%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU257+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 : Thu Sep 24 08:58:45 AM UTC 2026
% Result : Theorem 0.20s 18.82s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 106 ( 53 unt; 0 def)
% Number of atoms : 238 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 231 ( 99 ~; 91 |; 24 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 6 sgn 45 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_wellord1,axiom,
! [A] :
( relation(A)
=> ( well_ordering(A)
<=> ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) ) ) ),
file('theBenchmark.p',d4_wellord1) ).
fof(dt_k2_wellord1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('theBenchmark.p',dt_k2_wellord1) ).
fof(t22_wellord1,axiom,
! [A,B] :
( relation(B)
=> ( reflexive(B)
=> reflexive(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t22_wellord1) ).
fof(t23_wellord1,axiom,
! [A,B] :
( relation(B)
=> ( connected(B)
=> connected(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t23_wellord1) ).
fof(t24_wellord1,axiom,
! [A,B] :
( relation(B)
=> ( transitive(B)
=> transitive(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t24_wellord1) ).
fof(t25_wellord1,axiom,
! [A,B] :
( relation(B)
=> ( antisymmetric(B)
=> antisymmetric(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t25_wellord1) ).
fof(t31_wellord1,axiom,
! [A,B] :
( relation(B)
=> ( well_founded_relation(B)
=> well_founded_relation(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t31_wellord1) ).
fof(t32_wellord1,conjecture,
! [A,B] :
( relation(B)
=> ( well_ordering(B)
=> well_ordering(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t32_wellord1) ).
fof(f_2_1,plain,
! [A] :
( ( ( well_ordering(A)
| ~ well_founded_relation(A)
| ~ connected(A)
| ~ antisymmetric(A)
| ~ transitive(A)
| ~ reflexive(A) )
& ( ( well_founded_relation(A)
& connected(A)
& antisymmetric(A)
& transitive(A)
& reflexive(A) )
| ~ well_ordering(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d4_wellord1]) ).
fof(f_2_2,plain,
! [U_2] :
( ( ( well_ordering(U_2)
| ~ well_founded_relation(U_2)
| ~ connected(U_2)
| ~ antisymmetric(U_2)
| ~ transitive(U_2)
| ~ reflexive(U_2) )
& ( ( well_founded_relation(U_2)
& connected(U_2)
& antisymmetric(U_2)
& transitive(U_2)
& reflexive(U_2) )
| ~ well_ordering(U_2) ) )
| ~ relation(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( reflexive(U_2)
| ~ well_ordering(U_2)
| ~ relation(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( transitive(U_2)
| ~ well_ordering(U_2)
| ~ relation(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_5,plain,
( antisymmetric(U_2)
| ~ well_ordering(U_2)
| ~ relation(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_6,plain,
( connected(U_2)
| ~ well_ordering(U_2)
| ~ relation(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_7,plain,
( well_founded_relation(U_2)
| ~ well_ordering(U_2)
| ~ relation(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_8,plain,
( well_ordering(U_2)
| ~ well_founded_relation(U_2)
| ~ connected(U_2)
| ~ antisymmetric(U_2)
| ~ transitive(U_2)
| ~ reflexive(U_2)
| ~ relation(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_4_1,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_wellord1]) ).
fof(f_4_2,plain,
! [U_6,U_5] :
( relation(relation_restriction(U_6,U_5))
| ~ relation(U_6) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_6] :
( ! [U_5] : relation(relation_restriction(U_6,U_5))
| ~ relation(U_6) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( relation(relation_restriction(U_6,U_5))
| ~ relation(U_6) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_8_1,plain,
! [A,B] :
( reflexive(relation_restriction(B,A))
| ~ reflexive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t22_wellord1]) ).
fof(f_8_2,plain,
! [U_10,U_9] :
( reflexive(relation_restriction(U_9,U_10))
| ~ reflexive(U_9)
| ~ relation(U_9) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( reflexive(relation_restriction(U_9,U_10))
| ~ reflexive(U_9)
| ~ relation(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A,B] :
( connected(relation_restriction(B,A))
| ~ connected(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t23_wellord1]) ).
fof(f_9_2,plain,
! [U_12,U_11] :
( connected(relation_restriction(U_11,U_12))
| ~ connected(U_11)
| ~ relation(U_11) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( connected(relation_restriction(U_11,U_12))
| ~ connected(U_11)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A,B] :
( transitive(relation_restriction(B,A))
| ~ transitive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t24_wellord1]) ).
fof(f_10_2,plain,
! [U_14,U_13] :
( transitive(relation_restriction(U_13,U_14))
| ~ transitive(U_13)
| ~ relation(U_13) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( transitive(relation_restriction(U_13,U_14))
| ~ transitive(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A,B] :
( antisymmetric(relation_restriction(B,A))
| ~ antisymmetric(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t25_wellord1]) ).
fof(f_11_2,plain,
! [U_16,U_15] :
( antisymmetric(relation_restriction(U_15,U_16))
| ~ antisymmetric(U_15)
| ~ relation(U_15) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( antisymmetric(relation_restriction(U_15,U_16))
| ~ antisymmetric(U_15)
| ~ relation(U_15) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B] :
( well_founded_relation(relation_restriction(B,A))
| ~ well_founded_relation(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t31_wellord1]) ).
fof(f_12_2,plain,
! [U_18,U_17] :
( well_founded_relation(relation_restriction(U_17,U_18))
| ~ well_founded_relation(U_17)
| ~ relation(U_17) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( well_founded_relation(relation_restriction(U_17,U_18))
| ~ well_founded_relation(U_17)
| ~ relation(U_17) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( well_ordering(B)
=> well_ordering(relation_restriction(B,A)) ) ),
inference(negate,[status(cth)],[t32_wellord1]) ).
fof(f_13_2,negated_conjecture,
? [A,B] :
( ~ well_ordering(relation_restriction(B,A))
& well_ordering(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_13_1]) ).
fof(f_13_3,negated_conjecture,
? [U_20,U_19] :
( ~ well_ordering(relation_restriction(U_19,U_20))
& well_ordering(U_19)
& relation(U_19) ),
inference(variable_rename,[status(thm)],[f_13_2]) ).
fof(f_13_4,negated_conjecture,
? [U_19] :
( ~ well_ordering(relation_restriction(U_19,sK1))
& well_ordering(U_19)
& relation(U_19) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_20,sK1)],[f_13_3]) ).
fof(f_13_5,negated_conjecture,
( ~ well_ordering(relation_restriction(sK2,sK1))
& well_ordering(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_19,sK2)],[f_13_4]) ).
fof(f_13_6,negated_conjecture,
( ~ well_ordering(relation_restriction(sK2,sK1))
& well_ordering(sK2)
& relation(sK2) ),
inference(definitional_conversion,[status(esa)],[f_13_5]) ).
cnf(f_13_7,negated_conjecture,
relation(sK2),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_8,negated_conjecture,
well_ordering(sK2),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_9,negated_conjecture,
~ well_ordering(relation_restriction(sK2,sK1)),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(t1,plain,
~ well_ordering(relation_restriction(sK2,sK1)),
inference(start,[status(thm),parent(0:0)],[f_13_9]) ).
cnf(t2,plain,
( ~ reflexive(relation_restriction(sK2,sK1))
| ~ transitive(relation_restriction(sK2,sK1))
| ~ antisymmetric(relation_restriction(sK2,sK1))
| ~ connected(relation_restriction(sK2,sK1))
| ~ well_founded_relation(relation_restriction(sK2,sK1))
| ~ relation(relation_restriction(sK2,sK1))
| well_ordering(relation_restriction(sK2,sK1)) ),
inference(extension,[status(thm),parent(t1:1)],[f_2_8]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ relation(sK2)
| relation(relation_restriction(sK2,sK1)) ),
inference(extension,[status(thm),parent(t2:2)],[f_4_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
relation(sK2),
inference(extension,[status(thm),parent(t4:2)],[f_13_7]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ well_founded_relation(sK2)
| ~ relation(sK2)
| well_founded_relation(relation_restriction(sK2,sK1)) ),
inference(extension,[status(thm),parent(t2:3)],[f_12_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
relation(sK2),
inference(extension,[status(thm),parent(t8:2)],[f_13_7]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(l5,lemma,
relation(sK2),
inference(lemma,[status(cth),parent(t8:2),below(t2:3)],[t8:2]) ).
cnf(t12,plain,
( ~ well_ordering(sK2)
| ~ relation(sK2)
| well_founded_relation(sK2) ),
inference(extension,[status(thm),parent(t8:3)],[f_2_7]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
relation(sK2),
inference(lemma_extension,[status(thm),parent(t12:2)],[l5:1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
well_ordering(sK2),
inference(extension,[status(thm),parent(t12:3)],[f_13_8]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
( ~ connected(sK2)
| ~ relation(sK2)
| connected(relation_restriction(sK2,sK1)) ),
inference(extension,[status(thm),parent(t2:4)],[f_9_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:4]) ).
cnf(t20,plain,
relation(sK2),
inference(extension,[status(thm),parent(t18:2)],[f_13_7]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(l9,lemma,
relation(sK2),
inference(lemma,[status(cth),parent(t18:2),below(t2:4)],[t18:2]) ).
cnf(t22,plain,
( ~ well_ordering(sK2)
| ~ relation(sK2)
| connected(sK2) ),
inference(extension,[status(thm),parent(t18:3)],[f_2_6]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
relation(sK2),
inference(lemma_extension,[status(thm),parent(t22:2)],[l9:1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
well_ordering(sK2),
inference(extension,[status(thm),parent(t22:3)],[f_13_8]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
cnf(t28,plain,
( ~ antisymmetric(sK2)
| ~ relation(sK2)
| antisymmetric(relation_restriction(sK2,sK1)) ),
inference(extension,[status(thm),parent(t2:5)],[f_11_3]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t2:5]) ).
cnf(t30,plain,
relation(sK2),
inference(extension,[status(thm),parent(t28:2)],[f_13_7]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(l13,lemma,
relation(sK2),
inference(lemma,[status(cth),parent(t28:2),below(t2:5)],[t28:2]) ).
cnf(t32,plain,
( ~ well_ordering(sK2)
| ~ relation(sK2)
| antisymmetric(sK2) ),
inference(extension,[status(thm),parent(t28:3)],[f_2_5]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
relation(sK2),
inference(lemma_extension,[status(thm),parent(t32:2)],[l13:1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
well_ordering(sK2),
inference(extension,[status(thm),parent(t32:3)],[f_13_8]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t32:3]) ).
cnf(t38,plain,
( ~ transitive(sK2)
| ~ relation(sK2)
| transitive(relation_restriction(sK2,sK1)) ),
inference(extension,[status(thm),parent(t2:6)],[f_10_3]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t2:6]) ).
cnf(t40,plain,
relation(sK2),
inference(extension,[status(thm),parent(t38:2)],[f_13_7]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(l17,lemma,
relation(sK2),
inference(lemma,[status(cth),parent(t38:2),below(t2:6)],[t38:2]) ).
cnf(t42,plain,
( ~ well_ordering(sK2)
| ~ relation(sK2)
| transitive(sK2) ),
inference(extension,[status(thm),parent(t38:3)],[f_2_4]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t38:3]) ).
cnf(t44,plain,
relation(sK2),
inference(lemma_extension,[status(thm),parent(t42:2)],[l17:1]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
well_ordering(sK2),
inference(extension,[status(thm),parent(t42:3)],[f_13_8]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t42:3]) ).
cnf(t48,plain,
( ~ reflexive(sK2)
| ~ relation(sK2)
| reflexive(relation_restriction(sK2,sK1)) ),
inference(extension,[status(thm),parent(t2:7)],[f_8_3]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t2:7]) ).
cnf(t50,plain,
relation(sK2),
inference(extension,[status(thm),parent(t48:2)],[f_13_7]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(l21,lemma,
relation(sK2),
inference(lemma,[status(cth),parent(t48:2),below(t2:7)],[t48:2]) ).
cnf(t52,plain,
( ~ well_ordering(sK2)
| ~ relation(sK2)
| reflexive(sK2) ),
inference(extension,[status(thm),parent(t48:3)],[f_2_3]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t48:3]) ).
cnf(t54,plain,
relation(sK2),
inference(lemma_extension,[status(thm),parent(t52:2)],[l21:1]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
well_ordering(sK2),
inference(extension,[status(thm),parent(t52:3)],[f_13_8]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t52:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU257+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/18.78 % CPULimit : 300
% 0.08/18.78 % WCLimit : 300
% 0.08/18.78 % DateTime : Sat Sep 19 23:41:48 UTC 2026
% 0.08/18.79 % CPUTime :
% 0.20/18.82 % SZS status Theorem for theBenchmark
% 0.20/18.82 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------