%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU295+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 02:51:37 PM UTC 2026
% Result : Theorem 10.74s 2.17s
% Output : Proof 10.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 23 unt; 0 def)
% Number of atoms : 106 ( 8 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 108 ( 57 ~; 15 |; 32 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-4 aty)
% Number of variables : 59 ( 6 sgn 34 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [A,B] :
( finite(A)
=> finite(set_intersection2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
fof(f18_nnf,plain,
! [A,B] :
( finite(set_intersection2(A,B))
| ~ finite(A) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B] :
( finite(set_intersection2(A,B))
| ~ finite(A) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c28,plain,
( finite(set_intersection2(X0,X1))
| ~ finite(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi20,axiom,
ifeq(finite(X0),true,finite(set_intersection2(X0,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
fof(f46,conjecture,
! [A,B] :
( finite(A)
=> finite(set_intersection2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_finset_1) ).
fof(f46_neg,negated_conjecture,
~ ! [A,B] :
( finite(A)
=> finite(set_intersection2(A,B)) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f46_nnf,plain,
? [A,B] :
( ~ finite(set_intersection2(A,B))
& finite(A) ),
inference(nnf_transformation,[status(thm)],[f46_neg]) ).
fof(f46_sk,plain,
( ~ finite(set_intersection2(sk19,sk20))
& finite(sk19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk19,sk20])],[f46_nnf]) ).
cnf(c105,plain,
finite(sk19),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(hi91,negated_conjecture,
finite(sk19) = true,
inference(equality_encoding,[status(esa)],[c105]) ).
cnf(h113,plain,
finite(set_intersection2(sk19,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi20,hi91]) ).
cnf(c106,plain,
~ finite(set_intersection2(sk19,sk20)),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(hi108,negated_conjecture,
ifeq(finite(set_intersection2(sk19,sk20)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c106]) ).
cnf(t10,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi108,h113]) ).
cnf(t1099,plain,
false = true,
inference(orient,[status(thm)],[t10]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/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]) ).
fof(f21,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f21_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c33,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f26,axiom,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(f26_nnf,plain,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
( natural(sk1)
& ordinal(sk1)
& epsilon_connected(sk1)
& epsilon_transitive(sk1)
& ~ empty(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f26_nnf]) ).
cnf(c46,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
fof(f27,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f27_nnf,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
( finite(sk2)
& ~ empty(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f27_nnf]) ).
cnf(c51,plain,
~ empty(sk2),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f36,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f36_nnf,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
( relation(sk11)
& ~ empty(sk11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f36_nnf]) ).
cnf(c83,plain,
~ empty(sk11),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
fof(f38,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f38_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
~ empty(sk13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f38_nnf]) ).
cnf(c87,plain,
~ empty(sk13),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
fof(f41,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f41_nnf,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
( ordinal(sk16)
& epsilon_connected(sk16)
& epsilon_transitive(sk16)
& ~ empty(sk16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16])],[f41_nnf]) ).
cnf(c94,plain,
~ empty(sk16),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
fof(f53,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f53_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c114,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
fof(f55,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f55_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c116,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c33,c46,c51,c83,c87,c94,c106,c114,c116]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1099]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU295+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n015.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 : Thu Sep 24 13:38:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.74/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.74/2.17 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------