%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV374+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 : 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 09:07:35 AM UTC 2026
% Result : Theorem 238.26s 32.27s
% Output : CNFRefutation 238.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 8 unt; 0 def)
% Number of atoms : 102 ( 50 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 91 ( 26 ~; 49 |; 10 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 69 ( 25 sgn 22 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(totality,axiom,
! [U,V] :
( less_than(V,U)
| less_than(U,V) ),
file('theBenchmark.p',totality) ).
fof(stricly_smaller_definition,axiom,
! [U,V] :
( strictly_less_than(U,V)
<=> ( ~ less_than(V,U)
& less_than(U,V) ) ),
file('theBenchmark.p',stricly_smaller_definition) ).
fof(ax40,axiom,
! [U,V] :
( ok(triple(U,V,bad))
<=> $false ),
file('theBenchmark.p',ax40) ).
fof(ax46,axiom,
! [U,V] : findmin_cpq_eff(triple(U,create_slb,V)) = triple(U,create_slb,bad),
file('theBenchmark.p',ax46) ).
fof(ax47,axiom,
! [U,V,W,X] :
( ( ~ contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
=> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad) ),
file('theBenchmark.p',ax47) ).
fof(ax48,axiom,
! [U,V,W,X] :
( ( strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U)))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb )
=> findmin_cpq_eff(triple(U,V,W)) = triple(U,update_slb(V,findmin_pqp_res(U)),bad) ),
file('theBenchmark.p',ax48) ).
fof(l10_co,conjecture,
! [U,V,W] :
( ok(findmin_cpq_eff(triple(U,V,W)))
=> ( less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb ) ),
file('theBenchmark.p',l10_co) ).
fof(l10_co_neg,negated_conjecture,
~ ! [U,V,W] :
( ok(findmin_cpq_eff(triple(U,V,W)))
=> ( less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
& contains_slb(V,findmin_pqp_res(U))
& V != create_slb ) ),
inference(assume_negation,[status(cth)],[l10_co]) ).
cnf(c_43,plain,
( less_than(B,A)
| less_than(A,B) ),
inference(clausify,[status(thm)],[totality]) ).
cnf(c_47,plain,
( less_than(B,A)
| ~ less_than(A,B)
| strictly_less_than(A,B) ),
inference(clausify,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_78,plain,
~ ok(triple(A,B,bad)),
inference(clausify,[status(thm)],[ax40]) ).
cnf(c_84,plain,
triple(A,create_slb,bad) = findmin_cpq_eff(triple(A,create_slb,B)),
inference(clausify,[status(thm)],[ax46]) ).
cnf(c_85,plain,
( triple(B,update_slb(A,findmin_pqp_res(B)),bad) = findmin_cpq_eff(triple(B,A,C))
| contains_slb(A,findmin_pqp_res(B))
| create_slb = A ),
inference(clausify,[status(thm)],[ax47]) ).
cnf(c_86,plain,
( triple(B,update_slb(A,findmin_pqp_res(B)),bad) = findmin_cpq_eff(triple(B,A,C))
| ~ strictly_less_than(findmin_pqp_res(B),lookup_slb(A,findmin_pqp_res(B)))
| ~ contains_slb(A,findmin_pqp_res(B))
| create_slb = A ),
inference(clausify,[status(thm)],[ax48]) ).
fof(nnf_41,plain,
? [U,V,W] :
( ( ~ less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U))
| ~ contains_slb(V,findmin_pqp_res(U))
| create_slb = V )
& ok(findmin_cpq_eff(triple(U,V,W))) ),
inference(fof_nnf,[status(thm)],[l10_co_neg]) ).
fof(sk_l10_co_neg,plain,
( ( ~ less_than(lookup_slb(sK1,findmin_pqp_res(sK0)),findmin_pqp_res(sK0))
| ~ contains_slb(sK1,findmin_pqp_res(sK0))
| create_slb = sK1 )
& ok(findmin_cpq_eff(triple(sK0,sK1,sK2))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK2)],[nnf_41]) ).
cnf(c_92,negated_conjecture,
ok(findmin_cpq_eff(triple(sK0,sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_l10_co_neg]) ).
cnf(c_93,negated_conjecture,
( ~ less_than(lookup_slb(sK1,findmin_pqp_res(sK0)),findmin_pqp_res(sK0))
| ~ contains_slb(sK1,findmin_pqp_res(sK0))
| create_slb = sK1 ),
inference(split_conjunct,[status(thm)],[sk_l10_co_neg]) ).
cnf(c_94,negated_conjecture,
( ~ less_than(lookup_slb(sK1,findmin_pqp_res(sK0)),findmin_pqp_res(sK0))
| ~ contains_slb(sK1,findmin_pqp_res(sK0))
| sK1 = create_slb ),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_14709,plain,
( less_than(B,A)
| less_than(B,A)
| strictly_less_than(A,B) ),
inference(resolve,[status(thm)],[c_47,c_43]) ).
cnf(c_99,plain,
( less_than(B,A)
| strictly_less_than(A,B) ),
inference(copy,[status(thm)],[c_14709]) ).
cnf(c_145,plain,
~ ok(findmin_cpq_eff(triple(A,create_slb,B))),
inference(paramod,[status(thm)],[c_84,c_78]) ).
cnf(c_14710,plain,
( triple(B,update_slb(A,findmin_pqp_res(B)),bad) = findmin_cpq_eff(triple(B,A,D))
| create_slb = A
| triple(B,update_slb(A,findmin_pqp_res(B)),bad) = findmin_cpq_eff(triple(B,A,C))
| ~ strictly_less_than(findmin_pqp_res(B),lookup_slb(A,findmin_pqp_res(B)))
| create_slb = A ),
inference(resolve,[status(thm)],[c_86,c_85]) ).
cnf(c_156,plain,
( triple(B,update_slb(A,findmin_pqp_res(B)),bad) = findmin_cpq_eff(triple(B,A,D))
| triple(B,update_slb(A,findmin_pqp_res(B)),bad) = findmin_cpq_eff(triple(B,A,C))
| ~ strictly_less_than(findmin_pqp_res(B),lookup_slb(A,findmin_pqp_res(B)))
| create_slb = A ),
inference(copy,[status(thm)],[c_14710]) ).
cnf(c_159,plain,
( triple(B,update_slb(A,findmin_pqp_res(B)),bad) = findmin_cpq_eff(triple(B,A,C))
| ~ strictly_less_than(findmin_pqp_res(B),lookup_slb(A,findmin_pqp_res(B)))
| create_slb = A ),
inference(factor,[status(thm)],[c_156]) ).
cnf(c_14711,negated_conjecture,
( triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad) = findmin_cpq_eff(triple(sK0,sK1,A))
| create_slb = sK1
| ~ less_than(lookup_slb(sK1,findmin_pqp_res(sK0)),findmin_pqp_res(sK0))
| sK1 = create_slb ),
inference(resolve,[status(thm)],[c_94,c_85]) ).
cnf(c_14712,negated_conjecture,
( triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad) = findmin_cpq_eff(triple(sK0,sK1,A))
| sK1 = create_slb
| ~ less_than(lookup_slb(sK1,findmin_pqp_res(sK0)),findmin_pqp_res(sK0))
| sK1 = create_slb ),
inference(copy,[status(thm)],[c_14711]) ).
cnf(c_175,negated_conjecture,
( triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad) = findmin_cpq_eff(triple(sK0,sK1,A))
| ~ less_than(lookup_slb(sK1,findmin_pqp_res(sK0)),findmin_pqp_res(sK0))
| sK1 = create_slb ),
inference(copy,[status(thm)],[c_14712]) ).
cnf(c_13126,plain,
( less_than(lookup_slb(A,findmin_pqp_res(B)),findmin_pqp_res(B))
| triple(B,update_slb(A,findmin_pqp_res(B)),bad) = findmin_cpq_eff(triple(B,A,C))
| create_slb = A ),
inference(resolve,[status(thm)],[c_159,c_99]) ).
cnf(c_14713,plain,
( triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad) = findmin_cpq_eff(triple(sK0,sK1,B))
| sK1 = create_slb
| triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad) = findmin_cpq_eff(triple(sK0,sK1,A))
| create_slb = sK1 ),
inference(resolve,[status(thm)],[c_13126,c_175]) ).
cnf(c_14714,plain,
( triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad) = findmin_cpq_eff(triple(sK0,sK1,B))
| sK1 = create_slb
| triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad) = findmin_cpq_eff(triple(sK0,sK1,A))
| sK1 = create_slb ),
inference(copy,[status(thm)],[c_14713]) ).
cnf(c_14674,plain,
( triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad) = findmin_cpq_eff(triple(sK0,sK1,B))
| triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad) = findmin_cpq_eff(triple(sK0,sK1,A))
| sK1 = create_slb ),
inference(copy,[status(thm)],[c_14714]) ).
cnf(c_14681,plain,
( triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad) = findmin_cpq_eff(triple(sK0,sK1,A))
| sK1 = create_slb ),
inference(factor,[status(thm)],[c_14674]) ).
cnf(c_14715,plain,
( ok(triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad))
| sK1 = create_slb ),
inference(paramod,[status(thm)],[c_14681,c_92]) ).
cnf(c_14707,plain,
sK1 = create_slb,
inference(resolve,[status(thm)],[c_78,c_14715]) ).
cnf(c_14716,negated_conjecture,
ok(findmin_cpq_eff(triple(sK0,create_slb,sK2))),
inference(paramod,[status(thm)],[c_14707,c_92]) ).
cnf(c_14708,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_145,c_14716]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV374+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n013.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 13:39:06 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 2863113 was started by sandbox2 on n013,
% 0.12/0.38 % Sat Sep 26 13:39:06 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.39
% 0.12/0.39 % From the command line: assign(max_seconds, 300).
% 238.26/32.27
% 238.26/32.27 % given #500 (T,wt=36): 1138 succ_cpq(findmin_cpq_eff(findmin_cpq_eff(triple(A,create_slb,B))),findmin_cpq_eff(insert_cpq(triple(A,create_slb,bad),C))). [para(148(a,1),415(a,1))].
% 238.26/32.27
% 238.26/32.27 % given #1000 (T,wt=41): 2189 succ_cpq(A,findmin_cpq_eff(insert_cpq(findmin_cpq_eff(insert_cpq(remove_cpq(A,B),C)),D))). [resolve(566,a,70,a)].
% 238.26/32.27
% 238.26/32.27 % given #1500 (T,wt=43): 1791 insert_cpq(findmin_cpq_eff(remove_cpq(triple(A,create_slb,B),C)),D) = insert_cpq(remove_cpq(triple(A,create_slb,E),F),D). [para(366(a,1),364(a,1,1))].
% 238.26/32.27
% 238.26/32.27 % SZS status Theorem for theBenchmark
% 238.26/32.27
% 238.26/32.27 % Proof 1 at 5.79 (+ 1.49) seconds.
% 238.26/32.27 % Length of proof is 26.
% 238.26/32.27 % Level of proof is 8.
% 238.26/32.27 % Maximum clause weight is 56.000.
% 238.26/32.27 % Given clauses 1659.
% 238.26/32.27
% 238.26/32.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------