%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU257+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 : n026.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 3.23s 0.84s
% Output : Proof 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 70 ( 33 unt; 0 def)
% Number of atoms : 168 ( 29 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 167 ( 69 ~; 63 |; 18 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 89 ( 20 sgn 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f1_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)],[f1]) ).
fof(f1_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)],[f1_nnf]) ).
cnf(c5,plain,
( well_founded_relation(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi5,axiom,
ifeq(relation(X0),true,ifeq(well_ordering(X0),true,well_founded_relation(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
fof(f12,conjecture,
! [A,B] :
( relation(B)
=> ( well_ordering(B)
=> well_ordering(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_wellord1) ).
fof(f12_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( well_ordering(B)
=> well_ordering(relation_restriction(B,A)) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f12_nnf,plain,
? [A,B] :
( ~ well_ordering(relation_restriction(B,A))
& well_ordering(B)
& relation(B) ),
inference(nnf_transformation,[status(thm)],[f12_neg]) ).
fof(f12_sk,plain,
( ~ well_ordering(relation_restriction(sk1,sk0))
& well_ordering(sk1)
& relation(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f12_nnf]) ).
cnf(c17,plain,
relation(sk1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi15,negated_conjecture,
relation(sk1) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(c18,plain,
well_ordering(sk1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi16,negated_conjecture,
well_ordering(sk1) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h2,plain,
well_founded_relation(sk1) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi15,hi16]) ).
fof(f11,axiom,
! [A,B] :
( relation(B)
=> ( well_founded_relation(B)
=> well_founded_relation(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_wellord1) ).
fof(f11_nnf,plain,
! [A,B] :
( well_founded_relation(relation_restriction(B,A))
| ~ well_founded_relation(B)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [B,A] :
( well_founded_relation(relation_restriction(B,A))
| ~ well_founded_relation(B)
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c16,plain,
( well_founded_relation(relation_restriction(X1,X0))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi14,axiom,
ifeq(relation(X0),true,ifeq(well_founded_relation(X0),true,well_founded_relation(relation_restriction(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h7,plain,
well_founded_relation(relation_restriction(sk1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi15,h2]) ).
cnf(c4,plain,
( connected(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi4,axiom,
ifeq(relation(X0),true,ifeq(well_ordering(X0),true,connected(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h3,plain,
connected(sk1) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi15,hi16]) ).
fof(f8,axiom,
! [A,B] :
( relation(B)
=> ( connected(B)
=> connected(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_wellord1) ).
fof(f8_nnf,plain,
! [A,B] :
( connected(relation_restriction(B,A))
| ~ connected(B)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [B,A] :
( connected(relation_restriction(B,A))
| ~ connected(B)
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c13,plain,
( connected(relation_restriction(X1,X0))
| ~ connected(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi11,axiom,
ifeq(relation(X0),true,ifeq(connected(X0),true,connected(relation_restriction(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h10,plain,
connected(relation_restriction(sk1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi15,h3]) ).
cnf(c3,plain,
( antisymmetric(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi3,axiom,
ifeq(relation(X0),true,ifeq(well_ordering(X0),true,antisymmetric(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h4,plain,
antisymmetric(sk1) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi15,hi16]) ).
fof(f10,axiom,
! [A,B] :
( relation(B)
=> ( antisymmetric(B)
=> antisymmetric(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_wellord1) ).
fof(f10_nnf,plain,
! [A,B] :
( antisymmetric(relation_restriction(B,A))
| ~ antisymmetric(B)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [B,A] :
( antisymmetric(relation_restriction(B,A))
| ~ antisymmetric(B)
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c15,plain,
( antisymmetric(relation_restriction(X1,X0))
| ~ antisymmetric(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi13,axiom,
ifeq(relation(X0),true,ifeq(antisymmetric(X0),true,antisymmetric(relation_restriction(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(h11,plain,
antisymmetric(relation_restriction(sk1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi15,h4]) ).
cnf(c2,plain,
( transitive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi2,axiom,
ifeq(relation(X0),true,ifeq(well_ordering(X0),true,transitive(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h5,plain,
transitive(sk1) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi15,hi16]) ).
fof(f9,axiom,
! [A,B] :
( relation(B)
=> ( transitive(B)
=> transitive(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_wellord1) ).
fof(f9_nnf,plain,
! [A,B] :
( transitive(relation_restriction(B,A))
| ~ transitive(B)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [B,A] :
( transitive(relation_restriction(B,A))
| ~ transitive(B)
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c14,plain,
( transitive(relation_restriction(X1,X0))
| ~ transitive(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi12,axiom,
ifeq(relation(X0),true,ifeq(transitive(X0),true,transitive(relation_restriction(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h12,plain,
transitive(relation_restriction(sk1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi15,h5]) ).
cnf(c1,plain,
( reflexive(X0)
| ~ well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(relation(X0),true,ifeq(well_ordering(X0),true,reflexive(X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h6,plain,
reflexive(sk1) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi15,hi16]) ).
fof(f7,axiom,
! [A,B] :
( relation(B)
=> ( reflexive(B)
=> reflexive(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_wellord1) ).
fof(f7_nnf,plain,
! [A,B] :
( reflexive(relation_restriction(B,A))
| ~ reflexive(B)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [B,A] :
( reflexive(relation_restriction(B,A))
| ~ reflexive(B)
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c12,plain,
( reflexive(relation_restriction(X1,X0))
| ~ reflexive(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi10,axiom,
ifeq(relation(X0),true,ifeq(reflexive(X0),true,reflexive(relation_restriction(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h13,plain,
reflexive(relation_restriction(sk1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi15,h6]) ).
fof(f3,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f3_nnf,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c8,plain,
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi8,axiom,
ifeq(relation(X0),true,relation(relation_restriction(X0,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h0,plain,
relation(relation_restriction(sk1,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi15]) ).
cnf(c6,plain,
( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi6,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)],[c6]) ).
cnf(t14,plain,
well_ordering(relation_restriction(sk1,X1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,h0,h13,h12,h11,h10,h7]) ).
cnf(t106,plain,
well_ordering(relation_restriction(sk1,X1)) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(c19,plain,
~ well_ordering(relation_restriction(sk1,sk0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
well_ordering(relation_restriction(sk1,sk0)) != true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t106]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU257+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n026.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 13:28:53 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.23/0.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.23/0.84 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------