%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET662+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 : Fri Sep 25 02:43:45 PM UTC 2026
% Result : Theorem 4.62s 11.27s
% Output : Proof 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 14
% Syntax : Number of formulae : 115 ( 83 unt; 0 def)
% Number of atoms : 232 ( 77 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 198 ( 81 ~; 68 |; 25 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 175 ( 38 sgn 52 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(empty_set,relation_type(B,C)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_25) ).
fof(f21_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(empty_set,relation_type(B,C)) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f21_nnf,plain,
? [B] :
( ? [C] :
( ~ ilf_type(empty_set,relation_type(B,C))
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f21_neg]) ).
fof(f21_sk,plain,
( ~ ilf_type(empty_set,relation_type(sk9,sk10))
& ilf_type(sk10,set_type)
& ilf_type(sk9,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10])],[f21_nnf]) ).
cnf(c40,plain,
~ ilf_type(empty_set,relation_type(sk9,sk10)),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(t15,plain,
ilf_type(empty_set,relation_type(sk9,sk10)) = false,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t158,plain,
ilf_type(empty_set,relation_type(sk9,sk10)) = false,
inference(orient,[status(thm)],[t15]) ).
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f1_nnf,plain,
! [B] :
( ! [C] :
( ( ! [E] :
( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ! [D] :
( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D,E] :
( ( ( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t68,plain,
ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,set_type),true,ifeq(ilf_type(X3,subset_type(cross_product(X1,X2))),true,ilf_type(X3,relation_type(X1,X2)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
fof(f20,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
fof(f20_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c37,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t4,plain,
ilf_type(X1,set_type) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(t78,plain,
ilf_type(X1,set_type) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t253,plain,
ifeq(true,true,ifeq(ilf_type(X2,set_type),true,ifeq(ilf_type(X3,subset_type(cross_product(X1,X2))),true,ilf_type(X3,relation_type(X1,X2)),true),true),true) = true,
inference(step,[status(thm)],[t68,t78]) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t75,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t14]) ).
cnf(t254,plain,
ifeq(ilf_type(X2,set_type),true,ifeq(ilf_type(X3,subset_type(cross_product(X1,X2))),true,ilf_type(X3,relation_type(X1,X2)),true),true) = true,
inference(step,[status(thm)],[t253,t75]) ).
cnf(t255,plain,
ifeq(true,true,ifeq(ilf_type(X3,subset_type(cross_product(X1,X2))),true,ilf_type(X3,relation_type(X1,X2)),true),true) = true,
inference(step,[status(thm)],[t254,t78]) ).
cnf(t256,plain,
ifeq(ilf_type(X3,subset_type(cross_product(X1,X2))),true,ilf_type(X3,relation_type(X1,X2)),true) = true,
inference(step,[status(thm)],[t255,t75]) ).
cnf(t86,plain,
ifeq(ilf_type(X1,subset_type(cross_product(X2,X3))),true,ilf_type(X1,relation_type(X2,X3)),true) = true,
inference(orient,[status(thm)],[t256]) ).
fof(f7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(f7_nnf,plain,
! [B] :
( ! [C] :
( ( ( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [B,C] :
( ( ( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c9,plain,
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t62,plain,
ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,set_type),true,ifeq(ilf_type(X2,member_type(power_set(X1))),true,ilf_type(X2,subset_type(X1)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t269,plain,
ifeq(true,true,ifeq(ilf_type(X2,set_type),true,ifeq(ilf_type(X2,member_type(power_set(X1))),true,ilf_type(X2,subset_type(X1)),true),true),true) = true,
inference(step,[status(thm)],[t62,t78]) ).
cnf(t270,plain,
ifeq(ilf_type(X2,set_type),true,ifeq(ilf_type(X2,member_type(power_set(X1))),true,ilf_type(X2,subset_type(X1)),true),true) = true,
inference(step,[status(thm)],[t269,t75]) ).
cnf(t271,plain,
ifeq(true,true,ifeq(ilf_type(X2,member_type(power_set(X1))),true,ilf_type(X2,subset_type(X1)),true),true) = true,
inference(step,[status(thm)],[t270,t78]) ).
cnf(t272,plain,
ifeq(ilf_type(X2,member_type(power_set(X1))),true,ilf_type(X2,subset_type(X1)),true) = true,
inference(step,[status(thm)],[t271,t75]) ).
cnf(t92,plain,
ifeq(ilf_type(X1,member_type(power_set(X2))),true,ilf_type(X1,subset_type(X2)),true) = true,
inference(orient,[status(thm)],[t272]) ).
fof(f14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
fof(f14_nnf,plain,
! [B] :
( ! [C] :
( ( ( ~ member(B,C)
| ilf_type(B,member_type(C)) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [B,C] :
( ( ( ~ member(B,C)
| ilf_type(B,member_type(C)) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c26,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t66,plain,
ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,set_type),true,ifeq(member(X1,X2),true,or(empty(X2),ilf_type(X1,member_type(X2))),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t277,plain,
ifeq(true,true,ifeq(ilf_type(X2,set_type),true,ifeq(member(X1,X2),true,or(empty(X2),ilf_type(X1,member_type(X2))),true),true),true) = true,
inference(step,[status(thm)],[t66,t78]) ).
cnf(t278,plain,
ifeq(ilf_type(X2,set_type),true,ifeq(member(X1,X2),true,or(empty(X2),ilf_type(X1,member_type(X2))),true),true) = true,
inference(step,[status(thm)],[t277,t75]) ).
cnf(t279,plain,
ifeq(true,true,ifeq(member(X1,X2),true,or(empty(X2),ilf_type(X1,member_type(X2))),true),true) = true,
inference(step,[status(thm)],[t278,t78]) ).
cnf(t280,plain,
ifeq(member(X1,X2),true,or(empty(X2),ilf_type(X1,member_type(X2))),true) = true,
inference(step,[status(thm)],[t279,t75]) ).
cnf(t96,plain,
ifeq(member(X1,X2),true,or(empty(X2),ilf_type(X1,member_type(X2))),true) = true,
inference(orient,[status(thm)],[t280]) ).
fof(f12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).
fof(f12_nnf,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| member(B,power_set(C)) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk4(B,C),C)
& member(sk4(B,C),B)
& ilf_type(sk4(B,C),set_type) )
| member(B,power_set(C)) )
& ( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f12_nnf]) ).
cnf(c21,plain,
( member(sk4(X0,X1),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t58,plain,
ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,set_type),true,or(member(X1,power_set(X2)),member(sk4(X1,X2),X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t306,plain,
ifeq(true,true,ifeq(ilf_type(X2,set_type),true,or(member(X1,power_set(X2)),member(sk4(X1,X2),X1)),true),true) = true,
inference(step,[status(thm)],[t58,t78]) ).
cnf(t307,plain,
ifeq(ilf_type(X2,set_type),true,or(member(X1,power_set(X2)),member(sk4(X1,X2),X1)),true) = true,
inference(step,[status(thm)],[t306,t75]) ).
cnf(t308,plain,
ifeq(true,true,or(member(X1,power_set(X2)),member(sk4(X1,X2),X1)),true) = true,
inference(step,[status(thm)],[t307,t78]) ).
cnf(t309,plain,
or(member(X1,power_set(X2)),member(sk4(X1,X2),X1)) = true,
inference(step,[status(thm)],[t308,t75]) ).
cnf(t104,plain,
or(member(X1,power_set(X2)),member(sk4(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t309]) ).
cnf(t19,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t166,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t19]) ).
fof(f3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ~ member(B,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f3_nnf,plain,
! [B] :
( ~ member(B,empty_set)
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B] :
( ~ member(B,empty_set)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c4,plain,
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t34,plain,
or(not(ilf_type(X1,set_type)),not(member(X1,empty_set))) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t354,plain,
or(not(true),not(member(X1,empty_set))) = true,
inference(step,[status(thm)],[t34,t78]) ).
cnf(t136,plain,
or(not(true),not(member(X1,empty_set))) = true,
inference(orient,[status(thm)],[t354]) ).
cnf(t2,plain,
not(true) = false,
introduced(definition) ).
cnf(t167,plain,
not(true) = false,
inference(orient,[status(thm)],[t2]) ).
cnf(t361,plain,
or(false,not(member(X1,empty_set))) = true,
inference(step,[status(thm)],[t136,t167]) ).
cnf(t9,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t77,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t362,plain,
not(member(X1,empty_set)) = true,
inference(step,[status(thm)],[t361,t77]) ).
cnf(t169,plain,
not(member(X1,empty_set)) = true,
inference(rw,[status(thm)],[t362]) ).
cnf(t172,plain,
not(member(X1,empty_set)) = true,
inference(orient,[status(thm)],[t169]) ).
cnf(t173,plain,
false = ifeq(true,true,member(X1,empty_set),false),
inference(cp,[status(thm)],[t166,t172]) ).
cnf(t369,plain,
false = member(X1,empty_set),
inference(step,[status(thm)],[t173,t75]) ).
cnf(t174,plain,
member(X1,empty_set) = false,
inference(orient,[status(thm)],[t369]) ).
cnf(t178,plain,
true = or(member(empty_set,power_set(X1)),false),
inference(cp,[status(thm)],[t104,t174]) ).
cnf(t7,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t76,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t378,plain,
true = member(empty_set,power_set(X1)),
inference(step,[status(thm)],[t178,t76]) ).
cnf(t204,plain,
member(empty_set,power_set(X1)) = true,
inference(orient,[status(thm)],[t378]) ).
cnf(t215,plain,
true = ifeq(true,true,or(empty(power_set(X1)),ilf_type(empty_set,member_type(power_set(X1)))),true),
inference(cp,[status(thm)],[t96,t204]) ).
cnf(t381,plain,
true = or(empty(power_set(X1)),ilf_type(empty_set,member_type(power_set(X1)))),
inference(step,[status(thm)],[t215,t75]) ).
fof(f13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
fof(f13_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c23,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t33,plain,
or(not(ilf_type(X1,set_type)),not(empty(power_set(X1)))) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t355,plain,
or(not(true),not(empty(power_set(X1)))) = true,
inference(step,[status(thm)],[t33,t78]) ).
cnf(t137,plain,
or(not(true),not(empty(power_set(X1)))) = true,
inference(orient,[status(thm)],[t355]) ).
cnf(t363,plain,
or(false,not(empty(power_set(X1)))) = true,
inference(step,[status(thm)],[t137,t167]) ).
cnf(t364,plain,
not(empty(power_set(X1))) = true,
inference(step,[status(thm)],[t363,t77]) ).
cnf(t170,plain,
not(empty(power_set(X1))) = true,
inference(rw,[status(thm)],[t364]) ).
cnf(t192,plain,
not(empty(power_set(X1))) = true,
inference(orient,[status(thm)],[t170]) ).
cnf(t193,plain,
false = ifeq(true,true,empty(power_set(X1)),false),
inference(cp,[status(thm)],[t166,t192]) ).
cnf(t372,plain,
false = empty(power_set(X1)),
inference(step,[status(thm)],[t193,t75]) ).
cnf(t194,plain,
empty(power_set(X1)) = false,
inference(orient,[status(thm)],[t372]) ).
cnf(t382,plain,
true = or(false,ilf_type(empty_set,member_type(power_set(X1)))),
inference(step,[status(thm)],[t381,t194]) ).
cnf(t383,plain,
true = ilf_type(empty_set,member_type(power_set(X1))),
inference(step,[status(thm)],[t382,t77]) ).
cnf(t228,plain,
ilf_type(empty_set,member_type(power_set(X1))) = true,
inference(orient,[status(thm)],[t383]) ).
cnf(t229,plain,
true = ifeq(true,true,ilf_type(empty_set,subset_type(X1)),true),
inference(cp,[status(thm)],[t92,t228]) ).
cnf(t384,plain,
true = ilf_type(empty_set,subset_type(X1)),
inference(step,[status(thm)],[t229,t75]) ).
cnf(t231,plain,
ilf_type(empty_set,subset_type(X1)) = true,
inference(orient,[status(thm)],[t384]) ).
cnf(t233,plain,
true = ifeq(true,true,ilf_type(empty_set,relation_type(X1,X2)),true),
inference(cp,[status(thm)],[t86,t231]) ).
cnf(t385,plain,
true = ilf_type(empty_set,relation_type(X1,X2)),
inference(step,[status(thm)],[t233,t75]) ).
cnf(t234,plain,
ilf_type(empty_set,relation_type(X1,X2)) = true,
inference(orient,[status(thm)],[t385]) ).
cnf(t386,plain,
true = false,
inference(step,[status(thm)],[t158,t234]) ).
cnf(t235,plain,
true = false,
inference(rw,[status(thm)],[t386]) ).
cnf(t236,plain,
false = true,
inference(orient,[status(thm)],[t235]) ).
fof(f11,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
fof(f11_nnf,plain,
! [B] :
( ( ( ? [C] :
( member(C,B)
& ilf_type(C,set_type) )
| empty(B) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [B,C] :
( ( ( ( member(sk3(B),B)
& ilf_type(sk3(B),set_type) )
| empty(B) )
& ( ~ member(C,B)
| ~ ilf_type(C,set_type)
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f11_nnf]) ).
cnf(c16,plain,
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4,c16,c23,c40]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t236]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET662+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/10.59 % Computer : n010.cluster.edu
% 0.10/10.59 % Model : x86_64 x86_64
% 0.10/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.59 % Memory : 8046.5625MB
% 0.10/10.59 % OS : Linux 6.8.0-71-generic
% 0.10/10.60 % CPULimit : 300
% 0.10/10.60 % WCLimit : 300
% 0.10/10.60 % DateTime : Thu Sep 24 11:36:40 UTC 2026
% 0.15/10.60 % CPUTime :
% 0.15/10.60 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.62/11.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.62/11.27 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------