%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV379+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 : n010.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 115.28s 15.00s
% Output : CNFRefutation 115.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 19 unt; 0 def)
% Number of atoms : 112 ( 56 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 91 ( 30 ~; 44 |; 8 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 108 ( 27 sgn 34 !; 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(ax20,axiom,
! [U] : ~ contains_slb(create_slb,U),
file('theBenchmark.p',ax20) ).
fof(ax40,axiom,
! [U,V] :
( ok(triple(U,V,bad))
<=> $false ),
file('theBenchmark.p',ax40) ).
fof(ax41,axiom,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> W = bad ),
file('theBenchmark.p',ax41) ).
fof(ax43,axiom,
! [U,V,W,X] :
( ~ contains_slb(V,X)
=> remove_cpq(triple(U,V,W),X) = triple(U,V,bad) ),
file('theBenchmark.p',ax43) ).
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(ax49,axiom,
! [U,V,W,X] :
( ( less_than(lookup_slb(V,findmin_pqp_res(U)),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)),W) ),
file('theBenchmark.p',ax49) ).
fof(l15_co,conjecture,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
file('theBenchmark.p',l15_co) ).
fof(l15_co_neg,negated_conjecture,
~ ! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ~ ok(findmin_cpq_eff(triple(U,V,W))) ),
inference(assume_negation,[status(cth)],[l15_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_51,plain,
~ contains_slb(create_slb,A),
inference(clausify,[status(thm)],[ax20]) ).
cnf(c_78,plain,
~ ok(triple(A,B,bad)),
inference(clausify,[status(thm)],[ax40]) ).
cnf(c_79,plain,
( bad = C
| ok(triple(A,B,C)) ),
inference(clausify,[status(thm)],[ax41]) ).
cnf(c_81,plain,
( triple(C,A,bad) = remove_cpq(triple(C,A,D),B)
| contains_slb(A,B) ),
inference(clausify,[status(thm)],[ax43]) ).
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]) ).
cnf(c_87,plain,
( triple(B,update_slb(A,findmin_pqp_res(B)),C) = findmin_cpq_eff(triple(B,A,C))
| ~ less_than(lookup_slb(A,findmin_pqp_res(B)),findmin_pqp_res(B))
| ~ contains_slb(A,findmin_pqp_res(B))
| create_slb = A ),
inference(clausify,[status(thm)],[ax49]) ).
fof(nnf_41,plain,
? [U,V,W] :
( ok(findmin_cpq_eff(triple(U,V,W)))
& ~ ok(triple(U,V,W)) ),
inference(fof_nnf,[status(thm)],[l15_co_neg]) ).
fof(sk_l15_co_neg,plain,
( ok(findmin_cpq_eff(triple(sK0,sK1,sK2)))
& ~ ok(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(triple(sK0,sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_l15_co_neg]) ).
cnf(c_93,negated_conjecture,
ok(findmin_cpq_eff(triple(sK0,sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_l15_co_neg]) ).
cnf(c_14641,plain,
( less_than(B,A)
| less_than(B,A)
| strictly_less_than(A,B) ),
inference(resolve,[status(thm)],[c_47,c_43]) ).
cnf(c_98,plain,
( less_than(B,A)
| strictly_less_than(A,B) ),
inference(copy,[status(thm)],[c_14641]) ).
cnf(c_128,plain,
triple(A,create_slb,bad) = remove_cpq(triple(A,create_slb,B),C),
inference(resolve,[status(thm)],[c_81,c_51]) ).
cnf(c_14642,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_155,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_14642]) ).
cnf(c_158,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_155]) ).
cnf(c_14643,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)),C) = findmin_cpq_eff(triple(B,A,C))
| ~ less_than(lookup_slb(A,findmin_pqp_res(B)),findmin_pqp_res(B))
| create_slb = A ),
inference(resolve,[status(thm)],[c_87,c_85]) ).
cnf(c_159,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)),C) = findmin_cpq_eff(triple(B,A,C))
| ~ less_than(lookup_slb(A,findmin_pqp_res(B)),findmin_pqp_res(B))
| create_slb = A ),
inference(copy,[status(thm)],[c_14643]) ).
cnf(c_163,plain,
( triple(B,update_slb(A,findmin_pqp_res(B)),bad) = findmin_cpq_eff(triple(B,A,bad))
| ~ less_than(lookup_slb(A,findmin_pqp_res(B)),findmin_pqp_res(B))
| create_slb = A ),
inference(factor,[status(thm)],[c_159]) ).
cnf(c_14644,negated_conjecture,
bad = sK2,
inference(resolve,[status(thm)],[c_92,c_79]) ).
cnf(c_174,negated_conjecture,
sK2 = bad,
inference(copy,[status(thm)],[c_14644]) ).
cnf(c_175,negated_conjecture,
ok(findmin_cpq_eff(triple(sK0,sK1,bad))),
inference(paramod,[status(thm)],[c_174,c_93]) ).
cnf(c_361,plain,
triple(A,create_slb,bad) = findmin_cpq_eff(remove_cpq(triple(A,create_slb,B),C)),
inference(paramod,[status(thm)],[c_128,c_84]) ).
cnf(c_14645,plain,
triple(A,create_slb,bad) = findmin_cpq_eff(triple(A,create_slb,bad)),
inference(paramod,[status(thm)],[c_128,c_361]) ).
cnf(c_799,plain,
findmin_cpq_eff(triple(A,create_slb,bad)) = triple(A,create_slb,bad),
inference(copy,[status(thm)],[c_14645]) ).
cnf(c_13011,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_158,c_98]) ).
cnf(c_14646,plain,
( triple(B,update_slb(A,findmin_pqp_res(B)),bad) = findmin_cpq_eff(triple(B,A,bad))
| create_slb = A
| 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_13011,c_163]) ).
cnf(c_14530,plain,
( triple(B,update_slb(A,findmin_pqp_res(B)),bad) = findmin_cpq_eff(triple(B,A,bad))
| triple(B,update_slb(A,findmin_pqp_res(B)),bad) = findmin_cpq_eff(triple(B,A,C))
| create_slb = A ),
inference(copy,[status(thm)],[c_14646]) ).
cnf(c_14535,plain,
( triple(B,update_slb(A,findmin_pqp_res(B)),bad) = findmin_cpq_eff(triple(B,A,bad))
| create_slb = A ),
inference(factor,[status(thm)],[c_14530]) ).
cnf(c_14556,plain,
( ~ ok(findmin_cpq_eff(triple(B,A,bad)))
| create_slb = A ),
inference(paramod,[status(thm)],[c_14535,c_78]) ).
cnf(c_14647,negated_conjecture,
create_slb = sK1,
inference(resolve,[status(thm)],[c_14556,c_175]) ).
cnf(c_14637,negated_conjecture,
sK1 = create_slb,
inference(copy,[status(thm)],[c_14647]) ).
cnf(c_14648,negated_conjecture,
ok(findmin_cpq_eff(triple(sK0,create_slb,bad))),
inference(paramod,[status(thm)],[c_14637,c_175]) ).
cnf(c_14649,negated_conjecture,
ok(triple(sK0,create_slb,bad)),
inference(paramod,[status(thm)],[c_799,c_14648]) ).
cnf(c_14640,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_78,c_14649]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV379+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 13:39:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3446805 was started by sandbox2 on n010,
% 0.11/0.37 % Sat Sep 26 13:39:45 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 115.28/15.00
% 115.28/15.00 % given #500 (T,wt=36): 1202 succ_cpq(findmin_cpq_eff(remove_cpq(triple(A,create_slb,B),C)),remove_cpq(insert_cpq(triple(A,create_slb,bad),D),E)). [para(361(a,1),423(a,1))].
% 115.28/15.00
% 115.28/15.00 % given #1000 (T,wt=41): 3892 check_cpq(triple(A,insert_slb(create_slb,pair(B,C)),D)) | less_than(E,C) | less_than(B,F) | -less_than(V6,F) | less_than(V6,E). [resolve(731,c,42,b)].
% 115.28/15.00
% 115.28/15.00 % given #1500 (T,wt=43): 2219 succ_cpq(A,findmin_cpq_eff(findmin_cpq_eff(insert_cpq(remove_cpq(insert_cpq(A,B),C),D)))). [resolve(632,a,70,a)].
% 115.28/15.00
% 115.28/15.00 % SZS status Theorem for theBenchmark
% 115.28/15.00
% 115.28/15.00 % Proof 1 at 5.14 (+ 1.40) seconds.
% 115.28/15.00 % Length of proof is 39.
% 115.28/15.00 % Level of proof is 9.
% 115.28/15.00 % Maximum clause weight is 56.000.
% 115.28/15.00 % Given clauses 1630.
% 115.28/15.00
% 115.28/15.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------