%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV415+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 : n020.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 0.07s 0.39s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 54 ( 15 sgn 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax42,axiom,
! [U,V,W,X] : insert_cpq(triple(U,V,W),X) = triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W),
file('theBenchmark.p',ax42) ).
fof(ax55,axiom,
! [U,V,W,X,Y] : i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X),
file('theBenchmark.p',ax55) ).
fof(main2_l12,axiom,
! [U,V,W,X,Y] : i(triple(U,W,X)) = i(triple(V,W,Y)),
file('theBenchmark.p',main2_l12) ).
fof(co2,conjecture,
! [U,V,W,X] : i(insert_cpq(triple(U,V,W),X)) = insert_pq(i(triple(U,V,W)),X),
file('theBenchmark.p',co2) ).
fof(co2_neg,negated_conjecture,
~ ! [U,V,W,X] : i(insert_cpq(triple(U,V,W),X)) = insert_pq(i(triple(U,V,W)),X),
inference(assume_negation,[status(cth)],[co2]) ).
fof(nnf_62,plain,
? [U,V,W,X] : i(insert_cpq(triple(U,V,W),X)) != insert_pq(i(triple(U,V,W)),X),
inference(fof_nnf,[status(thm)],[co2_neg]) ).
fof(sk_co2_neg,plain,
i(insert_cpq(triple(sK0,sK1,sK2),sK3)) != insert_pq(i(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_62]) ).
cnf(c_133,negated_conjecture,
i(insert_cpq(triple(sK0,sK1,sK2),sK3)) != insert_pq(i(triple(sK0,sK1,sK2)),sK3),
inference(split_conjunct,[status(thm)],[sk_co2_neg]) ).
cnf(c_134,plain,
i(triple(A,B,C)) = i(triple(D,B,E)),
inference(clausify,[status(thm)],[main2_l12]) ).
cnf(c_136,plain,
i(triple(A,insert_slb(B,pair(C,D)),E)) = insert_pq(i(triple(A,B,E)),C),
inference(clausify,[status(thm)],[ax55]) ).
cnf(c_149,plain,
triple(insert_pqp(A,B),insert_slb(C,pair(B,bottom)),D) = insert_cpq(triple(A,C,D),B),
inference(clausify,[status(thm)],[ax42]) ).
cnf(c_201,plain,
i(insert_cpq(triple(sK0,sK1,sK2),sK3)) != insert_pq(i(triple(A,sK1,B)),sK3),
inference(paramod,[status(thm)],[c_134,c_133]) ).
cnf(c_216,plain,
i(insert_cpq(triple(A,B,C),D)) = i(triple(E,insert_slb(B,pair(D,bottom)),F)),
inference(paramod,[status(thm)],[c_149,c_134]) ).
cnf(c_214,plain,
i(insert_cpq(triple(A,B,C),D)) = insert_pq(i(triple(E,B,F)),D),
inference(paramod,[status(thm)],[c_136,c_216]) ).
cnf(c_215,plain,
$false,
inference(resolve,[status(thm)],[c_214,c_201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV415+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n020.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 13:43:04 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 1710263 was started by sandbox2 on n020,
% 0.07/0.35 % Sat Sep 26 13:43:04 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.07/0.39
% 0.07/0.39 % SZS status Theorem for theBenchmark
% 0.07/0.39
% 0.07/0.39 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.07/0.39 % Length of proof is 11.
% 0.07/0.39 % Level of proof is 3.
% 0.07/0.39 % Maximum clause weight is 17.000.
% 0.07/0.39 % Given clauses 37.
% 0.07/0.39
% 0.07/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------