%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV416+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 09:07:40 AM UTC 2026
% Result : Theorem 0.23s 0.53s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 36 ( 8 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 31 ( 12 ~; 6 |; 6 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 16 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax56,axiom,
! [U,V] :
( pi_sharp_remove(U,V)
<=> contains_pq(U,V) ),
file('theBenchmark.p',ax56) ).
fof(ax57,axiom,
! [U,V] :
( pi_remove(U,V)
<=> pi_sharp_remove(i(U),V) ),
file('theBenchmark.p',ax57) ).
fof(main3_li34,axiom,
! [U,V,W,X] :
( contains_pq(i(triple(U,V,W)),X)
=> i(remove_cpq(triple(U,V,W),X)) = remove_pq(i(triple(U,V,W)),X) ),
file('theBenchmark.p',main3_li34) ).
fof(co3,conjecture,
! [U,V,W,X] :
( pi_remove(triple(U,V,W),X)
=> ( phi(remove_cpq(triple(U,V,W),X))
=> ( i(remove_cpq(triple(U,V,W),X)) = remove_pq(i(triple(U,V,W)),X)
& pi_sharp_remove(i(triple(U,V,W)),X) ) ) ),
file('theBenchmark.p',co3) ).
fof(co3_neg,negated_conjecture,
~ ! [U,V,W,X] :
( pi_remove(triple(U,V,W),X)
=> ( phi(remove_cpq(triple(U,V,W),X))
=> ( i(remove_cpq(triple(U,V,W),X)) = remove_pq(i(triple(U,V,W)),X)
& pi_sharp_remove(i(triple(U,V,W)),X) ) ) ),
inference(assume_negation,[status(cth)],[co3]) ).
cnf(c_75,plain,
( pi_sharp_remove(i(A),B)
| ~ pi_remove(A,B) ),
inference(clausify,[status(thm)],[ax57]) ).
fof(nnf_63,plain,
? [U,V,W,X] :
( ( i(remove_cpq(triple(U,V,W),X)) != remove_pq(i(triple(U,V,W)),X)
| ~ pi_sharp_remove(i(triple(U,V,W)),X) )
& phi(remove_cpq(triple(U,V,W),X))
& pi_remove(triple(U,V,W),X) ),
inference(fof_nnf,[status(thm)],[co3_neg]) ).
fof(sk_co3_neg,plain,
( ( i(remove_cpq(triple(sK0,sK1,sK2),sK3)) != remove_pq(i(triple(sK0,sK1,sK2)),sK3)
| ~ pi_sharp_remove(i(triple(sK0,sK1,sK2)),sK3) )
& phi(remove_cpq(triple(sK0,sK1,sK2),sK3))
& pi_remove(triple(sK0,sK1,sK2),sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(U,sK0),skolemize(V,sK1),skolemize(W,sK2),skolemize(X,sK3)],[nnf_63]) ).
cnf(c_77,negated_conjecture,
pi_remove(triple(sK0,sK1,sK2),sK3),
inference(split_conjunct,[status(thm)],[sk_co3_neg]) ).
cnf(c_103,negated_conjecture,
pi_sharp_remove(i(triple(sK0,sK1,sK2)),sK3),
inference(resolve,[status(thm)],[c_75,c_77]) ).
cnf(c_165,plain,
( contains_pq(A,B)
| ~ pi_sharp_remove(A,B) ),
inference(clausify,[status(thm)],[ax56]) ).
cnf(c_169,plain,
( i(remove_cpq(triple(A,B,C),D)) = remove_pq(i(triple(A,B,C)),D)
| ~ contains_pq(i(triple(A,B,C)),D) ),
inference(clausify,[status(thm)],[main3_li34]) ).
cnf(c_170,negated_conjecture,
( i(remove_cpq(triple(sK0,sK1,sK2),sK3)) != remove_pq(i(triple(sK0,sK1,sK2)),sK3)
| ~ pi_sharp_remove(i(triple(sK0,sK1,sK2)),sK3) ),
inference(split_conjunct,[status(thm)],[sk_co3_neg]) ).
cnf(c_171,negated_conjecture,
i(remove_cpq(triple(sK0,sK1,sK2),sK3)) != remove_pq(i(triple(sK0,sK1,sK2)),sK3),
inference(resolve,[status(thm)],[c_103,c_170]) ).
cnf(c_399,plain,
contains_pq(i(triple(sK0,sK1,sK2)),sK3),
inference(resolve,[status(thm)],[c_165,c_103]) ).
cnf(c_411,negated_conjecture,
~ contains_pq(i(triple(sK0,sK1,sK2)),sK3),
inference(resolve,[status(thm)],[c_169,c_171]) ).
cnf(c_410,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_399,c_411]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV416+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n004.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 13:42:07 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 1856453 was started by sandbox on n004,
% 0.18/0.44 % Sat Sep 26 13:42:07 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.23/0.53
% 0.23/0.53 % SZS status Theorem for theBenchmark
% 0.23/0.53
% 0.23/0.53 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.23/0.53 % Length of proof is 13.
% 0.23/0.53 % Level of proof is 4.
% 0.23/0.53 % Maximum clause weight is 42.000.
% 0.23/0.53 % Given clauses 74.
% 0.23/0.53
% 0.23/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------