%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV406+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:02:16 AM UTC 2026
% Result : Theorem 29.92s 6.21s
% Output : CNFRefutation 29.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 6
% Syntax : Number of formulae : 82 ( 4 unt; 0 def)
% Number of atoms : 250 ( 45 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 244 ( 76 ~; 150 |; 2 &)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-3 aty)
% Number of variables : 133 ( 16 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(totality,axiom,
! [X0,X1] :
( 'less$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ) ).
fof(stricly_smaller_definition,axiom,
! [X0,X1] :
( 'strictly$uless$uthan'(X0,X1)
<=> ( ~ 'less$uthan'(X1,X0)
& 'less$uthan'(X0,X1) ) ) ).
fof(ax23,axiom,
! [X0,X1,X2,X3,X4] :
( 'pair$uin$ulist'('insert$uslb'(X0,pair(X1,X3)),X2,X4)
<=> ( ( X3 = X4
& X1 = X2 )
| 'pair$uin$ulist'(X0,X2,X4) ) ) ).
fof(ax37,axiom,
! [X0,X1,X2,X3,X4] :
( 'less$uthan'(X4,X3)
=> ( 'check$ucpq'(triple(X0,'insert$uslb'(X1,pair(X3,X4)),X2))
<=> 'check$ucpq'(triple(X0,X1,X2)) ) ) ).
fof(ax38,axiom,
! [X0,X1,X2,X3,X4] :
( 'strictly$uless$uthan'(X3,X4)
=> ( 'check$ucpq'(triple(X0,'insert$uslb'(X1,pair(X3,X4)),X2))
<=> $false ) ) ).
fof(l42_co,conjecture,
! [X0] :
( ! [X1,X2] :
( 'check$ucpq'(triple(X1,X0,X2))
<=> ! [X3,X4] :
( 'pair$uin$ulist'(X0,X3,X4)
=> 'less$uthan'(X4,X3) ) )
=> ! [X5,X6,X7,X8] :
( 'check$ucpq'(triple(X5,'insert$uslb'(X0,pair(X7,X8)),X6))
<=> ! [X9,X10] :
( 'pair$uin$ulist'('insert$uslb'(X0,pair(X7,X8)),X9,X10)
=> 'less$uthan'(X10,X9) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ! [X1,X2] :
( 'check$ucpq'(triple(X1,X0,X2))
<=> ! [X3,X4] :
( 'pair$uin$ulist'(X0,X3,X4)
=> 'less$uthan'(X4,X3) ) )
=> ! [X5,X6,X7,X8] :
( 'check$ucpq'(triple(X5,'insert$uslb'(X0,pair(X7,X8)),X6))
<=> ! [X9,X10] :
( 'pair$uin$ulist'('insert$uslb'(X0,pair(X7,X8)),X9,X10)
=> 'less$uthan'(X10,X9) ) ) ),
inference(negate_conjecture,[status(cth)],[l42_co]) ).
cnf(c1,plain,
( 'less$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[totality]) ).
cnf(c5,plain,
( 'less$uthan'(X1,X0)
| ~ 'less$uthan'(X0,X1)
| 'strictly$uless$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[stricly_smaller_definition]) ).
cnf(c14,plain,
( X1 = X3
| 'pair$uin$ulist'(X0,X3,X4)
| ~ 'pair$uin$ulist'('insert$uslb'(X0,pair(X1,X2)),X3,X4) ),
inference(clausification,[status(esa)],[ax23]) ).
cnf(c15,plain,
( X2 = X4
| 'pair$uin$ulist'(X0,X3,X4)
| ~ 'pair$uin$ulist'('insert$uslb'(X0,pair(X1,X2)),X3,X4) ),
inference(clausification,[status(esa)],[ax23]) ).
cnf(c16,plain,
( ~ 'pair$uin$ulist'(X0,X3,X4)
| 'pair$uin$ulist'('insert$uslb'(X0,pair(X1,X2)),X3,X4) ),
inference(clausification,[status(esa)],[ax23]) ).
cnf(c17,plain,
( X2 != X4
| X1 != X3
| 'pair$uin$ulist'('insert$uslb'(X0,pair(X1,X2)),X3,X4) ),
inference(clausification,[status(esa)],[ax23]) ).
cnf(c31,plain,
( 'check$ucpq'(triple(X2,X3,X4))
| ~ 'check$ucpq'(triple(X2,'insert$uslb'(X3,pair(X1,X0)),X4))
| ~ 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[ax37]) ).
cnf(c32,plain,
( ~ 'check$ucpq'(triple(X2,X3,X4))
| 'check$ucpq'(triple(X2,'insert$uslb'(X3,pair(X1,X0)),X4))
| ~ 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[ax37]) ).
cnf(c33,plain,
( ~ 'check$ucpq'(triple(X2,'insert$uslb'(X3,pair(X0,X1)),X4))
| ~ 'strictly$uless$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[ax38]) ).
cnf(c50,plain,
( 'less$uthan'(X3,X2)
| ~ 'pair$uin$ulist'(sK117,X2,X3)
| ~ 'check$ucpq'(triple(X0,sK117,X1)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c51,plain,
( 'pair$uin$ulist'(sK117,sK122,sK123)
| 'check$ucpq'(triple(X0,sK117,X1)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c52,plain,
( ~ 'less$uthan'(sK123,sK122)
| 'check$ucpq'(triple(X0,sK117,X1)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c54,plain,
( 'less$uthan'(X1,X0)
| ~ 'pair$uin$ulist'('insert$uslb'(sK117,pair(sK126,sK127)),X0,X1)
| 'check$ucpq'(triple(sK124,'insert$uslb'(sK117,pair(sK126,sK127)),sK125)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c55,plain,
( ~ 'check$ucpq'(triple(sK124,'insert$uslb'(sK117,pair(sK126,sK127)),sK125))
| 'pair$uin$ulist'('insert$uslb'(sK117,pair(sK126,sK127)),sK128,sK129) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c56,plain,
( 'less$uthan'(X1,X0)
| ~ 'pair$uin$ulist'('insert$uslb'(sK117,pair(sK126,sK127)),X0,X1)
| 'pair$uin$ulist'('insert$uslb'(sK117,pair(sK126,sK127)),sK128,sK129) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c57,plain,
( ~ 'check$ucpq'(triple(sK124,'insert$uslb'(sK117,pair(sK126,sK127)),sK125))
| ~ 'less$uthan'(sK129,sK128) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c58,plain,
( 'less$uthan'(X1,X0)
| ~ 'pair$uin$ulist'('insert$uslb'(sK117,pair(sK126,sK127)),X0,X1)
| ~ 'less$uthan'(sK129,sK128) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'less$uthan'(sK129,sK128)
| 'less$uthan'(X1,X0)
| ~ 'pair$uin$ulist'(sK117,X0,X1) ),
inference(resolution,[status(thm)],[c16,c58]) ).
cnf(d1,plain,
( ~ 'less$uthan'(sK129,sK128)
| ~ 'check$ucpq'(triple(sK124,sK117,sK125))
| ~ 'less$uthan'(sK127,sK126) ),
inference(resolution,[status(thm)],[c32,c57]) ).
cnf(d2,plain,
( 'less$uthan'(X0,X1)
| 'strictly$uless$uthan'(X1,X0)
| 'less$uthan'(X0,X1) ),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(d3,plain,
( ~ 'pair$uin$ulist'('insert$uslb'(sK117,pair(sK126,sK127)),X1,X0)
| 'less$uthan'(X0,X1)
| ~ 'strictly$uless$uthan'(sK126,sK127) ),
inference(resolution,[status(thm)],[c33,c54]) ).
cnf(d4,plain,
( 'pair$uin$ulist'('insert$uslb'(X2,pair(X0,X3)),X1,X3)
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[c17]) ).
cnf(d5,plain,
'pair$uin$ulist'('insert$uslb'(X0,pair(X1,X2)),X1,X2),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( ~ 'strictly$uless$uthan'(sK126,sK127)
| 'less$uthan'(sK127,sK126) ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( 'less$uthan'(sK127,sK126)
| 'less$uthan'(sK127,sK126) ),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( ~ 'check$ucpq'(triple(sK124,sK117,sK125))
| ~ 'less$uthan'(sK129,sK128) ),
inference(resolution,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
( 'pair$uin$ulist'(sK117,sK122,sK123)
| ~ 'less$uthan'(sK129,sK128) ),
inference(resolution,[status(thm)],[d8,c51]) ).
cnf(d10,plain,
( ~ 'less$uthan'(sK129,sK128)
| 'less$uthan'(sK123,sK122)
| ~ 'less$uthan'(sK129,sK128) ),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
( 'pair$uin$ulist'('insert$uslb'(sK117,pair(sK126,sK127)),sK128,sK129)
| 'less$uthan'(X1,X0)
| ~ 'pair$uin$ulist'(sK117,X0,X1) ),
inference(resolution,[status(thm)],[c16,c56]) ).
cnf(d12,plain,
( ~ 'pair$uin$ulist'(sK117,X1,X0)
| 'less$uthan'(X0,X1)
| 'pair$uin$ulist'(sK117,sK128,sK129)
| sK127 = sK129 ),
inference(resolution,[status(thm)],[c15,d11]) ).
cnf(d13,plain,
( 'pair$uin$ulist'(sK117,sK122,sK123)
| ~ 'pair$uin$ulist'(sK117,X1,X0)
| 'less$uthan'(X0,X1) ),
inference(resolution,[status(thm)],[c50,c51]) ).
cnf(d14,plain,
( 'pair$uin$ulist'('insert$uslb'(sK117,pair(sK126,sK127)),sK128,sK129)
| ~ 'check$ucpq'(triple(sK124,sK117,sK125))
| ~ 'less$uthan'(sK127,sK126) ),
inference(resolution,[status(thm)],[c32,c55]) ).
cnf(d15,plain,
( ~ 'check$ucpq'(triple(sK124,sK117,sK125))
| 'pair$uin$ulist'('insert$uslb'(sK117,pair(sK126,sK127)),sK128,sK129) ),
inference(resolution,[status(thm)],[d7,d14]) ).
cnf(d16,plain,
( 'pair$uin$ulist'(sK117,sK128,sK129)
| sK127 = sK129
| ~ 'check$ucpq'(triple(sK124,sK117,sK125)) ),
inference(resolution,[status(thm)],[d15,c15]) ).
cnf(d17,plain,
( 'pair$uin$ulist'(sK117,sK122,sK123)
| 'pair$uin$ulist'(sK117,sK128,sK129)
| sK127 = sK129 ),
inference(resolution,[status(thm)],[d16,c51]) ).
cnf(d18,plain,
( 'pair$uin$ulist'(sK117,sK122,sK123)
| 'less$uthan'(sK129,sK128)
| 'pair$uin$ulist'(sK117,sK122,sK123)
| sK127 = sK129 ),
inference(resolution,[status(thm)],[d17,d13]) ).
cnf(d19,plain,
( 'pair$uin$ulist'(sK117,sK128,sK129)
| 'less$uthan'(sK123,sK122)
| sK127 = sK129
| 'less$uthan'(sK129,sK128)
| sK127 = sK129 ),
inference(resolution,[status(thm)],[d18,d12]) ).
cnf(d20,plain,
( ~ 'pair$uin$ulist'('insert$uslb'(sK117,pair(sK126,sK127)),X1,X0)
| 'less$uthan'(X0,X1)
| 'check$ucpq'(triple(sK124,sK117,sK125))
| ~ 'less$uthan'(sK127,sK126) ),
inference(resolution,[status(thm)],[c31,c54]) ).
cnf(d21,plain,
( 'check$ucpq'(triple(sK124,sK117,sK125))
| ~ 'pair$uin$ulist'('insert$uslb'(sK117,pair(sK126,sK127)),X1,X0)
| 'less$uthan'(X0,X1) ),
inference(resolution,[status(thm)],[d7,d20]) ).
cnf(d22,plain,
( ~ 'pair$uin$ulist'(sK117,X1,X0)
| 'check$ucpq'(triple(sK124,sK117,sK125))
| 'less$uthan'(X0,X1) ),
inference(resolution,[status(thm)],[d21,c16]) ).
cnf(d23,plain,
( ~ 'pair$uin$ulist'(sK117,X3,X2)
| 'less$uthan'(X2,X3)
| ~ 'pair$uin$ulist'(sK117,X1,X0)
| 'less$uthan'(X0,X1) ),
inference(resolution,[status(thm)],[d22,c50]) ).
cnf(d24,plain,
( ~ 'pair$uin$ulist'(sK117,X1,X0)
| 'less$uthan'(sK123,sK122)
| 'less$uthan'(X0,X1)
| 'less$uthan'(sK129,sK128)
| sK127 = sK129 ),
inference(resolution,[status(thm)],[d18,d23]) ).
cnf(d25,plain,
( 'less$uthan'(sK129,sK128)
| 'less$uthan'(sK123,sK122)
| sK127 = sK129
| 'less$uthan'(sK129,sK128)
| 'less$uthan'(sK123,sK122)
| 'less$uthan'(sK129,sK128)
| sK127 = sK129 ),
inference(resolution,[status(thm)],[d24,d19]) ).
cnf(d26,plain,
( 'less$uthan'(sK123,sK122)
| 'less$uthan'(sK123,sK122)
| sK127 = sK129 ),
inference(resolution,[status(thm)],[d25,d10]) ).
cnf(d27,plain,
( ~ 'less$uthan'(sK123,sK122)
| ~ 'less$uthan'(sK129,sK128) ),
inference(resolution,[status(thm)],[d8,c52]) ).
cnf(d28,plain,
( ~ 'less$uthan'(sK123,sK122)
| ~ 'pair$uin$ulist'(sK117,X1,X0)
| 'less$uthan'(X0,X1) ),
inference(resolution,[status(thm)],[c50,c52]) ).
cnf(d29,plain,
( ~ 'less$uthan'(sK123,sK122)
| 'pair$uin$ulist'(sK117,sK128,sK129)
| sK127 = sK129 ),
inference(resolution,[status(thm)],[d16,c52]) ).
cnf(d30,plain,
( ~ 'less$uthan'(sK123,sK122)
| 'less$uthan'(sK129,sK128)
| ~ 'less$uthan'(sK123,sK122)
| sK127 = sK129 ),
inference(resolution,[status(thm)],[d29,d28]) ).
cnf(d31,plain,
( 'less$uthan'(sK129,sK128)
| sK127 = sK129
| sK127 = sK129 ),
inference(resolution,[status(thm)],[d26,d30]) ).
cnf(d32,plain,
( ~ 'less$uthan'(sK123,sK122)
| sK127 = sK129 ),
inference(resolution,[status(thm)],[d31,d27]) ).
cnf(d33,plain,
( sK127 = sK129
| sK127 = sK129 ),
inference(resolution,[status(thm)],[d32,d26]) ).
cnf(d34,plain,
( ~ 'less$uthan'(sK127,sK128)
| 'less$uthan'(sK123,sK122) ),
inference(demodulation,[status(thm)],[d10,d33]) ).
cnf(d35,plain,
( ~ 'pair$uin$ulist'(sK117,X1,X0)
| 'less$uthan'(X0,X1)
| 'pair$uin$ulist'(sK117,sK128,sK129)
| sK126 = sK128 ),
inference(resolution,[status(thm)],[c14,d11]) ).
cnf(d36,plain,
( 'pair$uin$ulist'(sK117,sK128,sK129)
| sK126 = sK128
| ~ 'check$ucpq'(triple(sK124,sK117,sK125)) ),
inference(resolution,[status(thm)],[d15,c14]) ).
cnf(d37,plain,
( 'pair$uin$ulist'(sK117,sK122,sK123)
| 'pair$uin$ulist'(sK117,sK128,sK129)
| sK126 = sK128 ),
inference(resolution,[status(thm)],[d36,c51]) ).
cnf(d38,plain,
( 'pair$uin$ulist'(sK117,sK122,sK123)
| 'less$uthan'(sK129,sK128)
| 'pair$uin$ulist'(sK117,sK122,sK123)
| sK126 = sK128 ),
inference(resolution,[status(thm)],[d37,d13]) ).
cnf(d39,plain,
( 'pair$uin$ulist'(sK117,sK128,sK129)
| 'less$uthan'(sK123,sK122)
| sK126 = sK128
| 'less$uthan'(sK129,sK128)
| sK126 = sK128 ),
inference(resolution,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
( 'pair$uin$ulist'(sK117,sK128,sK129)
| 'less$uthan'(sK127,sK128)
| 'less$uthan'(sK123,sK122)
| sK126 = sK128 ),
inference(demodulation,[status(thm)],[d39,d33]) ).
cnf(d41,plain,
( 'pair$uin$ulist'(sK117,sK128,sK127)
| 'less$uthan'(sK127,sK128)
| 'less$uthan'(sK123,sK122)
| sK126 = sK128 ),
inference(demodulation,[status(thm)],[d40,d33]) ).
cnf(d42,plain,
( ~ 'pair$uin$ulist'(sK117,X1,X0)
| 'less$uthan'(sK123,sK122)
| 'less$uthan'(X0,X1)
| 'less$uthan'(sK129,sK128)
| sK126 = sK128 ),
inference(resolution,[status(thm)],[d38,d23]) ).
cnf(d43,plain,
( ~ 'pair$uin$ulist'(sK117,X1,X0)
| 'less$uthan'(sK127,sK128)
| 'less$uthan'(sK123,sK122)
| 'less$uthan'(X0,X1)
| sK126 = sK128 ),
inference(demodulation,[status(thm)],[d42,d33]) ).
cnf(d44,plain,
( 'less$uthan'(sK127,sK128)
| 'less$uthan'(sK123,sK122)
| sK126 = sK128
| 'less$uthan'(sK127,sK128)
| 'less$uthan'(sK123,sK122)
| 'less$uthan'(sK127,sK128)
| sK126 = sK128 ),
inference(resolution,[status(thm)],[d43,d41]) ).
cnf(d45,plain,
( 'less$uthan'(sK123,sK122)
| 'less$uthan'(sK123,sK122)
| sK126 = sK128 ),
inference(resolution,[status(thm)],[d44,d34]) ).
cnf(d46,plain,
( ~ 'less$uthan'(sK127,sK128)
| ~ 'less$uthan'(sK123,sK122) ),
inference(demodulation,[status(thm)],[d27,d33]) ).
cnf(d47,plain,
( ~ 'less$uthan'(sK123,sK122)
| 'pair$uin$ulist'(sK117,sK128,sK129)
| sK126 = sK128 ),
inference(resolution,[status(thm)],[d36,c52]) ).
cnf(d48,plain,
( ~ 'less$uthan'(sK123,sK122)
| 'less$uthan'(sK129,sK128)
| ~ 'less$uthan'(sK123,sK122)
| sK126 = sK128 ),
inference(resolution,[status(thm)],[d47,d28]) ).
cnf(d49,plain,
( 'less$uthan'(sK127,sK128)
| ~ 'less$uthan'(sK123,sK122)
| sK126 = sK128 ),
inference(demodulation,[status(thm)],[d48,d33]) ).
cnf(d50,plain,
( 'less$uthan'(sK127,sK128)
| sK126 = sK128
| sK126 = sK128 ),
inference(resolution,[status(thm)],[d45,d49]) ).
cnf(d51,plain,
( ~ 'less$uthan'(sK123,sK122)
| sK126 = sK128 ),
inference(resolution,[status(thm)],[d50,d46]) ).
cnf(d52,plain,
( sK126 = sK128
| sK126 = sK128 ),
inference(resolution,[status(thm)],[d51,d45]) ).
cnf(d53,plain,
( ~ 'less$uthan'(sK127,sK126)
| ~ 'less$uthan'(sK123,sK122) ),
inference(demodulation,[status(thm)],[d46,d52]) ).
cnf(d54,plain,
~ 'less$uthan'(sK123,sK122),
inference(resolution,[status(thm)],[d7,d53]) ).
cnf(d55,plain,
( ~ 'less$uthan'(sK127,sK126)
| 'less$uthan'(sK123,sK122) ),
inference(demodulation,[status(thm)],[d34,d52]) ).
cnf(d56,plain,
'less$uthan'(sK123,sK122),
inference(resolution,[status(thm)],[d7,d55]) ).
cnf(d57,plain,
$false,
inference(resolution,[status(thm)],[d56,d54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV406+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 13:41:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.92/6.21 % SZS status Theorem for theBenchmark.p
% 29.92/6.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------