%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV366+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 : n006.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 09:07:34 AM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 7 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 57 ( 10 sgn 35 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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(l2_co,conjecture,
! [U] :
( ! [V,W,X,Y] : i(triple(V,U,X)) = i(triple(W,U,Y))
=> ! [Z,X1,X2,X3,X4,X5] : i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) = i(triple(X1,insert_slb(U,pair(X4,X5)),X3)) ),
file('theBenchmark.p',l2_co) ).
fof(l2_co_neg,negated_conjecture,
~ ! [U] :
( ! [V,W,X,Y] : i(triple(V,U,X)) = i(triple(W,U,Y))
=> ! [Z,X1,X2,X3,X4,X5] : i(triple(Z,insert_slb(U,pair(X4,X5)),X2)) = i(triple(X1,insert_slb(U,pair(X4,X5)),X3)) ),
inference(assume_negation,[status(cth)],[l2_co]) ).
fof(nnf_61,plain,
? [U] :
( ? [Z,X1,X2,X3,X4,X5] : i(triple(X1,insert_slb(U,pair(X4,X5)),X3)) != i(triple(Z,insert_slb(U,pair(X4,X5)),X2))
& ! [V,W,X,Y] : i(triple(W,U,Y)) = i(triple(V,U,X)) ),
inference(fof_nnf,[status(thm)],[l2_co_neg]) ).
fof(sk_l2_co_neg,plain,
( i(triple(sK0,insert_slb(sK1,pair(sK2,sK3)),sK4)) != i(triple(sK5,insert_slb(sK1,pair(sK2,sK3)),sK6))
& ! [V,W,X,Y] : i(triple(W,sK1,Y)) = i(triple(V,sK1,X)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2,sK3,sK4,sK5,sK6]),skolemize(U,sK1),skolemize(Z,sK5),skolemize(X1,sK0),skolemize(X2,sK6),skolemize(X3,sK4),skolemize(X4,sK2),skolemize(X5,sK3)],[nnf_61]) ).
cnf(c_132,negated_conjecture,
i(triple(sK0,insert_slb(sK1,pair(sK2,sK3)),sK4)) != i(triple(sK5,insert_slb(sK1,pair(sK2,sK3)),sK6)),
inference(split_conjunct,[status(thm)],[sk_l2_co_neg]) ).
cnf(c_133,negated_conjecture,
i(triple(A,sK1,B)) = i(triple(C,sK1,D)),
inference(split_conjunct,[status(thm)],[sk_l2_co_neg]) ).
cnf(c_135,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_200,plain,
i(triple(sK0,insert_slb(sK1,pair(sK2,sK3)),sK4)) != insert_pq(i(triple(sK5,sK1,sK6)),sK2),
inference(paramod,[status(thm)],[c_135,c_132]) ).
cnf(c_201,plain,
i(triple(A,insert_slb(sK1,pair(B,C)),D)) = insert_pq(i(triple(E,sK1,F)),B),
inference(paramod,[status(thm)],[c_133,c_135]) ).
cnf(c_202,plain,
$false,
inference(resolve,[status(thm)],[c_201,c_200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV366+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 13:38:40 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 1391437 was started by sandbox on n006,
% 0.12/0.36 % Sat Sep 26 13:38:40 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.12/0.40
% 0.12/0.40 % SZS status Theorem for theBenchmark
% 0.12/0.40
% 0.12/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.40 % Length of proof is 8.
% 0.12/0.40 % Level of proof is 3.
% 0.12/0.40 % Maximum clause weight is 44.000.
% 0.12/0.40 % Given clauses 24.
% 0.12/0.40
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------