%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU261+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 : Sun Sep 27 08:45:37 AM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 71 ( 19 unt; 0 def)
% Number of atoms : 256 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 336 ( 151 ~; 141 |; 25 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 44 ( 0 sgn 10 !; 3 ?)
% 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(t53_wellord1,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('theBenchmark.p',t53_wellord1) ).
fof(t54_wellord1,conjecture,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( ( relation_isomorphism(A,B,C)
& well_ordering(A) )
=> well_ordering(B) ) ) ) ),
file('theBenchmark.p',t54_wellord1) ).
fof(t54_wellord1_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(assume_negation,[status(cth)],[t54_wellord1]) ).
cnf(c_5,plain,
( ~ well_founded_relation(A)
| ~ connected(A)
| ~ antisymmetric(A)
| ~ transitive(A)
| ~ reflexive(A)
| well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_6,plain,
( well_founded_relation(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_7,plain,
( connected(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_8,plain,
( antisymmetric(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_9,plain,
( transitive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_10,plain,
( reflexive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
fof(nnf_4,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ well_ordering(B)
& relation_isomorphism(A,B,C)
& well_ordering(A)
& function(C)
& relation(C) )
& relation(B) )
& relation(A) ),
inference(fof_nnf,[status(thm)],[t54_wellord1_neg]) ).
fof(sk_t54_wellord1_neg,plain,
( ~ well_ordering(sK1)
& relation_isomorphism(sK0,sK1,sK2)
& well_ordering(sK0)
& function(sK2)
& relation(sK2)
& relation(sK1)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_4]) ).
cnf(c_11,negated_conjecture,
well_ordering(sK0),
inference(split_conjunct,[status(thm)],[sk_t54_wellord1_neg]) ).
cnf(c_12,negated_conjecture,
~ well_ordering(sK1),
inference(split_conjunct,[status(thm)],[sk_t54_wellord1_neg]) ).
cnf(c_13,plain,
( well_founded_relation(B)
| ~ well_founded_relation(A)
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C)
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t53_wellord1]) ).
cnf(c_14,negated_conjecture,
function(sK2),
inference(split_conjunct,[status(thm)],[sk_t54_wellord1_neg]) ).
cnf(c_15,plain,
( antisymmetric(B)
| ~ antisymmetric(A)
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C)
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t53_wellord1]) ).
cnf(c_16,plain,
( connected(B)
| ~ connected(A)
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C)
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t53_wellord1]) ).
cnf(c_17,plain,
( transitive(B)
| ~ transitive(A)
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C)
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t53_wellord1]) ).
cnf(c_18,plain,
( reflexive(B)
| ~ reflexive(A)
| ~ relation_isomorphism(A,B,C)
| ~ function(C)
| ~ relation(C)
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t53_wellord1]) ).
cnf(c_20,negated_conjecture,
relation_isomorphism(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t54_wellord1_neg]) ).
cnf(c_21,negated_conjecture,
( well_founded_relation(B)
| ~ well_founded_relation(A)
| ~ relation_isomorphism(A,B,sK2)
| ~ relation(sK2)
| ~ relation(B)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_13,c_14]) ).
cnf(c_22,negated_conjecture,
( antisymmetric(B)
| ~ antisymmetric(A)
| ~ relation_isomorphism(A,B,sK2)
| ~ relation(sK2)
| ~ relation(B)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_23,negated_conjecture,
( connected(B)
| ~ connected(A)
| ~ relation_isomorphism(A,B,sK2)
| ~ relation(sK2)
| ~ relation(B)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_24,negated_conjecture,
( transitive(B)
| ~ transitive(A)
| ~ relation_isomorphism(A,B,sK2)
| ~ relation(sK2)
| ~ relation(B)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_25,negated_conjecture,
( reflexive(B)
| ~ reflexive(A)
| ~ relation_isomorphism(A,B,sK2)
| ~ relation(sK2)
| ~ relation(B)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_31,negated_conjecture,
( reflexive(sK1)
| ~ reflexive(sK0)
| ~ relation(sK2)
| ~ relation(sK1)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_20,c_25]) ).
cnf(c_32,negated_conjecture,
( transitive(sK1)
| ~ transitive(sK0)
| ~ relation(sK2)
| ~ relation(sK1)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_20,c_24]) ).
cnf(c_33,negated_conjecture,
( connected(sK1)
| ~ connected(sK0)
| ~ relation(sK2)
| ~ relation(sK1)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_20,c_23]) ).
cnf(c_34,negated_conjecture,
( antisymmetric(sK1)
| ~ antisymmetric(sK0)
| ~ relation(sK2)
| ~ relation(sK1)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_20,c_22]) ).
cnf(c_35,negated_conjecture,
( well_founded_relation(sK1)
| ~ well_founded_relation(sK0)
| ~ relation(sK2)
| ~ relation(sK1)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_20,c_21]) ).
cnf(c_36,negated_conjecture,
( ~ well_founded_relation(sK1)
| ~ connected(sK1)
| ~ antisymmetric(sK1)
| ~ transitive(sK1)
| ~ reflexive(sK1)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_12,c_5]) ).
cnf(c_37,negated_conjecture,
( reflexive(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_11,c_10]) ).
cnf(c_38,negated_conjecture,
( transitive(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_11,c_9]) ).
cnf(c_39,negated_conjecture,
( antisymmetric(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_11,c_8]) ).
cnf(c_40,negated_conjecture,
( connected(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_11,c_7]) ).
cnf(c_41,negated_conjecture,
( well_founded_relation(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_11,c_6]) ).
cnf(c_42,negated_conjecture,
relation(sK2),
inference(split_conjunct,[status(thm)],[sk_t54_wellord1_neg]) ).
cnf(c_43,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t54_wellord1_neg]) ).
cnf(c_44,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t54_wellord1_neg]) ).
cnf(c_63,negated_conjecture,
( well_founded_relation(sK1)
| ~ well_founded_relation(sK0)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_44,c_35]) ).
cnf(c_64,negated_conjecture,
( well_founded_relation(sK1)
| ~ well_founded_relation(sK0)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_43,c_63]) ).
cnf(c_46,negated_conjecture,
( well_founded_relation(sK1)
| ~ well_founded_relation(sK0) ),
inference(resolve,[status(thm)],[c_42,c_64]) ).
cnf(c_65,negated_conjecture,
( antisymmetric(sK1)
| ~ antisymmetric(sK0)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_44,c_34]) ).
cnf(c_66,negated_conjecture,
( antisymmetric(sK1)
| ~ antisymmetric(sK0)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_43,c_65]) ).
cnf(c_47,negated_conjecture,
( antisymmetric(sK1)
| ~ antisymmetric(sK0) ),
inference(resolve,[status(thm)],[c_42,c_66]) ).
cnf(c_67,negated_conjecture,
( connected(sK1)
| ~ connected(sK0)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_44,c_33]) ).
cnf(c_68,negated_conjecture,
( connected(sK1)
| ~ connected(sK0)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_43,c_67]) ).
cnf(c_48,negated_conjecture,
( connected(sK1)
| ~ connected(sK0) ),
inference(resolve,[status(thm)],[c_42,c_68]) ).
cnf(c_69,negated_conjecture,
( transitive(sK1)
| ~ transitive(sK0)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_44,c_32]) ).
cnf(c_70,negated_conjecture,
( transitive(sK1)
| ~ transitive(sK0)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_43,c_69]) ).
cnf(c_49,negated_conjecture,
( transitive(sK1)
| ~ transitive(sK0) ),
inference(resolve,[status(thm)],[c_42,c_70]) ).
cnf(c_71,negated_conjecture,
( reflexive(sK1)
| ~ reflexive(sK0)
| ~ relation(sK2)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_44,c_31]) ).
cnf(c_72,negated_conjecture,
( reflexive(sK1)
| ~ reflexive(sK0)
| ~ relation(sK2) ),
inference(resolve,[status(thm)],[c_43,c_71]) ).
cnf(c_50,negated_conjecture,
( reflexive(sK1)
| ~ reflexive(sK0) ),
inference(resolve,[status(thm)],[c_42,c_72]) ).
cnf(c_51,negated_conjecture,
( ~ well_founded_relation(sK1)
| ~ connected(sK1)
| ~ antisymmetric(sK1)
| ~ transitive(sK1)
| ~ reflexive(sK1) ),
inference(resolve,[status(thm)],[c_43,c_36]) ).
cnf(c_52,negated_conjecture,
well_founded_relation(sK0),
inference(resolve,[status(thm)],[c_44,c_41]) ).
cnf(c_53,negated_conjecture,
connected(sK0),
inference(resolve,[status(thm)],[c_44,c_40]) ).
cnf(c_54,negated_conjecture,
antisymmetric(sK0),
inference(resolve,[status(thm)],[c_44,c_39]) ).
cnf(c_55,negated_conjecture,
transitive(sK0),
inference(resolve,[status(thm)],[c_44,c_38]) ).
cnf(c_56,negated_conjecture,
reflexive(sK0),
inference(resolve,[status(thm)],[c_44,c_37]) ).
cnf(c_57,negated_conjecture,
well_founded_relation(sK1),
inference(resolve,[status(thm)],[c_52,c_46]) ).
cnf(c_58,negated_conjecture,
connected(sK1),
inference(resolve,[status(thm)],[c_53,c_48]) ).
cnf(c_59,negated_conjecture,
antisymmetric(sK1),
inference(resolve,[status(thm)],[c_54,c_47]) ).
cnf(c_60,negated_conjecture,
transitive(sK1),
inference(resolve,[status(thm)],[c_55,c_49]) ).
cnf(c_61,negated_conjecture,
reflexive(sK1),
inference(resolve,[status(thm)],[c_56,c_50]) ).
cnf(c_73,negated_conjecture,
( ~ well_founded_relation(sK1)
| ~ connected(sK1)
| ~ antisymmetric(sK1)
| ~ transitive(sK1) ),
inference(resolve,[status(thm)],[c_61,c_51]) ).
cnf(c_74,negated_conjecture,
( ~ well_founded_relation(sK1)
| ~ connected(sK1)
| ~ antisymmetric(sK1) ),
inference(resolve,[status(thm)],[c_60,c_73]) ).
cnf(c_75,negated_conjecture,
( ~ well_founded_relation(sK1)
| ~ connected(sK1) ),
inference(resolve,[status(thm)],[c_59,c_74]) ).
cnf(c_76,negated_conjecture,
~ well_founded_relation(sK1),
inference(resolve,[status(thm)],[c_58,c_75]) ).
cnf(c_62,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_57,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU261+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 09:00:32 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2718738 was started by sandbox2 on n014,
% 0.09/0.37 % Sat Sep 26 09:00:32 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 54.
% 0.09/0.39 % Level of proof is 6.
% 0.09/0.39 % Maximum clause weight is 12.000.
% 0.09/0.39 % Given clauses 0.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------