%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV221+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 09:07:03 AM UTC 2026
% Result : Theorem 27.67s 8.99s
% Output : CNFRefutation 27.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 258 ( 63 equ)
% Maximal formula atoms : 47 ( 14 avg)
% Number of connectives : 350 ( 110 ~; 94 |; 120 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 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 : 70 ( 0 sgn 64 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quaternion_ds1_symm_0401,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('theBenchmark.p',quaternion_ds1_symm_0401) ).
fof(quaternion_ds1_symm_0401_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(assume_negation,[status(cth)],[quaternion_ds1_symm_0401]) ).
fof(nnf_56,plain,
( ? [M] :
( ? [N] :
( a_select3(id_ds1_filter,M,N) != a_select3(id_ds1_filter,N,M)
& pv57 != M
& ( M != N
| 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,J,I) = a_select3(id_ds1_filter,I,J)
| ~ gt(pv57,I)
| ~ leq(J,n5)
| ~ leq(I,n5)
| ~ leq(n0,J)
| ~ leq(n0,I) )
& ! [G,H] :
( a_select3(id_ds1_filter,H,G) = a_select3(id_ds1_filter,G,H)
| ~ 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,D,C) = a_select3(r_ds1_filter,C,D)
| ~ leq(D,n2)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q_ds1_filter,B,A) = a_select3(q_ds1_filter,A,B)
| ~ 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(fof_nnf,[status(thm)],[quaternion_ds1_symm_0401_neg]) ).
fof(sk_quaternion_ds1_symm_0401_neg_sk,plain,
( a_select3(id_ds1_filter,sK0,sK1) != a_select3(id_ds1_filter,sK1,sK0)
& pv57 != sK0
& ( sK0 != sK1
| pv57 != sK1 )
& leq(sK1,n5)
& leq(n0,sK1)
& leq(sK0,pred(pv57))
& leq(n0,sK0)
& ! [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,J,I) = a_select3(id_ds1_filter,I,J)
| ~ gt(pv57,I)
| ~ leq(J,n5)
| ~ leq(I,n5)
| ~ leq(n0,J)
| ~ leq(n0,I) )
& ! [G,H] :
( a_select3(id_ds1_filter,H,G) = a_select3(id_ds1_filter,G,H)
| ~ 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,D,C) = a_select3(r_ds1_filter,C,D)
| ~ leq(D,n2)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q_ds1_filter,B,A) = a_select3(q_ds1_filter,A,B)
| ~ 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(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(M,sK0),skolemize(N,sK1)],[nnf_56]) ).
fof(sk_quaternion_ds1_symm_0401_neg,plain,
( a_select3(id_ds1_filter,sK0,sK1) != a_select3(id_ds1_filter,sK1,sK0)
& pv57 != sK0
& ( sK0 != sK1
| pv57 != sK1 )
& leq(sK1,n5)
& leq(n0,sK1)
& leq(sK0,pred(pv57))
& leq(n0,sK0)
& ! [VAR_0,VAR_1] :
( a_select3(id_ds1_filter,VAR_0,VAR_1) = a_select3(id_ds1_filter,VAR_1,VAR_0)
| ~ leq(VAR_1,n5)
| ~ leq(n0,VAR_1)
| ~ leq(VAR_0,pred(pv57))
| ~ leq(n0,VAR_0) )
& ! [VAR_0,VAR_1] :
( a_select3(id_ds1_filter,VAR_1,VAR_0) = a_select3(id_ds1_filter,VAR_0,VAR_1)
| ~ gt(pv57,VAR_0)
| ~ leq(VAR_1,n5)
| ~ leq(VAR_0,n5)
| ~ leq(n0,VAR_1)
| ~ leq(n0,VAR_0) )
& ! [VAR_0,VAR_1] :
( a_select3(id_ds1_filter,VAR_1,VAR_0) = a_select3(id_ds1_filter,VAR_0,VAR_1)
| ~ gt(pv58,VAR_1)
| VAR_0 != pv57
| ~ leq(VAR_1,n5)
| ~ leq(VAR_0,n5)
| ~ leq(n0,VAR_1)
| ~ leq(n0,VAR_0) )
& ! [VAR_0,VAR_1] :
( a_select3(pminus_ds1_filter,VAR_0,VAR_1) = a_select3(pminus_ds1_filter,VAR_1,VAR_0)
| ~ leq(VAR_1,n5)
| ~ leq(VAR_0,n5)
| ~ leq(n0,VAR_1)
| ~ leq(n0,VAR_0) )
& ! [VAR_0,VAR_1] :
( a_select3(r_ds1_filter,VAR_1,VAR_0) = a_select3(r_ds1_filter,VAR_0,VAR_1)
| ~ leq(VAR_1,n2)
| ~ leq(VAR_0,n2)
| ~ leq(n0,VAR_1)
| ~ leq(n0,VAR_0) )
& ! [VAR_0,VAR_1] :
( a_select3(q_ds1_filter,VAR_1,VAR_0) = a_select3(q_ds1_filter,VAR_0,VAR_1)
| ~ leq(VAR_1,n5)
| ~ leq(VAR_0,n5)
| ~ leq(n0,VAR_1)
| ~ leq(n0,VAR_0) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5) ),
inference(cnf_transformation,[status(thm)],[sk_quaternion_ds1_symm_0401_neg_sk]) ).
cnf(c_377,negated_conjecture,
( a_select3(id_ds1_filter,A,B) = a_select3(id_ds1_filter,B,A)
| ~ leq(B,n5)
| ~ leq(n0,B)
| ~ leq(A,pred(pv57))
| ~ leq(n0,A) ),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0401_neg]) ).
cnf(c_378,negated_conjecture,
leq(n0,sK0),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0401_neg]) ).
cnf(c_379,negated_conjecture,
leq(sK0,pred(pv57)),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0401_neg]) ).
cnf(c_380,negated_conjecture,
leq(n0,sK1),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0401_neg]) ).
cnf(c_381,negated_conjecture,
leq(sK1,n5),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0401_neg]) ).
cnf(c_386,negated_conjecture,
a_select3(id_ds1_filter,sK0,sK1) != a_select3(id_ds1_filter,sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_quaternion_ds1_symm_0401_neg]) ).
cnf(c_387,negated_conjecture,
a_select3(id_ds1_filter,sK1,sK0) != a_select3(id_ds1_filter,sK0,sK1),
inference(copy,[status(thm)],[c_386]) ).
cnf(c_4840,negated_conjecture,
( a_select3(id_ds1_filter,sK0,A) = a_select3(id_ds1_filter,A,sK0)
| ~ leq(A,n5)
| ~ leq(n0,A)
| ~ leq(sK0,pred(pv57)) ),
inference(resolve,[status(thm)],[c_377,c_378]) ).
cnf(c_4841,negated_conjecture,
( a_select3(id_ds1_filter,sK0,A) = a_select3(id_ds1_filter,A,sK0)
| ~ leq(A,n5)
| ~ leq(n0,A) ),
inference(resolve,[status(thm)],[c_4840,c_379]) ).
cnf(c_4842,negated_conjecture,
( a_select3(id_ds1_filter,sK0,sK1) = a_select3(id_ds1_filter,sK1,sK0)
| ~ leq(sK1,n5) ),
inference(resolve,[status(thm)],[c_4841,c_380]) ).
cnf(c_4843,negated_conjecture,
a_select3(id_ds1_filter,sK0,sK1) = a_select3(id_ds1_filter,sK1,sK0),
inference(resolve,[status(thm)],[c_4842,c_381]) ).
cnf(c_4844,negated_conjecture,
a_select3(id_ds1_filter,sK1,sK0) = a_select3(id_ds1_filter,sK0,sK1),
inference(copy,[status(thm)],[c_4843]) ).
cnf(c_4839,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_387,c_4844]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV221+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n010.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 13:20:51 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 3422482 was started by sandbox on n010,
% 0.10/5.38 % Sat Sep 26 13:20:51 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/5.44
% 0.14/5.44 % From the command line: assign(max_seconds, 300).
% 27.67/8.99
% 27.67/8.99 % SZS status Theorem for theBenchmark
% 27.67/8.99
% 27.67/8.99 % Proof 1 at 3.23 (+ 0.27) seconds.
% 27.67/8.99 % Length of proof is 9.
% 27.67/8.99 % Level of proof is 3.
% 27.67/8.99 % Maximum clause weight is 32.000.
% 27.67/8.99 % Given clauses 306.
% 27.67/8.99
% 27.67/8.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------