%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU275+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 : 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 02:51:34 PM UTC 2026
% Result : Theorem 3.42s 0.89s
% Output : Proof 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 33 unt; 0 def)
% Number of atoms : 97 ( 14 equ)
% Maximal formula atoms : 13 ( 1 avg)
% Number of connectives : 80 ( 32 ~; 26 |; 16 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 38 ( 8 sgn 23 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A] :
( ordinal(A)
=> well_founded_relation(inclusion_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_wellord2) ).
fof(f9_nnf,plain,
! [A] :
( well_founded_relation(inclusion_relation(A))
| ~ ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] :
( well_founded_relation(inclusion_relation(A))
| ~ ordinal(A) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c17,plain,
( well_founded_relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi17,axiom,
ifeq(ordinal(X0),true,well_founded_relation(inclusion_relation(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
fof(f10,conjecture,
! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_wellord2) ).
fof(f10_neg,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> well_ordering(inclusion_relation(A)) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [A] :
( ~ well_ordering(inclusion_relation(A))
& ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( ~ well_ordering(inclusion_relation(sk1))
& ordinal(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f10_nnf]) ).
cnf(c18,plain,
ordinal(sk1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi18,negated_conjecture,
ordinal(sk1) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h2,plain,
well_founded_relation(inclusion_relation(sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi17,hi18]) ).
fof(f7,axiom,
! [A] :
( ordinal(A)
=> connected(inclusion_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_wellord2) ).
fof(f7_nnf,plain,
! [A] :
( connected(inclusion_relation(A))
| ~ ordinal(A) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A] :
( connected(inclusion_relation(A))
| ~ ordinal(A) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c15,plain,
( connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi15,axiom,
ifeq(ordinal(X0),true,connected(inclusion_relation(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(h3,plain,
connected(inclusion_relation(sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi18]) ).
fof(f2,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
fof(f2_nnf,plain,
! [A] :
( ( ( ~ well_founded_relation(A)
| ~ connected(A)
| ~ antisymmetric(A)
| ~ transitive(A)
| ~ reflexive(A)
| well_ordering(A) )
& ( ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) )
| ~ well_ordering(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] :
( ( ( ~ well_founded_relation(A)
| ~ connected(A)
| ~ antisymmetric(A)
| ~ transitive(A)
| ~ reflexive(A)
| well_ordering(A) )
& ( ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) )
| ~ well_ordering(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c8,plain,
( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi8,axiom,
ifeq(relation(X0),true,ifeq(reflexive(X0),true,ifeq(transitive(X0),true,ifeq(antisymmetric(X0),true,ifeq(connected(X0),true,ifeq(well_founded_relation(X0),true,well_ordering(X0),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
fof(f3,axiom,
! [A] : relation(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f3_nnf,plain,
! [A] : relation(inclusion_relation(A)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] : relation(inclusion_relation(A)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c9,plain,
relation(inclusion_relation(X0)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi9,axiom,
relation(inclusion_relation(X0)) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
fof(f5,axiom,
! [A] : reflexive(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_wellord2) ).
fof(f5_nnf,plain,
! [A] : reflexive(inclusion_relation(A)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A] : reflexive(inclusion_relation(A)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c13,plain,
reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi13,axiom,
reflexive(inclusion_relation(X0)) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
fof(f6,axiom,
! [A] : transitive(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_wellord2) ).
fof(f6_nnf,plain,
! [A] : transitive(inclusion_relation(A)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] : transitive(inclusion_relation(A)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c14,plain,
transitive(inclusion_relation(X0)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi14,axiom,
transitive(inclusion_relation(X0)) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
fof(f8,axiom,
! [A] : antisymmetric(inclusion_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord2) ).
fof(f8_nnf,plain,
! [A] : antisymmetric(inclusion_relation(A)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A] : antisymmetric(inclusion_relation(A)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c16,plain,
antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi16,axiom,
antisymmetric(inclusion_relation(X0)) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t15,plain,
well_ordering(inclusion_relation(sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi9,hi13,hi14,hi16,h3,h2]) ).
cnf(t47,plain,
well_ordering(inclusion_relation(sk1)) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(c19,plain,
~ well_ordering(inclusion_relation(sk1)),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(goal_0,negated_conjecture,
well_ordering(inclusion_relation(sk1)) != true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t47]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU275+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 13:33:57 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.42/0.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.42/0.89 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------