%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU103+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 08:40:52 AM UTC 2026
% Result : Theorem 63.88s 9.90s
% Output : CNFRefutation 63.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 19 unt; 0 def)
% Number of atoms : 154 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 161 ( 62 ~; 73 |; 16 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 58 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k5_xboole_0,axiom,
! [X0,X1] : 'symmetric$udifference'(X0,X1) = 'symmetric$udifference'(X1,X0) ).
fof(d6_xboole_0,axiom,
! [X0,X1] : 'symmetric$udifference'(X0,X1) = 'set$uunion2'('set$udifference'(X0,X1),'set$udifference'(X1,X0)) ).
fof(dt_k1_finsub_1,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0)
& preboolean(X0)
& ~ empty(X0) )
=> element('prebool$uunion2'(X0,X1,X2),X0) ) ).
fof(dt_k2_finsub_1,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0)
& preboolean(X0)
& ~ empty(X0) )
=> element('prebool$udifference'(X0,X1,X2),X0) ) ).
fof(redefinition_k1_finsub_1,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0)
& preboolean(X0)
& ~ empty(X0) )
=> 'prebool$uunion2'(X0,X1,X2) = 'set$uunion2'(X1,X2) ) ).
fof(redefinition_k2_finsub_1,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0)
& preboolean(X0)
& ~ empty(X0) )
=> 'prebool$udifference'(X0,X1,X2) = 'set$udifference'(X1,X2) ) ).
fof(t1_subset,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ) ).
fof(t2_subset,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ) ).
fof(t14_finsub_1,conjecture,
! [X0,X1,X2] :
( ( preboolean(X2)
& ~ empty(X2) )
=> ( ( element(X1,X2)
& element(X0,X2) )
=> element('symmetric$udifference'(X0,X1),X2) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( preboolean(X2)
& ~ empty(X2) )
=> ( ( element(X1,X2)
& element(X0,X2) )
=> element('symmetric$udifference'(X0,X1),X2) ) ),
inference(negate_conjecture,[status(cth)],[t14_finsub_1]) ).
cnf(c8,plain,
'symmetric$udifference'(X0,X1) = 'symmetric$udifference'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k5_xboole_0]) ).
cnf(c9,plain,
'set$uunion2'('set$udifference'(X0,X1),'set$udifference'(X1,X0)) = 'symmetric$udifference'(X0,X1),
inference(clausification,[status(esa)],[d6_xboole_0]) ).
cnf(c10,plain,
( element('prebool$uunion2'(X1,X0,X2),X1)
| ~ preboolean(X1)
| empty(X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[dt_k1_finsub_1]) ).
cnf(c11,plain,
( ~ preboolean(X1)
| element('prebool$udifference'(X1,X0,X2),X1)
| ~ element(X2,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[dt_k2_finsub_1]) ).
cnf(c51,plain,
( ~ preboolean(X2)
| empty(X2)
| ~ element(X1,X2)
| ~ element(X0,X2)
| 'set$uunion2'(X0,X1) = 'prebool$uunion2'(X2,X0,X1) ),
inference(clausification,[status(esa)],[redefinition_k1_finsub_1]) ).
cnf(c52,plain,
( ~ element(X1,X0)
| ~ preboolean(X0)
| ~ element(X2,X0)
| 'set$udifference'(X1,X2) = 'prebool$udifference'(X0,X1,X2)
| empty(X0) ),
inference(clausification,[status(esa)],[redefinition_k2_finsub_1]) ).
cnf(c55,plain,
( element(X0,X1)
| ~ in(X0,X1) ),
inference(clausification,[status(esa)],[t1_subset]) ).
cnf(c56,plain,
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(clausification,[status(esa)],[t2_subset]) ).
cnf(c67,plain,
preboolean(sK85),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c68,plain,
~ empty(sK85),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c69,plain,
~ element('symmetric$udifference'(sK83,sK84),sK85),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c70,plain,
element(sK83,sK85),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c71,plain,
element(sK84,sK85),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ element(X1,X0)
| ~ element(X2,X0)
| ~ preboolean(X0)
| empty(X0)
| empty(X0)
| in('prebool$uunion2'(X0,X1,X2),X0) ),
inference(resolution,[status(thm)],[c56,c10]) ).
cnf(d1,plain,
( ~ element(X0,sK85)
| ~ preboolean(sK85)
| empty(sK85)
| 'set$udifference'(X0,sK84) = 'prebool$udifference'(sK85,X0,sK84) ),
inference(resolution,[status(thm)],[c52,c71]) ).
cnf(d2,plain,
( ~ element(X0,sK85)
| empty(sK85)
| 'set$udifference'(X0,sK84) = 'prebool$udifference'(sK85,X0,sK84) ),
inference(resolution,[status(thm)],[c67,d1]) ).
cnf(d3,plain,
( ~ element(X0,sK85)
| 'set$udifference'(X0,sK84) = 'prebool$udifference'(sK85,X0,sK84) ),
inference(resolution,[status(thm)],[c68,d2]) ).
cnf(d4,plain,
'set$udifference'(sK83,sK84) = 'prebool$udifference'(sK85,sK83,sK84),
inference(resolution,[status(thm)],[d3,c70]) ).
cnf(d5,plain,
( ~ element(sK84,sK85)
| ~ element(sK83,sK85)
| ~ preboolean(sK85)
| empty(sK85)
| element('set$udifference'(sK83,sK84),sK85) ),
inference(superposition,[status(thm)],[d4,c11]) ).
cnf(d6,plain,
( ~ element(sK84,sK85)
| ~ element(sK83,sK85)
| element('set$udifference'(sK83,sK84),sK85)
| empty(sK85) ),
inference(resolution,[status(thm)],[c67,d5]) ).
cnf(d7,plain,
( ~ element(sK84,sK85)
| ~ element(sK83,sK85)
| element('set$udifference'(sK83,sK84),sK85) ),
inference(resolution,[status(thm)],[c68,d6]) ).
cnf(d8,plain,
( ~ element(sK84,sK85)
| element('set$udifference'(sK83,sK84),sK85) ),
inference(resolution,[status(thm)],[c70,d7]) ).
cnf(d9,plain,
element('set$udifference'(sK83,sK84),sK85),
inference(resolution,[status(thm)],[c71,d8]) ).
cnf(d10,plain,
( ~ element(X0,sK85)
| ~ preboolean(sK85)
| empty(sK85)
| 'set$udifference'(X0,sK83) = 'prebool$udifference'(sK85,X0,sK83) ),
inference(resolution,[status(thm)],[c52,c70]) ).
cnf(d11,plain,
( ~ element(X0,sK85)
| empty(sK85)
| 'set$udifference'(X0,sK83) = 'prebool$udifference'(sK85,X0,sK83) ),
inference(resolution,[status(thm)],[c67,d10]) ).
cnf(d12,plain,
( ~ element(X0,sK85)
| 'set$udifference'(X0,sK83) = 'prebool$udifference'(sK85,X0,sK83) ),
inference(resolution,[status(thm)],[c68,d11]) ).
cnf(d13,plain,
'set$udifference'(sK84,sK83) = 'prebool$udifference'(sK85,sK84,sK83),
inference(resolution,[status(thm)],[d12,c71]) ).
cnf(d14,plain,
( ~ element(sK83,sK85)
| ~ element(sK84,sK85)
| ~ preboolean(sK85)
| empty(sK85)
| element('set$udifference'(sK84,sK83),sK85) ),
inference(superposition,[status(thm)],[d13,c11]) ).
cnf(d15,plain,
( ~ element(sK84,sK85)
| ~ element(sK83,sK85)
| element('set$udifference'(sK84,sK83),sK85)
| empty(sK85) ),
inference(resolution,[status(thm)],[c67,d14]) ).
cnf(d16,plain,
( ~ element(sK84,sK85)
| ~ element(sK83,sK85)
| element('set$udifference'(sK84,sK83),sK85) ),
inference(resolution,[status(thm)],[c68,d15]) ).
cnf(d17,plain,
( ~ element(sK84,sK85)
| element('set$udifference'(sK84,sK83),sK85) ),
inference(resolution,[status(thm)],[c70,d16]) ).
cnf(d18,plain,
element('set$udifference'(sK84,sK83),sK85),
inference(resolution,[status(thm)],[c71,d17]) ).
cnf(d19,plain,
( ~ element(X0,sK85)
| ~ preboolean(sK85)
| empty(sK85)
| 'set$uunion2'('set$udifference'(sK84,sK83),X0) = 'prebool$uunion2'(sK85,'set$udifference'(sK84,sK83),X0) ),
inference(resolution,[status(thm)],[d18,c51]) ).
cnf(d20,plain,
( ~ element(X0,sK85)
| empty(sK85)
| 'set$uunion2'('set$udifference'(sK84,sK83),X0) = 'prebool$uunion2'(sK85,'set$udifference'(sK84,sK83),X0) ),
inference(resolution,[status(thm)],[c67,d19]) ).
cnf(d21,plain,
( ~ element(X0,sK85)
| 'set$uunion2'('set$udifference'(sK84,sK83),X0) = 'prebool$uunion2'(sK85,'set$udifference'(sK84,sK83),X0) ),
inference(resolution,[status(thm)],[c68,d20]) ).
cnf(d22,plain,
'set$uunion2'('set$udifference'(sK84,sK83),'set$udifference'(sK83,sK84)) = 'prebool$uunion2'(sK85,'set$udifference'(sK84,sK83),'set$udifference'(sK83,sK84)),
inference(resolution,[status(thm)],[d21,d9]) ).
cnf(d23,plain,
'symmetric$udifference'(sK84,sK83) = 'prebool$uunion2'(sK85,'set$udifference'(sK84,sK83),'set$udifference'(sK83,sK84)),
inference(demodulation,[status(thm)],[d22,c9]) ).
cnf(d24,plain,
'symmetric$udifference'(sK83,sK84) = 'prebool$uunion2'(sK85,'set$udifference'(sK84,sK83),'set$udifference'(sK83,sK84)),
inference(demodulation,[status(thm)],[d23,c8]) ).
cnf(d25,plain,
( ~ element('set$udifference'(sK84,sK83),sK85)
| ~ element('set$udifference'(sK83,sK84),sK85)
| ~ preboolean(sK85)
| empty(sK85)
| in('symmetric$udifference'(sK83,sK84),sK85) ),
inference(superposition,[status(thm)],[d24,d0]) ).
cnf(d26,plain,
( ~ element('set$udifference'(sK84,sK83),sK85)
| ~ element('set$udifference'(sK83,sK84),sK85)
| empty(sK85)
| in('symmetric$udifference'(sK83,sK84),sK85) ),
inference(resolution,[status(thm)],[c67,d25]) ).
cnf(d27,plain,
( ~ element('set$udifference'(sK84,sK83),sK85)
| ~ element('set$udifference'(sK83,sK84),sK85)
| in('symmetric$udifference'(sK83,sK84),sK85) ),
inference(resolution,[status(thm)],[c68,d26]) ).
cnf(d28,plain,
( ~ element('set$udifference'(sK83,sK84),sK85)
| in('symmetric$udifference'(sK83,sK84),sK85) ),
inference(resolution,[status(thm)],[d18,d27]) ).
cnf(d29,plain,
in('symmetric$udifference'(sK83,sK84),sK85),
inference(resolution,[status(thm)],[d9,d28]) ).
cnf(d30,plain,
element('symmetric$udifference'(sK83,sK84),sK85),
inference(resolution,[status(thm)],[d29,c55]) ).
cnf(d31,plain,
$false,
inference(resolution,[status(thm)],[c69,d30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU103+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n018.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 08:38:21 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 63.88/9.90 % SZS status Theorem for theBenchmark.p
% 63.88/9.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------