%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU261+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 : n016.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 02:51:31 PM UTC 2026
% Result : Theorem 0.14s 5.94s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 60 ( 39 unt; 0 def)
% Number of atoms : 202 ( 31 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 228 ( 86 ~; 80 |; 43 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 63 ( 0 sgn 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,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(f0_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)],[f0]) ).
fof(f0_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)],[f0_nnf]) ).
cnf(c4,plain,
( well_founded_relation(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi4,axiom,
ifeq(relation(X0),true,ifeq(well_ordering(X0),true,well_founded_relation(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
fof(f3,conjecture,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_isomorphism(A,B,C)
& well_ordering(A) )
=> well_ordering(B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_wellord1) ).
fof(f3_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_isomorphism(A,B,C)
& well_ordering(A) )
=> well_ordering(B) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f3_nnf,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ well_ordering(B)
& relation_isomorphism(A,B,C)
& well_ordering(A)
& function(C)
& relation(C) )
& relation(B) )
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f3_neg]) ).
fof(f3_sk,plain,
( ~ well_ordering(sk2)
& relation_isomorphism(sk1,sk2,sk3)
& well_ordering(sk1)
& function(sk3)
& relation(sk3)
& relation(sk2)
& relation(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f3_nnf]) ).
cnf(c13,plain,
relation(sk1),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi13,negated_conjecture,
relation(sk1) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(c17,plain,
well_ordering(sk1),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi17,negated_conjecture,
well_ordering(sk1) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h0,plain,
well_founded_relation(sk1) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi13,hi17]) ).
fof(f2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( relation_isomorphism(A,B,C)
=> ( ( well_founded_relation(A)
=> well_founded_relation(B) )
& ( antisymmetric(A)
=> antisymmetric(B) )
& ( connected(A)
=> connected(B) )
& ( transitive(A)
=> transitive(B) )
& ( reflexive(A)
=> reflexive(B) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_wellord1) ).
fof(f2_nnf,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( well_founded_relation(B)
| ~ well_founded_relation(A) )
& ( antisymmetric(B)
| ~ antisymmetric(A) )
& ( connected(B)
| ~ connected(A) )
& ( transitive(B)
| ~ transitive(A) )
& ( reflexive(B)
| ~ reflexive(A) ) )
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C) )
| ~ relation(B) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] :
( ( ( well_founded_relation(B)
| ~ well_founded_relation(A) )
& ( antisymmetric(B)
| ~ antisymmetric(A) )
& ( connected(B)
| ~ connected(A) )
& ( transitive(B)
| ~ transitive(A) )
& ( reflexive(B)
| ~ reflexive(A) ) )
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C)
| ~ relation(B)
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c12,plain,
( well_founded_relation(X1)
| ~ well_founded_relation(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi12,axiom,
ifeq(relation(X0),true,ifeq(relation(X1),true,ifeq(relation(X2),true,ifeq(function(X2),true,ifeq(relation_isomorphism(X0,X1,X2),true,ifeq(well_founded_relation(X0),true,well_founded_relation(X1),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(c14,plain,
relation(sk2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi14,negated_conjecture,
relation(sk2) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(c15,plain,
relation(sk3),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi15,negated_conjecture,
relation(sk3) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(c16,plain,
function(sk3),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi16,negated_conjecture,
function(sk3) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(c18,plain,
relation_isomorphism(sk1,sk2,sk3),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi18,negated_conjecture,
relation_isomorphism(sk1,sk2,sk3) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h5,plain,
well_founded_relation(sk2) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi13,hi14,hi15,hi16,hi18,h0]) ).
cnf(c3,plain,
( connected(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi3,axiom,
ifeq(relation(X0),true,ifeq(well_ordering(X0),true,connected(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h1,plain,
connected(sk1) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi13,hi17]) ).
cnf(c10,plain,
( connected(X1)
| ~ connected(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi10,axiom,
ifeq(relation(X0),true,ifeq(relation(X1),true,ifeq(relation(X2),true,ifeq(function(X2),true,ifeq(relation_isomorphism(X0,X1,X2),true,ifeq(connected(X0),true,connected(X1),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h7,plain,
connected(sk2) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi13,hi14,hi15,hi16,hi18,h1]) ).
cnf(c2,plain,
( antisymmetric(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,axiom,
ifeq(relation(X0),true,ifeq(well_ordering(X0),true,antisymmetric(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h2,plain,
antisymmetric(sk1) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi13,hi17]) ).
cnf(c11,plain,
( antisymmetric(X1)
| ~ antisymmetric(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi11,axiom,
ifeq(relation(X0),true,ifeq(relation(X1),true,ifeq(relation(X2),true,ifeq(function(X2),true,ifeq(relation_isomorphism(X0,X1,X2),true,ifeq(antisymmetric(X0),true,antisymmetric(X1),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h6,plain,
antisymmetric(sk2) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi13,hi14,hi15,hi16,hi18,h2]) ).
cnf(c1,plain,
( transitive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,axiom,
ifeq(relation(X0),true,ifeq(well_ordering(X0),true,transitive(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h3,plain,
transitive(sk1) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi13,hi17]) ).
cnf(c9,plain,
( transitive(X1)
| ~ transitive(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi9,axiom,
ifeq(relation(X0),true,ifeq(relation(X1),true,ifeq(relation(X2),true,ifeq(function(X2),true,ifeq(relation_isomorphism(X0,X1,X2),true,ifeq(transitive(X0),true,transitive(X1),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h8,plain,
transitive(sk2) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi13,hi14,hi15,hi16,hi18,h3]) ).
cnf(c0,plain,
( reflexive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(relation(X0),true,ifeq(well_ordering(X0),true,reflexive(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h4,plain,
reflexive(sk1) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi13,hi17]) ).
cnf(c8,plain,
( reflexive(X1)
| ~ reflexive(X0)
| ~ relation_isomorphism(X0,X1,X2)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi8,axiom,
ifeq(relation(X0),true,ifeq(relation(X1),true,ifeq(relation(X2),true,ifeq(function(X2),true,ifeq(relation_isomorphism(X0,X1,X2),true,ifeq(reflexive(X0),true,reflexive(X1),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h9,plain,
reflexive(sk2) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi13,hi14,hi15,hi16,hi18,h4]) ).
cnf(c5,plain,
( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi5,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)],[c5]) ).
cnf(t17,plain,
well_ordering(sk2) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi14,h9,h8,h6,h7,h5]) ).
cnf(t138,plain,
well_ordering(sk2) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(c19,plain,
~ well_ordering(sk2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
well_ordering(sk2) != true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t138]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU261+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/5.37 % Computer : n016.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % 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 13:31:18 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/5.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.94 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------