%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV417+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 : n014.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 09:07:40 AM UTC 2026
% Result : Theorem 0.12s 5.52s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 48 ( 12 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 45 ( 18 ~; 12 |; 8 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 33 ( 0 sgn 15 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax14,axiom,
! [U,V] :
( ( issmallestelement_pq(U,V)
& contains_pq(U,V) )
=> findmin_pq_res(U,V) = V ),
file('theBenchmark.p',ax14) ).
fof(ax58,axiom,
! [U,V] :
( pi_sharp_find_min(U,V)
<=> ( issmallestelement_pq(U,V)
& contains_pq(U,V) ) ),
file('theBenchmark.p',ax58) ).
fof(main4_l7,axiom,
! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> pi_sharp_find_min(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
file('theBenchmark.p',main4_l7) ).
fof(co4,conjecture,
! [U,V,W] :
( pi_find_min(triple(U,V,W))
=> ( phi(findmin_cpq_eff(triple(U,V,W)))
=> ? [X] :
( findmin_cpq_res(triple(U,V,W)) = findmin_pq_res(i(triple(U,V,W)),X)
& pi_sharp_find_min(i(triple(U,V,W)),X) ) ) ),
file('theBenchmark.p',co4) ).
fof(co4_neg,negated_conjecture,
~ ! [U,V,W] :
( pi_find_min(triple(U,V,W))
=> ( phi(findmin_cpq_eff(triple(U,V,W)))
=> ? [X] :
( findmin_cpq_res(triple(U,V,W)) = findmin_pq_res(i(triple(U,V,W)),X)
& pi_sharp_find_min(i(triple(U,V,W)),X) ) ) ),
inference(assume_negation,[status(cth)],[co4]) ).
cnf(c_67,plain,
( findmin_pq_res(A,B) = B
| ~ issmallestelement_pq(A,B)
| ~ contains_pq(A,B) ),
inference(clausify,[status(thm)],[ax14]) ).
cnf(c_70,plain,
( issmallestelement_pq(A,B)
| ~ pi_sharp_find_min(A,B) ),
inference(clausify,[status(thm)],[ax58]) ).
cnf(c_159,plain,
( contains_pq(A,B)
| ~ pi_sharp_find_min(A,B) ),
inference(clausify,[status(thm)],[ax58]) ).
cnf(c_164,plain,
( pi_sharp_find_min(i(triple(A,B,C)),findmin_cpq_res(triple(A,B,C)))
| ~ phi(findmin_cpq_eff(triple(A,B,C))) ),
inference(clausify,[status(thm)],[main4_l7]) ).
fof(nnf_62,plain,
? [U,V,W] :
( ! [X] :
( findmin_cpq_res(triple(U,V,W)) != findmin_pq_res(i(triple(U,V,W)),X)
| ~ pi_sharp_find_min(i(triple(U,V,W)),X) )
& phi(findmin_cpq_eff(triple(U,V,W)))
& pi_find_min(triple(U,V,W)) ),
inference(fof_nnf,[status(thm)],[co4_neg]) ).
fof(sk_co4_neg,plain,
( ! [X] :
( findmin_cpq_res(triple(sK0,sK1,sK2)) != findmin_pq_res(i(triple(sK0,sK1,sK2)),X)
| ~ pi_sharp_find_min(i(triple(sK0,sK1,sK2)),X) )
& phi(findmin_cpq_eff(triple(sK0,sK1,sK2)))
& pi_find_min(triple(sK0,sK1,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK2)],[nnf_62]) ).
cnf(c_165,negated_conjecture,
phi(findmin_cpq_eff(triple(sK0,sK1,sK2))),
inference(split_conjunct,[status(thm)],[sk_co4_neg]) ).
cnf(c_166,negated_conjecture,
( findmin_cpq_res(triple(sK0,sK1,sK2)) != findmin_pq_res(i(triple(sK0,sK1,sK2)),A)
| ~ pi_sharp_find_min(i(triple(sK0,sK1,sK2)),A) ),
inference(split_conjunct,[status(thm)],[sk_co4_neg]) ).
cnf(c_167,negated_conjecture,
( findmin_pq_res(i(triple(sK0,sK1,sK2)),A) != findmin_cpq_res(triple(sK0,sK1,sK2))
| ~ pi_sharp_find_min(i(triple(sK0,sK1,sK2)),A) ),
inference(copy,[status(thm)],[c_166]) ).
cnf(c_180,plain,
( findmin_pq_res(A,B) = B
| ~ contains_pq(A,B)
| ~ pi_sharp_find_min(A,B) ),
inference(resolve,[status(thm)],[c_70,c_67]) ).
cnf(c_267,plain,
pi_sharp_find_min(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))),
inference(resolve,[status(thm)],[c_165,c_164]) ).
cnf(c_651,plain,
( findmin_pq_res(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))) = findmin_cpq_res(triple(sK0,sK1,sK2))
| ~ contains_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))) ),
inference(resolve,[status(thm)],[c_267,c_180]) ).
cnf(c_654,plain,
findmin_pq_res(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))) != findmin_cpq_res(triple(sK0,sK1,sK2)),
inference(resolve,[status(thm)],[c_267,c_167]) ).
cnf(c_655,plain,
contains_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))),
inference(resolve,[status(thm)],[c_267,c_159]) ).
cnf(c_657,plain,
findmin_pq_res(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))) = findmin_cpq_res(triple(sK0,sK1,sK2)),
inference(resolve,[status(thm)],[c_655,c_651]) ).
cnf(c_656,plain,
$false,
inference(resolve,[status(thm)],[c_654,c_657]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV417+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n014.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sat Sep 26 13:42:08 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.36 % Process 3294641 was started by sandbox2 on n014,
% 0.08/5.36 % Sat Sep 26 13:42:08 2026
% 0.08/5.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/5.37
% 0.08/5.37 % From the command line: assign(max_seconds, 300).
% 0.12/5.52
% 0.12/5.52 % SZS status Theorem for theBenchmark
% 0.12/5.52
% 0.12/5.52 % Proof 1 at 0.10 (+ 0.03) seconds.
% 0.12/5.52 % Length of proof is 17.
% 0.12/5.52 % Level of proof is 4.
% 0.12/5.52 % Maximum clause weight is 48.000.
% 0.12/5.52 % Given clauses 183.
% 0.12/5.52
% 0.12/5.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------