%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU294+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 : n019.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 8.80s 6.72s
% Output : Proof 8.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 63 ( 27 unt; 0 def)
% Number of atoms : 130 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 132 ( 65 ~; 23 |; 38 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-4 aty)
% Number of variables : 68 ( 3 sgn 40 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f42,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f42_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c104,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi90,axiom,
ifeq(subset(X0,X1),true,element(X0,powerset(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c104]) ).
fof(f39,conjecture,
! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
fof(f39_neg,negated_conjecture,
~ ! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f39_nnf,plain,
? [A,B] :
( ~ finite(A)
& finite(B)
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f39_neg]) ).
fof(f39_sk,plain,
( ~ finite(sk19)
& finite(sk20)
& subset(sk19,sk20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk19,sk20])],[f39_nnf]) ).
cnf(c98,plain,
subset(sk19,sk20),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi85,negated_conjecture,
subset(sk19,sk20) = true,
inference(equality_encoding,[status(esa)],[c98]) ).
cnf(h55,plain,
element(sk19,powerset(sk20)) = true,
inference(hyper_resolution,[status(thm)],[hi90,hi85]) ).
fof(f7,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f7_nnf,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( finite(B)
| ~ element(B,powerset(A))
| ~ finite(A) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c13,plain,
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi11,axiom,
ifeq(finite(X0),true,ifeq(element(X1,powerset(X0)),true,finite(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(c99,plain,
finite(sk20),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi86,negated_conjecture,
finite(sk20) = true,
inference(equality_encoding,[status(esa)],[c99]) ).
cnf(h125,plain,
finite(sk19) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi86,h55]) ).
cnf(c100,plain,
~ finite(sk19),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi101,negated_conjecture,
ifeq(finite(sk19),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c100]) ).
cnf(t10,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi101,h125]) ).
cnf(t948,plain,
false = true,
inference(orient,[status(thm)],[t10]) ).
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]) ).
fof(f16,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f16_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c28,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f20,axiom,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(f20_nnf,plain,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
( natural(sk1)
& ordinal(sk1)
& epsilon_connected(sk1)
& epsilon_transitive(sk1)
& ~ empty(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f20_nnf]) ).
cnf(c40,plain,
~ empty(sk1),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f21,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f21_nnf,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
( finite(sk2)
& ~ empty(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f21_nnf]) ).
cnf(c45,plain,
~ empty(sk2),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f30,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f30_nnf,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
( relation(sk11)
& ~ empty(sk11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f30_nnf]) ).
cnf(c77,plain,
~ empty(sk11),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f32,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f32_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
~ empty(sk13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f32_nnf]) ).
cnf(c81,plain,
~ empty(sk13),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f35,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f35_nnf,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
( ordinal(sk16)
& epsilon_connected(sk16)
& epsilon_transitive(sk16)
& ~ empty(sk16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16])],[f35_nnf]) ).
cnf(c88,plain,
~ empty(sk16),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f44,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f44_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c106,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
fof(f46,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f46_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c108,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c28,c40,c45,c77,c81,c88,c100,c106,c108]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t948]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU294+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/5.36 % Computer : n019.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Thu Sep 24 13:34:42 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.80/6.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.80/6.72 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------