%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU174+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 02:51:13 PM UTC 2026
% Result : Theorem 18.01s 2.91s
% Output : Proof 18.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 75 ( 16 unt; 0 def)
% Number of atoms : 205 ( 31 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 224 ( 94 ~; 89 |; 28 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 121 ( 11 sgn 64 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ! [C] :
( element(C,powerset(powerset(A)))
=> ( C = complements_of_subsets(A,B)
<=> ! [D] :
( element(D,powerset(A))
=> ( in(D,C)
<=> in(subset_complement(A,D),B) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(f2_nnf,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D] :
( ( ( in(subset_complement(A,D),B)
& ~ in(D,C) )
| ( ~ in(subset_complement(A,D),B)
& in(D,C) ) )
& element(D,powerset(A)) )
| C = complements_of_subsets(A,B) )
& ( ! [D] :
( ( ( ~ in(subset_complement(A,D),B)
| in(D,C) )
& ( in(subset_complement(A,D),B)
| ~ in(D,C) ) )
| ~ element(D,powerset(A)) )
| C != complements_of_subsets(A,B) ) )
| ~ element(C,powerset(powerset(A))) )
| ~ element(B,powerset(powerset(A))) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,A,C,D] :
( ( ( ( ( ( in(subset_complement(A,sk1(A,B,C)),B)
& ~ in(sk1(A,B,C),C) )
| ( ~ in(subset_complement(A,sk1(A,B,C)),B)
& in(sk1(A,B,C),C) ) )
& element(sk1(A,B,C),powerset(A)) )
| C = complements_of_subsets(A,B) )
& ( ( ( ~ in(subset_complement(A,D),B)
| in(D,C) )
& ( in(subset_complement(A,D),B)
| ~ in(D,C) ) )
| ~ element(D,powerset(A))
| C != complements_of_subsets(A,B) ) )
| ~ element(C,powerset(powerset(A)))
| ~ element(B,powerset(powerset(A))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f2_nnf]) ).
cnf(c4,plain,
( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2)
| ~ element(X3,powerset(X0))
| X2 != complements_of_subsets(X0,X1)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f24,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f24_nnf,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c37,plain,
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f15,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f15_nnf,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A] :
( empty(sk5(A))
& element(sk5(A),powerset(A)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f15_nnf]) ).
cnf(c25,plain,
empty(sk5(X0)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p43,plain,
sk5(X0) = empty_set,
inference(resolution,[status(thm)],[c37,c25]) ).
cnf(c24,plain,
element(sk5(X0),powerset(X0)),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p44,plain,
element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[p43,c24]) ).
cnf(p49,plain,
( in(subset_complement(X1,X2),empty_set)
| ~ in(X2,X0)
| ~ element(X2,powerset(X1))
| X0 != complements_of_subsets(X1,empty_set)
| ~ element(X0,powerset(powerset(X1))) ),
inference(resolution,[status(thm)],[c4,p44]) ).
fof(f21,conjecture,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(f21_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f21_nnf,plain,
? [A,B] :
( complements_of_subsets(A,B) = empty_set
& B != empty_set
& element(B,powerset(powerset(A))) ),
inference(nnf_transformation,[status(thm)],[f21_neg]) ).
fof(f21_sk,plain,
( complements_of_subsets(sk7,sk8) = empty_set
& sk8 != empty_set
& element(sk8,powerset(powerset(sk7))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8])],[f21_nnf]) ).
cnf(c32,plain,
element(sk8,powerset(powerset(sk7))),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p533,plain,
( in(subset_complement(sk7,X0),empty_set)
| ~ in(X0,sk8)
| ~ element(X0,powerset(sk7))
| sk8 != sk8 ),
inference(resolution,[status(thm)],[p49,c32]) ).
cnf(p1279,plain,
( in(subset_complement(sk7,X0),empty_set)
| ~ in(X0,sk8)
| ~ element(X0,powerset(sk7)) ),
inference(equality_resolution,[status(thm)],[p533]) ).
fof(f20,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f20_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c30,plain,
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p371,plain,
subset(sk8,powerset(sk7)),
inference(resolution,[status(thm)],[c30,c32]) ).
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f1_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk0(A,B),B)
& in(sk0(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c1,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p386,plain,
( in(X0,powerset(sk7))
| ~ in(X0,sk8) ),
inference(resolution,[status(thm)],[p371,c1]) ).
cnf(c2,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p389,plain,
( subset(sk8,X0)
| in(sk0(sk8,X0),powerset(sk7)) ),
inference(resolution,[status(thm)],[p386,c2]) ).
fof(f18,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f18_nnf,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c28,plain,
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p405,plain,
( element(sk0(sk8,X0),powerset(sk7))
| subset(sk8,X0) ),
inference(resolution,[status(thm)],[p389,c28]) ).
cnf(p1286,plain,
( subset(sk8,X0)
| in(subset_complement(sk7,sk0(sk8,X0)),empty_set)
| ~ in(sk0(sk8,X0),sk8) ),
inference(resolution,[status(thm)],[p1279,p405]) ).
cnf(p1305,plain,
( subset(sk8,X0)
| subset(sk8,X0)
| in(subset_complement(sk7,sk0(sk8,X0)),empty_set) ),
inference(resolution,[status(thm)],[p1286,c2]) ).
cnf(p1306,plain,
( subset(sk8,X0)
| in(subset_complement(sk7,sk0(sk8,X0)),empty_set) ),
inference(factoring,[status(thm)],[p1305]) ).
fof(f25,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f25_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c38,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p1346,plain,
( ~ empty(empty_set)
| subset(sk8,X0) ),
inference(resolution,[status(thm)],[p1306,c38]) ).
fof(f10,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f10_nnf,plain,
empty(empty_set),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c18,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(p1347,plain,
subset(sk8,X0),
inference(resolution,[status(thm)],[p1346,c18]) ).
cnf(c31,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p1349,plain,
element(sk8,powerset(X0)),
inference(resolution,[status(thm)],[p1347,c31]) ).
fof(f23,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f23_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c36,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(c8,plain,
( in(subset_complement(X0,sk1(X0,X1,X2)),X1)
| in(sk1(X0,X1,X2),X2)
| X2 = complements_of_subsets(X0,X1)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p77,plain,
( in(subset_complement(sk7,sk1(sk7,sk8,X0)),sk8)
| in(sk1(sk7,sk8,X0),X0)
| X0 = empty_set
| ~ element(X0,powerset(powerset(sk7))) ),
inference(resolution,[status(thm)],[c8,c32]) ).
cnf(p80,plain,
( in(subset_complement(sk7,sk1(sk7,sk8,sk8)),sk8)
| in(sk1(sk7,sk8,sk8),sk8)
| sk8 = empty_set ),
inference(resolution,[status(thm)],[p77,c32]) ).
cnf(p414,plain,
( in(sk1(sk7,sk8,sk8),sk8)
| sk8 = empty_set
| ~ empty(X0)
| ~ element(sk8,powerset(X0)) ),
inference(resolution,[status(thm)],[c36,p80]) ).
cnf(p1384,plain,
( in(sk1(sk7,sk8,sk8),sk8)
| sk8 = empty_set
| ~ empty(X0) ),
inference(resolution,[status(thm)],[p1349,p414]) ).
cnf(p1733,plain,
( in(sk1(sk7,sk8,sk8),sk8)
| sk8 = empty_set ),
inference(resolution,[status(thm)],[p1384,c18]) ).
cnf(p1348,plain,
( in(X0,X1)
| ~ in(X0,sk8) ),
inference(resolution,[status(thm)],[p1347,c1]) ).
cnf(p1738,plain,
( in(sk1(sk7,sk8,sk8),X0)
| sk8 = empty_set ),
inference(resolution,[status(thm)],[p1733,p1348]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f0_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p40,plain,
~ in(X0,X0),
inference(factoring,[status(thm)],[c0]) ).
cnf(p1763,plain,
sk8 = empty_set,
inference(resolution,[status(thm)],[p1738,p40]) ).
cnf(c33,plain,
sk8 != empty_set,
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p1764,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p1763,c33]) ).
cnf(p2217,plain,
$false,
inference(equality_resolution,[status(thm)],[p1764]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU174+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n002.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 13:06:03 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 18.01/2.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.01/2.91 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------