%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU257+2 : 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 : n013.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 103.46s 14.82s
% Output : CNFRefutation 103.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% 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 : 133 ( 56 ~; 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 : 54 ( 18 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_560,plain,
( reflexive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_561,plain,
( transitive(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_562,plain,
( antisymmetric(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_563,plain,
( connected(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_564,plain,
( well_founded_relation(A)
| ~ well_ordering(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_wellord1]) ).
cnf(c_565,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_637,plain,
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_wellord1]) ).
cnf(c_830,plain,
( reflexive(relation_restriction(A,B))
| ~ reflexive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t22_wellord1]) ).
cnf(c_833,plain,
( connected(relation_restriction(A,B))
| ~ connected(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t23_wellord1]) ).
cnf(c_835,plain,
( transitive(relation_restriction(A,B))
| ~ transitive(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t24_wellord1]) ).
cnf(c_838,plain,
( antisymmetric(relation_restriction(A,B))
| ~ antisymmetric(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t25_wellord1]) ).
cnf(c_849,plain,
( well_founded_relation(relation_restriction(A,B))
| ~ well_founded_relation(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t31_wellord1]) ).
fof(nnf_314,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_314]) ).
cnf(c_966,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t32_wellord1_neg]) ).
cnf(c_967,negated_conjecture,
well_ordering(sK0),
inference(split_conjunct,[status(thm)],[sk_t32_wellord1_neg]) ).
cnf(c_968,negated_conjecture,
~ well_ordering(relation_restriction(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_t32_wellord1_neg]) ).
cnf(c_29823,negated_conjecture,
( reflexive(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_560,c_967]) ).
cnf(c_1143,negated_conjecture,
reflexive(sK0),
inference(resolve,[status(thm)],[c_966,c_29823]) ).
cnf(c_29824,negated_conjecture,
( transitive(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_561,c_967]) ).
cnf(c_1144,negated_conjecture,
transitive(sK0),
inference(resolve,[status(thm)],[c_966,c_29824]) ).
cnf(c_29825,negated_conjecture,
( antisymmetric(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_562,c_967]) ).
cnf(c_1145,negated_conjecture,
antisymmetric(sK0),
inference(resolve,[status(thm)],[c_966,c_29825]) ).
cnf(c_29826,negated_conjecture,
( connected(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_563,c_967]) ).
cnf(c_1146,negated_conjecture,
connected(sK0),
inference(resolve,[status(thm)],[c_966,c_29826]) ).
cnf(c_29827,negated_conjecture,
( well_founded_relation(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_564,c_967]) ).
cnf(c_1147,negated_conjecture,
well_founded_relation(sK0),
inference(resolve,[status(thm)],[c_966,c_29827]) ).
cnf(c_1190,plain,
relation(relation_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_637,c_966]) ).
cnf(c_29828,plain,
( reflexive(relation_restriction(sK0,A))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_830,c_1143]) ).
cnf(c_24289,negated_conjecture,
reflexive(relation_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_966,c_29828]) ).
cnf(c_29829,plain,
( connected(relation_restriction(sK0,A))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_833,c_1146]) ).
cnf(c_24440,negated_conjecture,
connected(relation_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_966,c_29829]) ).
cnf(c_29830,plain,
( transitive(relation_restriction(sK0,A))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_835,c_1144]) ).
cnf(c_24681,negated_conjecture,
transitive(relation_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_966,c_29830]) ).
cnf(c_29831,plain,
( antisymmetric(relation_restriction(sK0,A))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_838,c_1145]) ).
cnf(c_24759,negated_conjecture,
antisymmetric(relation_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_966,c_29831]) ).
cnf(c_29832,plain,
( well_founded_relation(relation_restriction(sK0,A))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_849,c_1147]) ).
cnf(c_25072,negated_conjecture,
well_founded_relation(relation_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_966,c_29832]) ).
cnf(c_29833,plain,
( ~ well_founded_relation(relation_restriction(sK0,A))
| ~ connected(relation_restriction(sK0,A))
| ~ antisymmetric(relation_restriction(sK0,A))
| ~ transitive(relation_restriction(sK0,A))
| well_ordering(relation_restriction(sK0,A))
| ~ relation(relation_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_24289,c_565]) ).
cnf(c_29834,plain,
( ~ well_founded_relation(relation_restriction(sK0,A))
| ~ connected(relation_restriction(sK0,A))
| ~ antisymmetric(relation_restriction(sK0,A))
| ~ transitive(relation_restriction(sK0,A))
| well_ordering(relation_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_1190,c_29833]) ).
cnf(c_29835,plain,
( ~ well_founded_relation(relation_restriction(sK0,A))
| ~ connected(relation_restriction(sK0,A))
| ~ antisymmetric(relation_restriction(sK0,A))
| well_ordering(relation_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_24681,c_29834]) ).
cnf(c_29836,plain,
( ~ well_founded_relation(relation_restriction(sK0,A))
| ~ connected(relation_restriction(sK0,A))
| well_ordering(relation_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_24759,c_29835]) ).
cnf(c_29837,plain,
( ~ well_founded_relation(relation_restriction(sK0,A))
| well_ordering(relation_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_24440,c_29836]) ).
cnf(c_29821,plain,
well_ordering(relation_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_25072,c_29837]) ).
cnf(c_29822,plain,
$false,
inference(resolve,[status(thm)],[c_29821,c_968]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU257+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n013.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 08:59:06 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 2392031 was started by sandbox2 on n013,
% 0.19/0.44 % Sat Sep 26 08:59:06 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.31/0.57
% 0.31/0.57 % From the command line: assign(max_seconds, 300).
% 0.31/0.57
% 0.31/0.57 % SInE: 269 to sos, 46 to usable, of 315 axioms (tolerance 2.00, depth 0 fixpoint).
% 103.46/14.82
% 103.46/14.82 % given #500 (F,wt=18): 6839 cartesian_product2(A,B) != unordered_triple(C,empty_set,D). [resolve(508,b,1872,a),unit_del(b,1480)].
% 103.46/14.82
% 103.46/14.82 % given #1000 (W,wt=14): 14795 relation(relation_dom_restriction(c11,A)). [resolve(645,a,353,a)].
% 103.46/14.82
% 103.46/14.82 % given #1500 (F,wt=14): 23400 set_meet(c10) != c8. [resolve(23101,b,16637,a)].
% 103.46/14.82
% 103.46/14.82 % given #2000 (T,wt=14): 21861 relation(relation_composition(c7,empty_set)). [resolve(752,a,14364,a)].
% 103.46/14.82
% 103.46/14.82 % SZS status Theorem for theBenchmark
% 103.46/14.82
% 103.46/14.82 % Proof 1 at 4.45 (+ 1.37) seconds.
% 103.46/14.82 % Length of proof is 36.
% 103.46/14.82 % Level of proof is 5.
% 103.46/14.82 % Maximum clause weight is 118.000.
% 103.46/14.82 % Given clauses 2311.
% 103.46/14.82
% 103.46/14.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------