%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM410+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 : n017.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 02:19:58 PM UTC 2026
% Result : Theorem 8.72s 1.67s
% Output : Proof 8.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 28 unt; 0 def)
% Number of atoms : 134 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 143 ( 67 ~; 37 |; 30 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 59 ( 4 sgn 37 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( transfinite_sequence(A)
<=> ordinal(relation_dom(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_ordinal1) ).
fof(f7_nnf,plain,
! [A] :
( ( ( ~ ordinal(relation_dom(A))
| transfinite_sequence(A) )
& ( ordinal(relation_dom(A))
| ~ transfinite_sequence(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A] :
( ( ( ~ ordinal(relation_dom(A))
| transfinite_sequence(A) )
& ( ordinal(relation_dom(A))
| ~ transfinite_sequence(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c13,plain,
( ~ ordinal(relation_dom(X0))
| transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi10,axiom,
ifeq(relation(X0),true,ifeq(function(X0),true,ifeq(ordinal(relation_dom(X0)),true,transfinite_sequence(X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
fof(f39,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( ordinal(relation_dom(A))
=> transfinite_sequence_of(A,relation_rng(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_ordinal1) ).
fof(f39_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( ordinal(relation_dom(A))
=> transfinite_sequence_of(A,relation_rng(A)) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f39_nnf,plain,
? [A] :
( ~ transfinite_sequence_of(A,relation_rng(A))
& ordinal(relation_dom(A))
& function(A)
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f39_neg]) ).
fof(f39_sk,plain,
( ~ transfinite_sequence_of(sk16,relation_rng(sk16))
& ordinal(relation_dom(sk16))
& function(sk16)
& relation(sk16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16])],[f39_nnf]) ).
cnf(c86,plain,
relation(sk16),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi80,negated_conjecture,
relation(sk16) = true,
inference(equality_encoding,[status(esa)],[c86]) ).
cnf(c87,plain,
function(sk16),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi81,negated_conjecture,
function(sk16) = true,
inference(equality_encoding,[status(esa)],[c87]) ).
cnf(c88,plain,
ordinal(relation_dom(sk16)),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi82,negated_conjecture,
ordinal(relation_dom(sk16)) = true,
inference(equality_encoding,[status(esa)],[c88]) ).
cnf(h49,plain,
transfinite_sequence(sk16) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi80,hi81,hi82]) ).
fof(f8,axiom,
! [A,B] :
( ( transfinite_sequence(B)
& function(B)
& relation(B) )
=> ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(f8_nnf,plain,
! [A,B] :
( ( ( ~ subset(relation_rng(B),A)
| transfinite_sequence_of(B,A) )
& ( subset(relation_rng(B),A)
| ~ transfinite_sequence_of(B,A) ) )
| ~ transfinite_sequence(B)
| ~ function(B)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [B,A] :
( ( ( ~ subset(relation_rng(B),A)
| transfinite_sequence_of(B,A) )
& ( subset(relation_rng(B),A)
| ~ transfinite_sequence_of(B,A) ) )
| ~ transfinite_sequence(B)
| ~ function(B)
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c15,plain,
( ~ subset(relation_rng(X1),X0)
| transfinite_sequence_of(X1,X0)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi12,axiom,
ifeq(relation(X0),true,ifeq(function(X0),true,ifeq(transfinite_sequence(X0),true,ifeq(subset(relation_rng(X0),X1),true,transfinite_sequence_of(X0,X1),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
fof(f35,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f35_nnf,plain,
! [A,B] : subset(A,A),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [A] : subset(A,A),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c81,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(hi75,axiom,
subset(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(h52,plain,
transfinite_sequence_of(sk16,relation_rng(sk16)) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi80,hi81,h49,hi75]) ).
cnf(c89,plain,
~ transfinite_sequence_of(sk16,relation_rng(sk16)),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(hi90,negated_conjecture,
ifeq(transfinite_sequence_of(sk16,relation_rng(sk16)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c89]) ).
cnf(t10,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi90,h52]) ).
cnf(t998,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(f27,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f27_nnf,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
( relation(sk8)
& ~ empty(sk8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8])],[f27_nnf]) ).
cnf(c60,plain,
~ empty(sk8),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f28,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f28_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
~ empty(sk9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f28_nnf]) ).
cnf(c62,plain,
~ empty(sk9),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
fof(f30,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f30_nnf,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
( ordinal(sk11)
& epsilon_connected(sk11)
& epsilon_transitive(sk11)
& ~ empty(sk11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f30_nnf]) ).
cnf(c66,plain,
~ empty(sk11),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f41,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f41_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c91,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
fof(f43,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f43_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c93,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c60,c62,c66,c89,c91,c93]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t998]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM410+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 03:47:00 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.72/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.72/1.67 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------