%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU116+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 02:50:58 PM UTC 2026
% Result : Theorem 4.10s 0.97s
% Output : Proof 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 23 unt; 0 def)
% Number of atoms : 112 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 114 ( 57 ~; 15 |; 38 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 62 ( 7 sgn 40 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
! [A,B] :
( element(B,finite_subsets(A))
=> finite(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_finsub_1) ).
fof(f20_nnf,plain,
! [A,B] :
( finite(B)
| ~ element(B,finite_subsets(A)) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [B,A] :
( finite(B)
| ~ element(B,finite_subsets(A)) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c28,plain,
( finite(X1)
| ~ element(X1,finite_subsets(X0)) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi22,axiom,
ifeq(element(X0,finite_subsets(X1)),true,finite(X0),true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
fof(f30,conjecture,
! [A,B] :
( element(B,finite_subsets(A))
=> finite(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_finsub_1) ).
fof(f30_neg,negated_conjecture,
~ ! [A,B] :
( element(B,finite_subsets(A))
=> finite(B) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f30_nnf,plain,
? [A,B] :
( ~ finite(B)
& element(B,finite_subsets(A)) ),
inference(nnf_transformation,[status(thm)],[f30_neg]) ).
fof(f30_sk,plain,
( ~ finite(sk11)
& element(sk11,finite_subsets(sk10)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10,sk11])],[f30_nnf]) ).
cnf(c58,plain,
element(sk11,finite_subsets(sk10)),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(hi49,negated_conjecture,
element(sk11,finite_subsets(sk10)) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(h20,plain,
finite(sk11) = true,
inference(hyper_resolution,[status(thm)],[hi22,hi49]) ).
cnf(c59,plain,
~ finite(sk11),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(hi59,negated_conjecture,
ifeq(finite(sk11),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c59]) ).
cnf(t1,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi59,h20]) ).
cnf(t180,plain,
false = true,
inference(orient,[status(thm)],[t1]) ).
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f1_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f5,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f5_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f7,axiom,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finsub_1) ).
fof(f7_nnf,plain,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f12,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f12_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c16,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f16,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f16_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c21,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f19,axiom,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_finsub_1) ).
fof(f19_nnf,plain,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c24,plain,
~ empty(finite_subsets(X0)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f21,axiom,
? [A] :
( preboolean(A)
& diff_closed(A)
& cap_closed(A)
& cup_closed(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finsub_1) ).
fof(f21_nnf,plain,
? [A] :
( preboolean(A)
& diff_closed(A)
& cap_closed(A)
& cup_closed(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
( preboolean(sk1)
& diff_closed(sk1)
& cap_closed(sk1)
& cup_closed(sk1)
& ~ empty(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f21_nnf]) ).
cnf(c29,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f22,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f22_nnf,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
( finite(sk2)
& ~ empty(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f22_nnf]) ).
cnf(c34,plain,
~ empty(sk2),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
fof(f29,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f29_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
~ empty(sk9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f29_nnf]) ).
cnf(c57,plain,
~ empty(sk9),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c1,c5,c7,c16,c21,c24,c29,c34,c57,c59]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t180]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU116+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:52:37 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.10/0.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.10/0.97 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------