%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU257+2 : 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 : n004.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 84.83s 85.77s
% Output : Proof 84.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 105 ( 53 unt; 0 def)
% Number of atoms : 235 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 228 ( 98 ~; 91 |; 22 &)
% ( 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,lemma,
! [A,B] :
( relation(B)
=> ( reflexive(B)
=> reflexive(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t22_wellord1) ).
fof(t23_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( connected(B)
=> connected(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t23_wellord1) ).
fof(t24_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( transitive(B)
=> transitive(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t24_wellord1) ).
fof(t25_wellord1,lemma,
! [A,B] :
( relation(B)
=> ( antisymmetric(B)
=> antisymmetric(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t25_wellord1) ).
fof(t31_wellord1,lemma,
! [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_51_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_51_2,plain,
! [U_415] :
( ( ( well_ordering(U_415)
| ~ well_founded_relation(U_415)
| ~ connected(U_415)
| ~ antisymmetric(U_415)
| ~ transitive(U_415)
| ~ reflexive(U_415) )
& ( ( well_founded_relation(U_415)
& connected(U_415)
& antisymmetric(U_415)
& transitive(U_415)
& reflexive(U_415) )
| ~ well_ordering(U_415) ) )
| ~ relation(U_415) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( reflexive(U_415)
| ~ well_ordering(U_415)
| ~ relation(U_415) ),
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(f_51_4,plain,
( transitive(U_415)
| ~ well_ordering(U_415)
| ~ relation(U_415) ),
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(f_51_5,plain,
( antisymmetric(U_415)
| ~ well_ordering(U_415)
| ~ relation(U_415) ),
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(f_51_6,plain,
( connected(U_415)
| ~ well_ordering(U_415)
| ~ relation(U_415) ),
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(f_51_7,plain,
( well_founded_relation(U_415)
| ~ well_ordering(U_415)
| ~ relation(U_415) ),
inference(clausify,[status(thm)],[f_51_2]) ).
cnf(f_51_8,plain,
( well_ordering(U_415)
| ~ well_founded_relation(U_415)
| ~ connected(U_415)
| ~ antisymmetric(U_415)
| ~ transitive(U_415)
| ~ reflexive(U_415)
| ~ relation(U_415) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_85_1,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_wellord1]) ).
fof(f_85_2,plain,
! [U_551,U_550] :
( relation(relation_restriction(U_551,U_550))
| ~ relation(U_551) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_551] :
( ! [U_550] : relation(relation_restriction(U_551,U_550))
| ~ relation(U_551) ),
inference(miniscope,[status(thm)],[f_85_2]) ).
cnf(f_85_4,plain,
( relation(relation_restriction(U_551,U_550))
| ~ relation(U_551) ),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_223_1,plain,
! [A,B] :
( reflexive(relation_restriction(B,A))
| ~ reflexive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t22_wellord1]) ).
fof(f_223_2,plain,
! [U_851,U_850] :
( reflexive(relation_restriction(U_850,U_851))
| ~ reflexive(U_850)
| ~ relation(U_850) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
cnf(f_223_3,plain,
( reflexive(relation_restriction(U_850,U_851))
| ~ reflexive(U_850)
| ~ relation(U_850) ),
inference(clausify,[status(thm)],[f_223_2]) ).
fof(f_226_1,plain,
! [A,B] :
( connected(relation_restriction(B,A))
| ~ connected(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t23_wellord1]) ).
fof(f_226_2,plain,
! [U_858,U_857] :
( connected(relation_restriction(U_857,U_858))
| ~ connected(U_857)
| ~ relation(U_857) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
cnf(f_226_3,plain,
( connected(relation_restriction(U_857,U_858))
| ~ connected(U_857)
| ~ relation(U_857) ),
inference(clausify,[status(thm)],[f_226_2]) ).
fof(f_228_1,plain,
! [A,B] :
( transitive(relation_restriction(B,A))
| ~ transitive(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t24_wellord1]) ).
fof(f_228_2,plain,
! [U_862,U_861] :
( transitive(relation_restriction(U_861,U_862))
| ~ transitive(U_861)
| ~ relation(U_861) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
cnf(f_228_3,plain,
( transitive(relation_restriction(U_861,U_862))
| ~ transitive(U_861)
| ~ relation(U_861) ),
inference(clausify,[status(thm)],[f_228_2]) ).
fof(f_230_1,plain,
! [A,B] :
( antisymmetric(relation_restriction(B,A))
| ~ antisymmetric(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[t25_wellord1]) ).
fof(f_230_2,plain,
! [U_866,U_865] :
( antisymmetric(relation_restriction(U_865,U_866))
| ~ antisymmetric(U_865)
| ~ relation(U_865) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
cnf(f_230_3,plain,
( antisymmetric(relation_restriction(U_865,U_866))
| ~ antisymmetric(U_865)
| ~ relation(U_865) ),
inference(clausify,[status(thm)],[f_230_2]) ).
fof(f_239_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_239_2,plain,
! [U_887,U_886] :
( well_founded_relation(relation_restriction(U_886,U_887))
| ~ well_founded_relation(U_886)
| ~ relation(U_886) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( well_founded_relation(relation_restriction(U_886,U_887))
| ~ well_founded_relation(U_886)
| ~ relation(U_886) ),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_241_1,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( well_ordering(B)
=> well_ordering(relation_restriction(B,A)) ) ),
inference(negate,[status(cth)],[t32_wellord1]) ).
fof(f_241_2,negated_conjecture,
? [A,B] :
( ~ well_ordering(relation_restriction(B,A))
& well_ordering(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[f_241_1]) ).
fof(f_241_3,negated_conjecture,
? [U_893,U_892] :
( ~ well_ordering(relation_restriction(U_892,U_893))
& well_ordering(U_892)
& relation(U_892) ),
inference(variable_rename,[status(thm)],[f_241_2]) ).
fof(f_241_4,negated_conjecture,
? [U_892] :
( ~ well_ordering(relation_restriction(U_892,sK139))
& well_ordering(U_892)
& relation(U_892) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_893,sK139)],[f_241_3]) ).
fof(f_241_5,negated_conjecture,
( ~ well_ordering(relation_restriction(sK140,sK139))
& well_ordering(sK140)
& relation(sK140) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_892,sK140)],[f_241_4]) ).
cnf(f_241_6,negated_conjecture,
relation(sK140),
inference(clausify,[status(thm)],[f_241_5]) ).
cnf(f_241_7,negated_conjecture,
well_ordering(sK140),
inference(clausify,[status(thm)],[f_241_5]) ).
cnf(f_241_8,negated_conjecture,
~ well_ordering(relation_restriction(sK140,sK139)),
inference(clausify,[status(thm)],[f_241_5]) ).
cnf(t1,plain,
~ well_ordering(relation_restriction(sK140,sK139)),
inference(start,[status(thm),parent(0:0)],[f_241_8]) ).
cnf(t2,plain,
( ~ reflexive(relation_restriction(sK140,sK139))
| ~ transitive(relation_restriction(sK140,sK139))
| ~ antisymmetric(relation_restriction(sK140,sK139))
| ~ connected(relation_restriction(sK140,sK139))
| ~ well_founded_relation(relation_restriction(sK140,sK139))
| ~ relation(relation_restriction(sK140,sK139))
| well_ordering(relation_restriction(sK140,sK139)) ),
inference(extension,[status(thm),parent(t1:1)],[f_51_8]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ relation(sK140)
| relation(relation_restriction(sK140,sK139)) ),
inference(extension,[status(thm),parent(t2:2)],[f_85_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
relation(sK140),
inference(extension,[status(thm),parent(t4:2)],[f_241_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ well_founded_relation(sK140)
| ~ relation(sK140)
| well_founded_relation(relation_restriction(sK140,sK139)) ),
inference(extension,[status(thm),parent(t2:3)],[f_239_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
relation(sK140),
inference(extension,[status(thm),parent(t8:2)],[f_241_6]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(l5,lemma,
relation(sK140),
inference(lemma,[status(cth),parent(t8:2),below(t2:3)],[t8:2]) ).
cnf(t12,plain,
( ~ well_ordering(sK140)
| ~ relation(sK140)
| well_founded_relation(sK140) ),
inference(extension,[status(thm),parent(t8:3)],[f_51_7]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
relation(sK140),
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(sK140),
inference(extension,[status(thm),parent(t12:3)],[f_241_7]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
( ~ connected(sK140)
| ~ relation(sK140)
| connected(relation_restriction(sK140,sK139)) ),
inference(extension,[status(thm),parent(t2:4)],[f_226_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:4]) ).
cnf(t20,plain,
relation(sK140),
inference(extension,[status(thm),parent(t18:2)],[f_241_6]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(l9,lemma,
relation(sK140),
inference(lemma,[status(cth),parent(t18:2),below(t2:4)],[t18:2]) ).
cnf(t22,plain,
( ~ well_ordering(sK140)
| ~ relation(sK140)
| connected(sK140) ),
inference(extension,[status(thm),parent(t18:3)],[f_51_6]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
relation(sK140),
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(sK140),
inference(extension,[status(thm),parent(t22:3)],[f_241_7]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
cnf(t28,plain,
( ~ antisymmetric(sK140)
| ~ relation(sK140)
| antisymmetric(relation_restriction(sK140,sK139)) ),
inference(extension,[status(thm),parent(t2:5)],[f_230_3]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t2:5]) ).
cnf(t30,plain,
relation(sK140),
inference(extension,[status(thm),parent(t28:2)],[f_241_6]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(l13,lemma,
relation(sK140),
inference(lemma,[status(cth),parent(t28:2),below(t2:5)],[t28:2]) ).
cnf(t32,plain,
( ~ well_ordering(sK140)
| ~ relation(sK140)
| antisymmetric(sK140) ),
inference(extension,[status(thm),parent(t28:3)],[f_51_5]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
relation(sK140),
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(sK140),
inference(extension,[status(thm),parent(t32:3)],[f_241_7]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t32:3]) ).
cnf(t38,plain,
( ~ transitive(sK140)
| ~ relation(sK140)
| transitive(relation_restriction(sK140,sK139)) ),
inference(extension,[status(thm),parent(t2:6)],[f_228_3]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t2:6]) ).
cnf(t40,plain,
relation(sK140),
inference(extension,[status(thm),parent(t38:2)],[f_241_6]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(l17,lemma,
relation(sK140),
inference(lemma,[status(cth),parent(t38:2),below(t2:6)],[t38:2]) ).
cnf(t42,plain,
( ~ well_ordering(sK140)
| ~ relation(sK140)
| transitive(sK140) ),
inference(extension,[status(thm),parent(t38:3)],[f_51_4]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t38:3]) ).
cnf(t44,plain,
relation(sK140),
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(sK140),
inference(extension,[status(thm),parent(t42:3)],[f_241_7]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t42:3]) ).
cnf(t48,plain,
( ~ reflexive(sK140)
| ~ relation(sK140)
| reflexive(relation_restriction(sK140,sK139)) ),
inference(extension,[status(thm),parent(t2:7)],[f_223_3]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t2:7]) ).
cnf(t50,plain,
relation(sK140),
inference(extension,[status(thm),parent(t48:2)],[f_241_6]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(l21,lemma,
relation(sK140),
inference(lemma,[status(cth),parent(t48:2),below(t2:7)],[t48:2]) ).
cnf(t52,plain,
( ~ well_ordering(sK140)
| ~ relation(sK140)
| reflexive(sK140) ),
inference(extension,[status(thm),parent(t48:3)],[f_51_3]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t48:3]) ).
cnf(t54,plain,
relation(sK140),
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(sK140),
inference(extension,[status(thm),parent(t52:3)],[f_241_7]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t52:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU257+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/1.00 % Computer : n004.cluster.edu
% 0.12/1.00 % Model : x86_64 x86_64
% 0.12/1.00 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/1.00 % Memory : 8046.5625MB
% 0.12/1.00 % OS : Linux 6.8.0-71-generic
% 0.12/1.00 % CPULimit : 300
% 0.12/1.00 % WCLimit : 300
% 0.12/1.00 % DateTime : Sat Sep 19 23:41:53 UTC 2026
% 0.12/1.00 % CPUTime :
% 84.83/85.77 % SZS status Theorem for theBenchmark
% 84.83/85.77 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------