK3,X2)))) )
| ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,vAPP(sTfun(a,$o),a,sK2,X2))),vAPP(a,a,cL,vAPP(sTfun(a,$o),a,sK3,X2)))) )
| ( ( cZ != vAPP(sTfun(a,$o),a,sK2,X2) )
& ( cZ = vAPP(sTfun(a,$o),a,sK3,X2) ) ) )
& ( $true = vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,$o),a,sK2,X2)),vAPP(sTfun(a,$o),a,sK3,X2))) ) ) ),
introduced(choice_axiom,[]) ).
thf(f13,plain,
( ? [X5: a > $o] :
( ! [X6: a,X7: a] :
( ( ( $true = vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X6)),vAPP(a,a,cR,X7))) )
& ( $true = vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X6)),vAPP(a,a,cL,X7))) )
& ( ( cZ = X6 )
| ( cZ != X7 ) ) )
| ( $true != vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)) ) )
& ( $true = vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,sK0),sK1)) ) )
=> ( ! [X7: a,X6: a] :
( ( ( $true = vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X6)),vAPP(a,a,cR,X7))) )
& ( $true = vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X6)),vAPP(a,a,cL,X7))) )
& ( ( cZ = X6 )
| ( cZ != X7 ) ) )
| ( $true != vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)) ) )
& ( $true = vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,sK0),sK1)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f14,plain,
! [X8: a > $o] :
( ? [X11: a,X12: a] :
( ( ( $true != vAPP(a,$o,X8,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X11)),vAPP(a,a,cR,X12))) )
| ( $true != vAPP(a,$o,X8,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X11)),vAPP(a,a,cL,X12))) )
| ( ( ( cZ != X12 )
| ( cZ != X11 ) )
& ( ( cZ = X12 )
| ( cZ = X11 ) ) ) )
& ( $true = vAPP(a,$o,X8,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X11),X12)) ) )
=> ( ( ( $true != vAPP(a,$o,X8,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,vAPP(sTfun(a,$o),a,sK5,X8))),vAPP(a,a,cR,vAPP(sTfun(a,$o),a,sK6,X8)))) )
| ( $true != vAPP(a,$o,X8,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,vAPP(sTfun(a,$o),a,sK5,X8))),vAPP(a,a,cL,vAPP(sTfun(a,$o),a,sK6,X8)))) )
| ( ( ( cZ != vAPP(sTfun(a,$o),a,sK6,X8) )
| ( cZ != vAPP(sTfun(a,$o),a,sK5,X8) ) )
& ( ( cZ = vAPP(sTfun(a,$o),a,sK6,X8) )
| ( cZ = vAPP(sTfun(a,$o),a,sK5,X8) ) ) ) )
& ( $true = vAPP(a,$o,X8,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,$o),a,sK5,X8)),vAPP(sTfun(a,$o),a,sK6,X8))) ) ) ),
introduced(choice_axiom,[]) ).
thf(f10,plain,
( ? [X0: a,X1: a] :
( ! [X2: a > $o] :
( ? [X3: a,X4: a] :
( ( ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X3)),vAPP(a,a,cR,X4))) )
| ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X3)),vAPP(a,a,cL,X4))) )
| ( ( cZ != X3 )
& ( cZ = X4 ) ) )
& ( $true = vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4)) ) )
| ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X0)),vAPP(a,a,cL,X1))) ) )
& ? [X5: a > $o] :
( ! [X6: a,X7: a] :
( ( ( $true = vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X6)),vAPP(a,a,cR,X7))) )
& ( $true = vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X6)),vAPP(a,a,cL,X7))) )
& ( ( cZ = X6 )
| ( cZ != X7 ) ) )
| ( $true != vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)) ) )
& ( $true = vAPP(a,$o,X5,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1)) ) ) )
& ! [X8: a > $o] :
( ! [X9: a,X10: a] :
( ( X9 = X10 )
| ( $true != vAPP(a,$o,X8,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X9),X10)) ) )
| ? [X11: a,X12: a] :
( ( ( $true != vAPP(a,$o,X8,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X11)),vAPP(a,a,cR,X12))) )
| ( $true != vAPP(a,$o,X8,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X11)),vAPP(a,a,cL,X12))) )
| ( ( ( cZ != X12 )
| ( cZ != X11 ) )
& ( ( cZ = X12 )
| ( cZ = X11 ) ) ) )
& ( $true = vAPP(a,$o,X8,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X11),X12)) ) ) )
& ! [X13: a] :
( ( ( cZ != X13 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X13)),vAPP(a,a,cR,X13)) != X13 ) )
& ( ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X13)),vAPP(a,a,cR,X13)) = X13 )
| ( cZ = X13 ) ) )
& ! [X14: a,X15: a] : ( vAPP(a,a,cR,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X14),X15)) = X15 )
& ! [X16: a,X17: a] : ( vAPP(a,a,cL,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17)) = X16 )
& ( cZ = vAPP(a,a,cR,cZ) )
& ( cZ = vAPP(a,a,cL,cZ) ) ),
inference(rectify,[],[f9]) ).
thf(f9,plain,
( ? [X10: a,X11: a] :
( ! [X15: a > $o] :
( ? [X16: a,X17: a] :
( ( ( $true != vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X16)),vAPP(a,a,cR,X17))) )
| ( $true != vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X16)),vAPP(a,a,cL,X17))) )
| ( ( cZ != X16 )
& ( cZ = X17 ) ) )
& ( $true = vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17)) ) )
| ( $true != vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X10)),vAPP(a,a,cL,X11))) ) )
& ? [X12: a > $o] :
( ! [X13: a,X14: a] :
( ( ( $true = vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X13)),vAPP(a,a,cR,X14))) )
& ( $true = vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X13)),vAPP(a,a,cL,X14))) )
& ( ( cZ = X13 )
| ( cZ != X14 ) ) )
| ( $true != vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X13),X14)) ) )
& ( $true = vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X10),X11)) ) ) )
& ! [X0: a > $o] :
( ! [X3: a,X4: a] :
( ( X3 = X4 )
| ( $true != vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4)) ) )
| ? [X1: a,X2: a] :
( ( ( $true != vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X1)),vAPP(a,a,cR,X2))) )
| ( $true != vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X1)),vAPP(a,a,cL,X2))) )
| ( ( ( cZ != X2 )
| ( cZ != X1 ) )
& ( ( cZ = X2 )
| ( cZ = X1 ) ) ) )
& ( $true = vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X2)) ) ) )
& ! [X5: a] :
( ( ( cZ != X5 )
| ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X5)),vAPP(a,a,cR,X5)) != X5 ) )
& ( ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X5)),vAPP(a,a,cR,X5)) = X5 )
| ( cZ = X5 ) ) )
& ! [X6: a,X7: a] : ( vAPP(a,a,cR,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)) = X7 )
& ! [X8: a,X9: a] : ( vAPP(a,a,cL,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9)) = X8 )
& ( cZ = vAPP(a,a,cR,cZ) )
& ( cZ = vAPP(a,a,cL,cZ) ) ),
inference(nnf_transformation,[],[f8]) ).
thf(f8,plain,
( ? [X10: a,X11: a] :
( ! [X15: a > $o] :
( ? [X16: a,X17: a] :
( ( ( $true != vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X16)),vAPP(a,a,cR,X17))) )
| ( $true != vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X16)),vAPP(a,a,cL,X17))) )
| ( ( cZ != X16 )
& ( cZ = X17 ) ) )
& ( $true = vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17)) ) )
| ( $true != vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X10)),vAPP(a,a,cL,X11))) ) )
& ? [X12: a > $o] :
( ! [X13: a,X14: a] :
( ( ( $true = vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X13)),vAPP(a,a,cR,X14))) )
& ( $true = vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X13)),vAPP(a,a,cL,X14))) )
& ( ( cZ = X13 )
| ( cZ != X14 ) ) )
| ( $true != vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X13),X14)) ) )
& ( $true = vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X10),X11)) ) ) )
& ! [X0: a > $o] :
( ! [X3: a,X4: a] :
( ( X3 = X4 )
| ( $true != vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4)) ) )
| ? [X1: a,X2: a] :
( ( ( $true != vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X1)),vAPP(a,a,cR,X2))) )
| ( $true != vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X1)),vAPP(a,a,cL,X2))) )
| ( ( cZ = X1 )
<~> ( cZ = X2 ) ) )
& ( $true = vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X2)) ) ) )
& ! [X5: a] :
( ( cZ != X5 )
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X5)),vAPP(a,a,cR,X5)) = X5 ) )
& ! [X6: a,X7: a] : ( vAPP(a,a,cR,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)) = X7 )
& ! [X8: a,X9: a] : ( vAPP(a,a,cL,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9)) = X8 )
& ( cZ = vAPP(a,a,cR,cZ) )
& ( cZ = vAPP(a,a,cL,cZ) ) ),
inference(flattening,[],[f7]) ).
thf(f7,plain,
( ? [X10: a,X11: a] :
( ! [X15: a > $o] :
( ? [X16: a,X17: a] :
( ( ( $true != vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X16)),vAPP(a,a,cR,X17))) )
| ( $true != vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X16)),vAPP(a,a,cL,X17))) )
| ( ( cZ != X16 )
& ( cZ = X17 ) ) )
& ( $true = vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17)) ) )
| ( $true != vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X10)),vAPP(a,a,cL,X11))) ) )
& ? [X12: a > $o] :
( ! [X13: a,X14: a] :
( ( ( $true = vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X13)),vAPP(a,a,cR,X14))) )
& ( $true = vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X13)),vAPP(a,a,cL,X14))) )
& ( ( cZ = X13 )
| ( cZ != X14 ) ) )
| ( $true != vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X13),X14)) ) )
& ( $true = vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X10),X11)) ) ) )
& ! [X0: a > $o] :
( ! [X3: a,X4: a] :
( ( X3 = X4 )
| ( $true != vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4)) ) )
| ? [X1: a,X2: a] :
( ( ( $true != vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X1)),vAPP(a,a,cR,X2))) )
| ( $true != vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X1)),vAPP(a,a,cL,X2))) )
| ( ( cZ = X1 )
<~> ( cZ = X2 ) ) )
& ( $true = vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X2)) ) ) )
& ! [X5: a] :
( ( cZ != X5 )
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X5)),vAPP(a,a,cR,X5)) = X5 ) )
& ! [X6: a,X7: a] : ( vAPP(a,a,cR,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)) = X7 )
& ! [X8: a,X9: a] : ( vAPP(a,a,cL,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9)) = X8 )
& ( cZ = vAPP(a,a,cR,cZ) )
& ( cZ = vAPP(a,a,cL,cZ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: a > $o] :
( ! [X1: a,X2: a] :
( ( $true = vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X2)) )
=> ( ( $true = vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X1)),vAPP(a,a,cR,X2))) )
& ( $true = vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X1)),vAPP(a,a,cL,X2))) )
& ( ( cZ = X1 )
<=> ( cZ = X2 ) ) ) )
=> ! [X3: a,X4: a] :
( ( $true = vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4)) )
=> ( X3 = X4 ) ) )
& ! [X5: a] :
( ( cZ != X5 )
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X5)),vAPP(a,a,cR,X5)) = X5 ) )
& ! [X6: a,X7: a] : ( vAPP(a,a,cR,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)) = X7 )
& ! [X8: a,X9: a] : ( vAPP(a,a,cL,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9)) = X8 )
& ( cZ = vAPP(a,a,cR,cZ) )
& ( cZ = vAPP(a,a,cL,cZ) ) )
=> ! [X10: a,X11: a] :
( ? [X12: a > $o] :
( ! [X13: a,X14: a] :
( ( $true = vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X13),X14)) )
=> ( ( $true = vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X13)),vAPP(a,a,cR,X14))) )
& ( $true = vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X13)),vAPP(a,a,cL,X14))) )
& ( ( cZ = X14 )
=> ( cZ = X13 ) ) ) )
& ( $true = vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X10),X11)) ) )
=> ? [X15: a > $o] :
( ! [X16: a,X17: a] :
( ( $true = vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17)) )
=> ( ( $true = vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X16)),vAPP(a,a,cR,X17))) )
& ( $true = vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X16)),vAPP(a,a,cL,X17))) )
& ( ( cZ = X17 )
=> ( cZ = X16 ) ) ) )
& ( $true = vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X10)),vAPP(a,a,cL,X11))) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: a > $o] :
( ! [X1: a,X2: a] :
( vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X1),X2))
=> ( vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X1)),vAPP(a,a,cR,X2)))
& vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X1)),vAPP(a,a,cL,X2)))
& ( ( cZ = X1 )
<=> ( cZ = X2 ) ) ) )
=> ! [X3: a,X4: a] :
( vAPP(a,$o,X0,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X3),X4))
=> ( X3 = X4 ) ) )
& ! [X5: a] :
( ( cZ != X5 )
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X5)),vAPP(a,a,cR,X5)) = X5 ) )
& ! [X6: a,X7: a] : ( vAPP(a,a,cR,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)) = X7 )
& ! [X8: a,X9: a] : ( vAPP(a,a,cL,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X8),X9)) = X8 )
& ( cZ = vAPP(a,a,cR,cZ) )
& ( cZ = vAPP(a,a,cL,cZ) ) )
=> ! [X10: a,X11: a] :
( ? [X12: a > $o] :
( ! [X13: a,X14: a] :
( vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X13),X14))
=> ( vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X13)),vAPP(a,a,cR,X14)))
& vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X13)),vAPP(a,a,cL,X14)))
& ( ( cZ = X14 )
=> ( cZ = X13 ) ) ) )
& vAPP(a,$o,X12,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X10),X11)) )
=> ? [X15: a > $o] :
( ! [X16: a,X17: a] :
( vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X16),X17))
=> ( vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X16)),vAPP(a,a,cR,X17)))
& vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X16)),vAPP(a,a,cL,X17)))
& ( ( cZ = X17 )
=> ( cZ = X16 ) ) ) )
& vAPP(a,$o,X15,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X10)),vAPP(a,a,cL,X11))) ) ) ),
inference(rectify,[],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: a > $o] :
( ! [X2: a,X4: a] :
( vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),X4))
=> ( vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X2)),vAPP(a,a,cR,X4)))
& vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X2)),vAPP(a,a,cL,X4)))
& ( ( cZ = X2 )
<=> ( cZ = X4 ) ) ) )
=> ! [X2: a,X4: a] :
( vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),X4))
=> ( X2 = X4 ) ) )
& ! [X2: a] :
( ( cZ != X2 )
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X2)),vAPP(a,a,cR,X2)) = X2 ) )
& ! [X0: a,X1: a] : ( vAPP(a,a,cR,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1)) = X1 )
& ! [X0: a,X1: a] : ( vAPP(a,a,cL,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1)) = X0 )
& ( cZ = vAPP(a,a,cR,cZ) )
& ( cZ = vAPP(a,a,cL,cZ) ) )
=> ! [X0: a,X1: a] :
( ? [X3: a > $o] :
( ! [X2: a,X4: a] :
( vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),X4))
=> ( vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X2)),vAPP(a,a,cR,X4)))
& vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X2)),vAPP(a,a,cL,X4)))
& ( ( cZ = X4 )
=> ( cZ = X2 ) ) ) )
& vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1)) )
=> ? [X3: a > $o] :
( ! [X2: a,X4: a] :
( vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),X4))
=> ( vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X2)),vAPP(a,a,cR,X4)))
& vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X2)),vAPP(a,a,cL,X4)))
& ( ( cZ = X4 )
=> ( cZ = X2 ) ) ) )
& vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X0)),vAPP(a,a,cL,X1))) ) ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
( ( ! [X3: a > $o] :
( ! [X2: a,X4: a] :
( vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),X4))
=> ( vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X2)),vAPP(a,a,cR,X4)))
& vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X2)),vAPP(a,a,cL,X4)))
& ( ( cZ = X2 )
<=> ( cZ = X4 ) ) ) )
=> ! [X2: a,X4: a] :
( vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),X4))
=> ( X2 = X4 ) ) )
& ! [X2: a] :
( ( cZ != X2 )
<=> ( vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X2)),vAPP(a,a,cR,X2)) = X2 ) )
& ! [X0: a,X1: a] : ( vAPP(a,a,cR,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1)) = X1 )
& ! [X0: a,X1: a] : ( vAPP(a,a,cL,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1)) = X0 )
& ( cZ = vAPP(a,a,cR,cZ) )
& ( cZ = vAPP(a,a,cL,cZ) ) )
=> ! [X0: a,X1: a] :
( ? [X3: a > $o] :
( ! [X2: a,X4: a] :
( vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),X4))
=> ( vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X2)),vAPP(a,a,cR,X4)))
& vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X2)),vAPP(a,a,cL,X4)))
& ( ( cZ = X4 )
=> ( cZ = X2 ) ) ) )
& vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X0),X1)) )
=> ? [X3: a > $o] :
( ! [X2: a,X4: a] :
( vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X2),X4))
=> ( vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X2)),vAPP(a,a,cR,X4)))
& vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X2)),vAPP(a,a,cL,X4)))
& ( ( cZ = X4 )
=> ( cZ = X2 ) ) ) )
& vAPP(a,$o,X3,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X0)),vAPP(a,a,cL,X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPU_LEM2B_pme) ).
thf(f241,plain,
$true = vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,vAPP(sTfun(a,$o),a,sK2,sK4))),vAPP(a,a,cR,vAPP(sTfun(a,$o),a,sK3,sK4)))),
inference(unit_resulting_resolution,[],[f230,f28]) ).
thf(f28,plain,
! [X6: a,X7: a] :
( ( $true != vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)) )
| ( $true = vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,X6)),vAPP(a,a,cR,X7))) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f230,plain,
$true = vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,$o),a,sK2,sK4)),vAPP(sTfun(a,$o),a,sK3,sK4))),
inference(unit_resulting_resolution,[],[f101,f29]) ).
thf(f29,plain,
! [X2: a > $o] :
( ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,sK0)),vAPP(a,a,cL,sK1))) )
| ( $true = vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,$o),a,sK2,X2)),vAPP(sTfun(a,$o),a,sK3,X2))) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f242,plain,
$true = vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,vAPP(sTfun(a,$o),a,sK2,sK4))),vAPP(a,a,cL,vAPP(sTfun(a,$o),a,sK3,sK4)))),
inference(unit_resulting_resolution,[],[f230,f27]) ).
thf(f27,plain,
! [X6: a,X7: a] :
( ( $true != vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)) )
| ( $true = vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,X6)),vAPP(a,a,cL,X7))) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f101,plain,
$true = vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,sK0)),vAPP(a,a,cL,sK1))),
inference(unit_resulting_resolution,[],[f25,f27]) ).
thf(f25,plain,
$true = vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,sK0),sK1)),
inference(cnf_transformation,[],[f15]) ).
thf(f334,plain,
cZ = vAPP(sTfun(a,$o),a,sK2,sK4),
inference(unit_resulting_resolution,[],[f330,f32]) ).
thf(f32,plain,
! [X6: a] :
( ( $true != vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),cZ)) )
| ( cZ = X6 ) ),
inference(equality_resolution,[],[f26]) ).
thf(f26,plain,
! [X6: a,X7: a] :
( ( cZ = X6 )
| ( cZ != X7 )
| ( $true != vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,X6),X7)) ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f330,plain,
$true = vAPP(a,$o,sK4,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(sTfun(a,$o),a,sK2,sK4)),cZ)),
inference(superposition,[],[f230,f317]) ).
thf(f317,plain,
cZ = vAPP(sTfun(a,$o),a,sK3,sK4),
inference(unit_resulting_resolution,[],[f101,f242,f241,f30]) ).
thf(f30,plain,
! [X2: a > $o] :
( ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cR,vAPP(sTfun(a,$o),a,sK2,X2))),vAPP(a,a,cR,vAPP(sTfun(a,$o),a,sK3,X2)))) )
| ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,vAPP(sTfun(a,$o),a,sK2,X2))),vAPP(a,a,cL,vAPP(sTfun(a,$o),a,sK3,X2)))) )
| ( cZ = vAPP(sTfun(a,$o),a,sK3,X2) )
| ( $true != vAPP(a,$o,X2,vAPP(a,a,vAPP(a,sTfun(a,a),cP,vAPP(a,a,cL,sK0)),vAPP(a,a,cL,sK1))) ) ),
inference(cnf_transformation,[],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU975^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 15:51:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (13240)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (13243)WARNING: value z3 for option sas not known
% 0.22/0.38 % (13244)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (13242)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (13241)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (13246)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.38 % (13243)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.38 % (13245)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.38 % (13247)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.39 % (13247)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.39 % Exception at run slice level% Exception at run slice level
% 0.22/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.39 % Exception at run slice level
% 0.22/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.39
% 0.22/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.40 % (13248)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.40 % (13249)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.22/0.40 % (13250)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.22/0.40 % (13249)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.40 % (13248)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.40 % Exception at run slice level
% 0.22/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.42 % (13251)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.22/0.43 % (13249)First to succeed.
% 0.22/0.43 % (13249)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13240"
% 0.22/0.43 % (13249)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Theorem for theBenchmark
% 0.22/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.44 % (13249)------------------------------
% 0.22/0.44 % (13249)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.44 % (13249)Termination reason: Refutation
% 0.22/0.44
% 0.22/0.44 % (13249)Memory used [KB]: 1049
% 0.22/0.44 % (13249)Time elapsed: 0.032 s
% 0.22/0.44 % (13249)Instructions burned: 63 (million)
% 0.22/0.44 % (13240)Success in time 0.055 s
%------------------------------------------------------------------------------