%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU257+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 : n019.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 08:45:36 AM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 16 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 138 ( 61 ~; 52 |; 8 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 49 ( 17 sgn 17 !; 2 ?)
% 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(t32_wellord1_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( well_ordering(B)
=> well_ordering(relation_restriction(B,A)) ) ),
inference(assume_negation,[status(cth)],[t32_wellord1]) ).
cnf(c_15,plain,
( reflexive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_16,plain,
( transitive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_17,plain,
( antisymmetric(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_18,plain,
( connected(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_19,plain,
( well_founded_relation(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_20,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_23,plain,
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_wellord1]) ).
cnf(c_25,plain,
( reflexive(relation_restriction(A,B))
| ~ reflexive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t22_wellord1]) ).
cnf(c_26,plain,
( connected(relation_restriction(A,B))
| ~ connected(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t23_wellord1]) ).
cnf(c_27,plain,
( transitive(relation_restriction(A,B))
| ~ transitive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t24_wellord1]) ).
cnf(c_28,plain,
( antisymmetric(relation_restriction(A,B))
| ~ antisymmetric(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t25_wellord1]) ).
cnf(c_29,plain,
( well_founded_relation(relation_restriction(A,B))
| ~ well_founded_relation(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t31_wellord1]) ).
fof(nnf_13,plain,
? [A,B] :
( ~ well_ordering(relation_restriction(B,A))
& well_ordering(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t32_wellord1_neg]) ).
fof(sk_t32_wellord1_neg,plain,
( ~ well_ordering(relation_restriction(sK0,sK1))
& well_ordering(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_13]) ).
cnf(c_30,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t32_wellord1_neg]) ).
cnf(c_31,negated_conjecture,
well_ordering(sK0),
inference(split_conjunct,[status(thm)],[sk_t32_wellord1_neg]) ).
cnf(c_32,negated_conjecture,
~ well_ordering(relation_restriction(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_t32_wellord1_neg]) ).
cnf(c_33,negated_conjecture,
relation(relation_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_23,c_30]) ).
cnf(c_55,negated_conjecture,
( well_founded_relation(sK0)
| ~ well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_19,c_30]) ).
cnf(c_35,negated_conjecture,
well_founded_relation(sK0),
inference(resolve,[status(thm)],[c_55,c_31]) ).
cnf(c_56,negated_conjecture,
( connected(sK0)
| ~ well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_18,c_30]) ).
cnf(c_36,negated_conjecture,
connected(sK0),
inference(resolve,[status(thm)],[c_56,c_31]) ).
cnf(c_57,negated_conjecture,
( antisymmetric(sK0)
| ~ well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_17,c_30]) ).
cnf(c_37,negated_conjecture,
antisymmetric(sK0),
inference(resolve,[status(thm)],[c_57,c_31]) ).
cnf(c_58,negated_conjecture,
( transitive(sK0)
| ~ well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_16,c_30]) ).
cnf(c_38,negated_conjecture,
transitive(sK0),
inference(resolve,[status(thm)],[c_58,c_31]) ).
cnf(c_59,negated_conjecture,
( reflexive(sK0)
| ~ well_ordering(sK0) ),
inference(resolve,[status(thm)],[c_15,c_30]) ).
cnf(c_39,negated_conjecture,
reflexive(sK0),
inference(resolve,[status(thm)],[c_59,c_31]) ).
cnf(c_60,negated_conjecture,
( well_founded_relation(relation_restriction(sK0,A))
| ~ well_founded_relation(sK0) ),
inference(resolve,[status(thm)],[c_29,c_30]) ).
cnf(c_42,negated_conjecture,
well_founded_relation(relation_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_60,c_35]) ).
cnf(c_61,negated_conjecture,
( connected(relation_restriction(sK0,A))
| ~ connected(sK0) ),
inference(resolve,[status(thm)],[c_26,c_30]) ).
cnf(c_43,negated_conjecture,
connected(relation_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_61,c_36]) ).
cnf(c_62,negated_conjecture,
( antisymmetric(relation_restriction(sK0,A))
| ~ antisymmetric(sK0) ),
inference(resolve,[status(thm)],[c_28,c_30]) ).
cnf(c_44,negated_conjecture,
antisymmetric(relation_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_62,c_37]) ).
cnf(c_63,negated_conjecture,
( transitive(relation_restriction(sK0,A))
| ~ transitive(sK0) ),
inference(resolve,[status(thm)],[c_27,c_30]) ).
cnf(c_45,negated_conjecture,
transitive(relation_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_63,c_38]) ).
cnf(c_64,negated_conjecture,
( reflexive(relation_restriction(sK0,A))
| ~ reflexive(sK0) ),
inference(resolve,[status(thm)],[c_25,c_30]) ).
cnf(c_46,negated_conjecture,
reflexive(relation_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_64,c_39]) ).
cnf(c_65,plain,
( ~ well_founded_relation(relation_restriction(sK0,A))
| ~ connected(relation_restriction(sK0,A))
| ~ antisymmetric(relation_restriction(sK0,A))
| ~ transitive(relation_restriction(sK0,A))
| ~ reflexive(relation_restriction(sK0,A))
| well_ordering(relation_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_20,c_33]) ).
cnf(c_66,negated_conjecture,
( ~ well_founded_relation(relation_restriction(sK0,sK1))
| ~ connected(relation_restriction(sK0,sK1))
| ~ antisymmetric(relation_restriction(sK0,sK1))
| ~ transitive(relation_restriction(sK0,sK1))
| ~ reflexive(relation_restriction(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_65,c_32]) ).
cnf(c_67,negated_conjecture,
( ~ well_founded_relation(relation_restriction(sK0,sK1))
| ~ connected(relation_restriction(sK0,sK1))
| ~ antisymmetric(relation_restriction(sK0,sK1))
| ~ reflexive(relation_restriction(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_66,c_45]) ).
cnf(c_68,negated_conjecture,
( ~ well_founded_relation(relation_restriction(sK0,sK1))
| ~ connected(relation_restriction(sK0,sK1))
| ~ reflexive(relation_restriction(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_67,c_44]) ).
cnf(c_69,negated_conjecture,
( ~ well_founded_relation(relation_restriction(sK0,sK1))
| ~ reflexive(relation_restriction(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_68,c_43]) ).
cnf(c_53,negated_conjecture,
~ reflexive(relation_restriction(sK0,sK1)),
inference(resolve,[status(thm)],[c_69,c_42]) ).
cnf(c_54,plain,
$false,
inference(resolve,[status(thm)],[c_53,c_46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU257+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38 % Computer : n019.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 08:59:48 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.39 % Process 922653 was started by sandbox2 on n019,
% 0.13/0.39 % Sat Sep 26 08:59:48 2026
% 0.13/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 0.13/0.40
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40
% 0.13/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.40 % Length of proof is 36.
% 0.13/0.40 % Level of proof is 5.
% 0.13/0.40 % Maximum clause weight is 14.000.
% 0.13/0.40 % Given clauses 30.
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------