%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV380+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 65.45s 17.12s
% Output : CNFRefutation 65.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 23 unt; 0 def)
% Number of atoms : 135 ( 63 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 110 ( 37 ~; 55 |; 8 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 129 ( 32 sgn 39 !; 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(ax52,axiom,
! [U] : removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U)),
file('theBenchmark.p',ax52) ).
fof(l16_l14,axiom,
! [U,V,W,X] :
( ~ ok(triple(U,V,W))
=> ~ ok(remove_cpq(triple(U,V,W),X)) ),
file('theBenchmark.p',l16_l14) ).
fof(l16_co,conjecture,
! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ~ ok(removemin_cpq_eff(triple(U,V,W))) ),
file('theBenchmark.p',l16_co) ).
fof(l16_co_neg,negated_conjecture,
~ ! [U,V,W] :
( ~ ok(triple(U,V,W))
=> ~ ok(removemin_cpq_eff(triple(U,V,W))) ),
inference(assume_negation,[status(cth)],[l16_co]) ).
cnf(c_44,plain,
( less_than(B,A)
| less_than(A,B) ),
inference(clausify,[status(thm)],[totality]) ).
cnf(c_48,plain,
( less_than(B,A)
| ~ less_than(A,B)
| strictly_less_than(A,B) ),
inference(clausify,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_52,plain,
~ contains_slb(create_slb,A),
inference(clausify,[status(thm)],[ax20]) ).
cnf(c_79,plain,
~ ok(triple(A,B,bad)),
inference(clausify,[status(thm)],[ax40]) ).
cnf(c_80,plain,
( bad = C
| ok(triple(A,B,C)) ),
inference(clausify,[status(thm)],[ax41]) ).
cnf(c_82,plain,
( triple(C,A,bad) = remove_cpq(triple(C,A,D),B)
| contains_slb(A,B) ),
inference(clausify,[status(thm)],[ax43]) ).
cnf(c_83,plain,
( remove_cpq(triple(C,A,D),B) = triple(C,A,bad)
| contains_slb(A,B) ),
inference(copy,[status(thm)],[c_82]) ).
cnf(c_86,plain,
triple(A,create_slb,bad) = findmin_cpq_eff(triple(A,create_slb,B)),
inference(clausify,[status(thm)],[ax46]) ).
cnf(c_87,plain,
findmin_cpq_eff(triple(A,create_slb,B)) = triple(A,create_slb,bad),
inference(copy,[status(thm)],[c_86]) ).
cnf(c_88,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_89,plain,
( findmin_cpq_eff(triple(B,A,C)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| contains_slb(A,findmin_pqp_res(B))
| create_slb = A ),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_90,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_91,plain,
( findmin_cpq_eff(triple(B,A,C)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| ~ 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(copy,[status(thm)],[c_90]) ).
cnf(c_92,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]) ).
cnf(c_93,plain,
( findmin_cpq_eff(triple(B,A,C)) = triple(B,update_slb(A,findmin_pqp_res(B)),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(copy,[status(thm)],[c_92]) ).
cnf(c_96,plain,
removemin_cpq_eff(A) = remove_cpq(findmin_cpq_eff(A),findmin_cpq_res(A)),
inference(clausify,[status(thm)],[ax52]) ).
cnf(c_98,plain,
( ~ ok(remove_cpq(triple(A,B,C),D))
| ok(triple(A,B,C)) ),
inference(clausify,[status(thm)],[l16_l14]) ).
fof(nnf_42,plain,
? [U,V,W] :
( ok(removemin_cpq_eff(triple(U,V,W)))
& ~ ok(triple(U,V,W)) ),
inference(fof_nnf,[status(thm)],[l16_co_neg]) ).
fof(sk_l16_co_neg,plain,
( ok(removemin_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_42]) ).
cnf(c_99,negated_conjecture,
~ ok(triple(sK0,sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_l16_co_neg]) ).
cnf(c_100,negated_conjecture,
ok(removemin_cpq_eff(triple(sK0,sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_l16_co_neg]) ).
cnf(c_101,negated_conjecture,
ok(remove_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))),
inference(paramod,[status(thm)],[c_96,c_100]) ).
cnf(c_2277,plain,
( less_than(B,A)
| less_than(B,A)
| strictly_less_than(A,B) ),
inference(resolve,[status(thm)],[c_48,c_44]) ).
cnf(c_106,plain,
( less_than(B,A)
| strictly_less_than(A,B) ),
inference(copy,[status(thm)],[c_2277]) ).
cnf(c_143,plain,
remove_cpq(triple(A,create_slb,B),C) = triple(A,create_slb,bad),
inference(resolve,[status(thm)],[c_83,c_52]) ).
cnf(c_2278,plain,
( findmin_cpq_eff(triple(B,A,D)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| create_slb = A
| findmin_cpq_eff(triple(B,A,C)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| ~ strictly_less_than(findmin_pqp_res(B),lookup_slb(A,findmin_pqp_res(B)))
| create_slb = A ),
inference(resolve,[status(thm)],[c_91,c_89]) ).
cnf(c_156,plain,
( findmin_cpq_eff(triple(B,A,D)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| findmin_cpq_eff(triple(B,A,C)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| ~ strictly_less_than(findmin_pqp_res(B),lookup_slb(A,findmin_pqp_res(B)))
| create_slb = A ),
inference(copy,[status(thm)],[c_2278]) ).
cnf(c_159,plain,
( findmin_cpq_eff(triple(B,A,C)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| ~ 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_2279,plain,
( findmin_cpq_eff(triple(B,A,D)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| create_slb = A
| findmin_cpq_eff(triple(B,A,C)) = triple(B,update_slb(A,findmin_pqp_res(B)),C)
| ~ less_than(lookup_slb(A,findmin_pqp_res(B)),findmin_pqp_res(B))
| create_slb = A ),
inference(resolve,[status(thm)],[c_93,c_89]) ).
cnf(c_160,plain,
( findmin_cpq_eff(triple(B,A,D)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| findmin_cpq_eff(triple(B,A,C)) = triple(B,update_slb(A,findmin_pqp_res(B)),C)
| ~ less_than(lookup_slb(A,findmin_pqp_res(B)),findmin_pqp_res(B))
| create_slb = A ),
inference(copy,[status(thm)],[c_2279]) ).
cnf(c_164,plain,
( findmin_cpq_eff(triple(B,A,bad)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| ~ less_than(lookup_slb(A,findmin_pqp_res(B)),findmin_pqp_res(B))
| create_slb = A ),
inference(factor,[status(thm)],[c_160]) ).
cnf(c_182,plain,
~ ok(remove_cpq(triple(A,B,bad),C)),
inference(resolve,[status(thm)],[c_98,c_79]) ).
cnf(c_2280,negated_conjecture,
bad = sK2,
inference(resolve,[status(thm)],[c_99,c_80]) ).
cnf(c_184,negated_conjecture,
sK2 = bad,
inference(copy,[status(thm)],[c_2280]) ).
cnf(c_2281,negated_conjecture,
ok(remove_cpq(findmin_cpq_eff(triple(sK0,sK1,bad)),findmin_cpq_res(triple(sK0,sK1,sK2)))),
inference(paramod,[status(thm)],[c_184,c_101]) ).
cnf(c_185,negated_conjecture,
ok(remove_cpq(findmin_cpq_eff(triple(sK0,sK1,bad)),findmin_cpq_res(triple(sK0,sK1,bad)))),
inference(paramod,[status(thm)],[c_184,c_2281]) ).
cnf(c_1740,plain,
( less_than(lookup_slb(A,findmin_pqp_res(B)),findmin_pqp_res(B))
| findmin_cpq_eff(triple(B,A,C)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| create_slb = A ),
inference(resolve,[status(thm)],[c_159,c_106]) ).
cnf(c_2282,plain,
( findmin_cpq_eff(triple(B,A,bad)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| create_slb = A
| findmin_cpq_eff(triple(B,A,C)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| create_slb = A ),
inference(resolve,[status(thm)],[c_1740,c_164]) ).
cnf(c_2136,plain,
( findmin_cpq_eff(triple(B,A,bad)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| findmin_cpq_eff(triple(B,A,C)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| create_slb = A ),
inference(copy,[status(thm)],[c_2282]) ).
cnf(c_2150,plain,
( findmin_cpq_eff(triple(B,A,bad)) = triple(B,update_slb(A,findmin_pqp_res(B)),bad)
| create_slb = A ),
inference(factor,[status(thm)],[c_2136]) ).
cnf(c_2283,plain,
( ok(remove_cpq(triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad),findmin_cpq_res(triple(sK0,sK1,bad))))
| create_slb = sK1 ),
inference(paramod,[status(thm)],[c_2150,c_185]) ).
cnf(c_2284,plain,
( ok(remove_cpq(triple(sK0,update_slb(sK1,findmin_pqp_res(sK0)),bad),findmin_cpq_res(triple(sK0,sK1,bad))))
| sK1 = create_slb ),
inference(copy,[status(thm)],[c_2283]) ).
cnf(c_2190,plain,
sK1 = create_slb,
inference(resolve,[status(thm)],[c_182,c_2284]) ).
cnf(c_2285,negated_conjecture,
ok(remove_cpq(findmin_cpq_eff(triple(sK0,create_slb,bad)),findmin_cpq_res(triple(sK0,sK1,bad)))),
inference(paramod,[status(thm)],[c_2190,c_185]) ).
cnf(c_2286,negated_conjecture,
ok(remove_cpq(triple(sK0,create_slb,bad),findmin_cpq_res(triple(sK0,sK1,bad)))),
inference(paramod,[status(thm)],[c_87,c_2285]) ).
cnf(c_2287,negated_conjecture,
ok(remove_cpq(triple(sK0,create_slb,bad),findmin_cpq_res(triple(sK0,create_slb,bad)))),
inference(paramod,[status(thm)],[c_2190,c_2286]) ).
cnf(c_2288,negated_conjecture,
ok(triple(sK0,create_slb,bad)),
inference(paramod,[status(thm)],[c_143,c_2287]) ).
cnf(c_2276,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_79,c_2288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV380+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.45 % Computer : n004.cluster.edu
% 0.13/5.45 % Model : x86_64 x86_64
% 0.13/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.45 % Memory : 8046.5625MB
% 0.13/5.45 % OS : Linux 6.8.0-71-generic
% 0.13/5.46 % CPULimit : 300
% 0.13/5.46 % WCLimit : 300
% 0.13/5.46 % DateTime : Sat Sep 26 13:39:57 UTC 2026
% 0.13/5.46 % CPUTime :
% 0.13/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/5.46 % Process 1850990 was started by sandbox on n004,
% 0.13/5.46 % Sat Sep 26 13:39:57 2026
% 0.13/5.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/5.48
% 0.13/5.48 % From the command line: assign(max_seconds, 300).
% 65.45/17.12
% 65.45/17.12 % given #500 (W,wt=43): 823 succ_cpq(A,findmin_cpq_eff(remove_cpq(remove_cpq(insert_cpq(findmin_cpq_eff(A),B),C),D))). [resolve(379,a,71,a)].
% 65.45/17.12
% 65.45/17.12 % SZS status Theorem for theBenchmark
% 65.45/17.12
% 65.45/17.12 % Proof 1 at 3.38 (+ 0.18) seconds.
% 65.45/17.12 % Length of proof is 47.
% 65.45/17.12 % Level of proof is 9.
% 65.45/17.12 % Maximum clause weight is 56.000.
% 65.45/17.12 % Given clauses 514.
% 65.45/17.12
% 65.45/17.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------