%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV221+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 03:12:31 PM UTC 2026
% Result : Theorem 26.72s 4.24s
% Output : Proof 26.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 7 unt; 0 def)
% Number of atoms : 209 ( 50 equ)
% Maximal formula atoms : 47 ( 13 avg)
% Number of connectives : 272 ( 78 ~; 66 |; 102 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-3 aty)
% Number of variables : 58 ( 0 sgn 52 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f52,conjecture,
( ( ! [K] :
( ( leq(K,pred(pv57))
& leq(n0,K) )
=> ! [L] :
( ( leq(L,n5)
& leq(n0,L) )
=> a_select3(id_ds1_filter,K,L) = a_select3(id_ds1_filter,L,K) ) )
& ! [I,J] :
( ( leq(J,n5)
& leq(I,n5)
& leq(n0,J)
& leq(n0,I) )
=> ( gt(pv57,I)
=> a_select3(id_ds1_filter,I,J) = a_select3(id_ds1_filter,J,I) ) )
& ! [G,H] :
( ( leq(H,n5)
& leq(G,n5)
& leq(n0,H)
& leq(n0,G) )
=> ( ( gt(pv58,H)
& G = pv57 )
=> a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G) ) )
& ! [E,F] :
( ( leq(F,n5)
& leq(E,n5)
& leq(n0,F)
& leq(n0,E) )
=> a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E) )
& ! [C,D] :
( ( leq(D,n2)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
& ! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5) )
=> ! [M] :
( ( leq(M,pred(pv57))
& leq(n0,M) )
=> ! [N] :
( ( leq(N,n5)
& leq(n0,N) )
=> ( ( pv57 != M
& ~ ( N = M
& pv57 = N ) )
=> a_select3(id_ds1_filter,M,N) = a_select3(id_ds1_filter,N,M) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0401) ).
fof(f52_neg,negated_conjecture,
~ ( ( ! [K] :
( ( leq(K,pred(pv57))
& leq(n0,K) )
=> ! [L] :
( ( leq(L,n5)
& leq(n0,L) )
=> a_select3(id_ds1_filter,K,L) = a_select3(id_ds1_filter,L,K) ) )
& ! [I,J] :
( ( leq(J,n5)
& leq(I,n5)
& leq(n0,J)
& leq(n0,I) )
=> ( gt(pv57,I)
=> a_select3(id_ds1_filter,I,J) = a_select3(id_ds1_filter,J,I) ) )
& ! [G,H] :
( ( leq(H,n5)
& leq(G,n5)
& leq(n0,H)
& leq(n0,G) )
=> ( ( gt(pv58,H)
& G = pv57 )
=> a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G) ) )
& ! [E,F] :
( ( leq(F,n5)
& leq(E,n5)
& leq(n0,F)
& leq(n0,E) )
=> a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E) )
& ! [C,D] :
( ( leq(D,n2)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
& ! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5) )
=> ! [M] :
( ( leq(M,pred(pv57))
& leq(n0,M) )
=> ! [N] :
( ( leq(N,n5)
& leq(n0,N) )
=> ( ( pv57 != M
& ~ ( N = M
& pv57 = N ) )
=> a_select3(id_ds1_filter,M,N) = a_select3(id_ds1_filter,N,M) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
( ? [M] :
( ? [N] :
( a_select3(id_ds1_filter,M,N) != a_select3(id_ds1_filter,N,M)
& pv57 != M
& ( N != M
| pv57 != N )
& leq(N,n5)
& leq(n0,N) )
& leq(M,pred(pv57))
& leq(n0,M) )
& ! [K] :
( ! [L] :
( a_select3(id_ds1_filter,K,L) = a_select3(id_ds1_filter,L,K)
| ~ leq(L,n5)
| ~ leq(n0,L) )
| ~ leq(K,pred(pv57))
| ~ leq(n0,K) )
& ! [I,J] :
( a_select3(id_ds1_filter,I,J) = a_select3(id_ds1_filter,J,I)
| ~ gt(pv57,I)
| ~ leq(J,n5)
| ~ leq(I,n5)
| ~ leq(n0,J)
| ~ leq(n0,I) )
& ! [G,H] :
( a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G)
| ~ gt(pv58,H)
| G != pv57
| ~ leq(H,n5)
| ~ leq(G,n5)
| ~ leq(n0,H)
| ~ leq(n0,G) )
& ! [E,F] :
( a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E)
| ~ leq(F,n5)
| ~ leq(E,n5)
| ~ leq(n0,F)
| ~ leq(n0,E) )
& ! [C,D] :
( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C)
| ~ leq(D,n2)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A)
| ~ leq(B,n5)
| ~ leq(A,n5)
| ~ leq(n0,B)
| ~ leq(n0,A) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5) ),
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
! [A,B,C,D,E,F,G,H,I,J,K,L] :
( a_select3(id_ds1_filter,sk27,sk28) != a_select3(id_ds1_filter,sk28,sk27)
& pv57 != sk27
& ( sk28 != sk27
| pv57 != sk28 )
& leq(sk28,n5)
& leq(n0,sk28)
& leq(sk27,pred(pv57))
& leq(n0,sk27)
& ( a_select3(id_ds1_filter,K,L) = a_select3(id_ds1_filter,L,K)
| ~ leq(L,n5)
| ~ leq(n0,L)
| ~ leq(K,pred(pv57))
| ~ leq(n0,K) )
& ( a_select3(id_ds1_filter,I,J) = a_select3(id_ds1_filter,J,I)
| ~ gt(pv57,I)
| ~ leq(J,n5)
| ~ leq(I,n5)
| ~ leq(n0,J)
| ~ leq(n0,I) )
& ( a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G)
| ~ gt(pv58,H)
| G != pv57
| ~ leq(H,n5)
| ~ leq(G,n5)
| ~ leq(n0,H)
| ~ leq(n0,G) )
& ( a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E)
| ~ leq(F,n5)
| ~ leq(E,n5)
| ~ leq(n0,F)
| ~ leq(n0,E) )
& ( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C)
| ~ leq(D,n2)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A)
| ~ leq(B,n5)
| ~ leq(A,n5)
| ~ leq(n0,B)
| ~ leq(n0,A) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk27,sk28])],[f52_nnf]) ).
cnf(c266,plain,
( a_select3(id_ds1_filter,X10,X11) = a_select3(id_ds1_filter,X11,X10)
| ~ leq(X11,n5)
| ~ leq(n0,X11)
| ~ leq(X10,pred(pv57))
| ~ leq(n0,X10) ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c267,plain,
leq(n0,sk27),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(p422,plain,
( a_select3(id_ds1_filter,sk27,X0) = a_select3(id_ds1_filter,X0,sk27)
| ~ leq(X0,n5)
| ~ leq(n0,X0)
| ~ leq(sk27,pred(pv57)) ),
inference(resolution,[status(thm)],[c266,c267]) ).
cnf(c268,plain,
leq(sk27,pred(pv57)),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(p425,plain,
( a_select3(id_ds1_filter,sk27,X0) = a_select3(id_ds1_filter,X0,sk27)
| ~ leq(X0,n5)
| ~ leq(n0,X0) ),
inference(resolution,[status(thm)],[p422,c268]) ).
cnf(c269,plain,
leq(n0,sk28),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(p429,plain,
( a_select3(id_ds1_filter,sk27,sk28) = a_select3(id_ds1_filter,sk28,sk27)
| ~ leq(sk28,n5) ),
inference(resolution,[status(thm)],[p425,c269]) ).
cnf(c270,plain,
leq(sk28,n5),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(p431,plain,
a_select3(id_ds1_filter,sk27,sk28) = a_select3(id_ds1_filter,sk28,sk27),
inference(resolution,[status(thm)],[p429,c270]) ).
cnf(c273,plain,
a_select3(id_ds1_filter,sk27,sk28) != a_select3(id_ds1_filter,sk28,sk27),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(p432,plain,
$false,
inference(resolution,[status(thm)],[p431,c273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV221+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.79 % Computer : n020.cluster.edu
% 0.11/0.79 % Model : x86_64 x86_64
% 0.11/0.79 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.79 % Memory : 8046.5625MB
% 0.11/0.79 % OS : Linux 6.8.0-71-generic
% 0.11/0.79 % CPULimit : 300
% 0.11/0.79 % WCLimit : 300
% 0.11/0.79 % DateTime : Thu Sep 24 18:48:50 UTC 2026
% 0.11/0.79 % CPUTime :
% 0.11/0.79 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.72/4.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.72/4.24 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------