%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM411+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 : n003.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 6.85s 1.61s
% Output : Proof 6.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 29 unt; 0 def)
% Number of atoms : 146 ( 19 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 151 ( 71 ~; 41 |; 30 &)
% ( 1 <=>; 8 =>; 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 : 11 ( 11 usr; 8 con; 0-4 aty)
% Number of variables : 90 ( 8 sgn 48 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B] :
( transfinite_sequence_of(B,A)
=> ( transfinite_sequence(B)
& function(B)
& relation(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(f8_nnf,plain,
! [A,B] :
( ( transfinite_sequence(B)
& function(B)
& relation(B) )
| ~ transfinite_sequence_of(B,A) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [B,A] :
( ( transfinite_sequence(B)
& function(B)
& relation(B) )
| ~ transfinite_sequence_of(B,A) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c16,plain,
( transfinite_sequence(X1)
| ~ transfinite_sequence_of(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi13,axiom,
ifeq(transfinite_sequence_of(X0,X1),true,transfinite_sequence(X0),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
fof(f37,conjecture,
! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_ordinal1) ).
fof(f37_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f37_nnf,plain,
? [A,B] :
( ? [C] :
( ~ transfinite_sequence_of(C,B)
& transfinite_sequence_of(C,A) )
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f37_neg]) ).
fof(f37_sk,plain,
( ~ transfinite_sequence_of(sk18,sk17)
& transfinite_sequence_of(sk18,sk16)
& subset(sk16,sk17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16,sk17,sk18])],[f37_nnf]) ).
cnf(c83,plain,
transfinite_sequence_of(sk18,sk16),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(hi77,negated_conjecture,
transfinite_sequence_of(sk18,sk16) = true,
inference(equality_encoding,[status(esa)],[c83]) ).
cnf(h39,plain,
transfinite_sequence(sk18) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi77]) ).
cnf(c15,plain,
( function(X1)
| ~ transfinite_sequence_of(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi12,axiom,
ifeq(transfinite_sequence_of(X0,X1),true,function(X0),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(h40,plain,
function(sk18) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi77]) ).
cnf(c14,plain,
( relation(X1)
| ~ transfinite_sequence_of(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi11,axiom,
ifeq(transfinite_sequence_of(X0,X1),true,relation(X0),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h41,plain,
relation(sk18) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi77]) ).
fof(f7,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(f7_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)],[f7]) ).
fof(f7_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)],[f7_nnf]) ).
cnf(c12,plain,
( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi9,axiom,
ifeq(relation(X0),true,ifeq(function(X0),true,ifeq(transfinite_sequence(X0),true,ifeq(transfinite_sequence_of(X0,X1),true,subset(relation_rng(X0),X1),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h43,plain,
subset(relation_rng(sk18),sk16) = true,
inference(hyper_resolution,[status(thm)],[hi9,h41,h40,h39,hi77]) ).
fof(f34,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f34_nnf,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c78,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi72,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X1,X2),true,subset(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c78]) ).
cnf(c82,plain,
subset(sk16,sk17),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(hi76,negated_conjecture,
subset(sk16,sk17) = true,
inference(equality_encoding,[status(esa)],[c82]) ).
cnf(h124,plain,
subset(relation_rng(sk18),sk17) = true,
inference(hyper_resolution,[status(thm)],[hi72,h43,hi76]) ).
cnf(c13,plain,
( ~ subset(relation_rng(X1),X0)
| transfinite_sequence_of(X1,X0)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi10,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)],[c13]) ).
cnf(h216,plain,
transfinite_sequence_of(sk18,sk17) = true,
inference(hyper_resolution,[status(thm)],[hi10,h41,h40,h39,h124]) ).
cnf(c84,plain,
~ transfinite_sequence_of(sk18,sk17),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(hi85,negated_conjecture,
ifeq(transfinite_sequence_of(sk18,sk17),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c84]) ).
cnf(t10,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi85,h216]) ).
cnf(t868,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(f24,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f24_nnf,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
( relation(sk8)
& ~ empty(sk8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8])],[f24_nnf]) ).
cnf(c55,plain,
~ empty(sk8),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f25,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f25_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
~ empty(sk9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f25_nnf]) ).
cnf(c57,plain,
~ empty(sk9),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
fof(f27,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f27_nnf,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
( ordinal(sk11)
& epsilon_connected(sk11)
& epsilon_transitive(sk11)
& ~ empty(sk11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f27_nnf]) ).
cnf(c61,plain,
~ empty(sk11),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f39,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f39_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c86,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
fof(f41,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f41_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c88,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c55,c57,c61,c84,c86,c88]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t868]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM411+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 03:53:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.85/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.85/1.61 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------