%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWV221+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 : Thu Sep 24 09:02:59 AM UTC 2026
% Result : Theorem 2.45s 12.90s
% Output : Proof 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 24 ( 15 unt; 0 def)
% Number of atoms : 354 ( 81 equ)
% Maximal formula atoms : 47 ( 14 avg)
% Number of connectives : 500 ( 170 ~; 148 |; 157 &)
% ( 0 <=>; 25 =>; 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 : 95 ( 0 sgn 88 !; 5 ?)
% 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(f_53_1,negated_conjecture,
( ~ ! [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) ) ) )
& ! [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) ),
inference(negate,[status(cth)],[quaternion_ds1_symm_0401]) ).
fof(f_53_2,negated_conjecture,
( ? [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(fof_nnf,[status(thm)],[f_53_1]) ).
fof(f_53_3,negated_conjecture,
( ? [U_195] :
( ? [U_194] :
( a_select3(id_ds1_filter,U_195,U_194) != a_select3(id_ds1_filter,U_194,U_195)
& pv57 != U_195
& ( U_194 != U_195
| pv57 != U_194 )
& leq(U_194,n5)
& leq(n0,U_194) )
& leq(U_195,pred(pv57))
& leq(n0,U_195) )
& ! [U_193] :
( ! [U_192] :
( a_select3(id_ds1_filter,U_193,U_192) = a_select3(id_ds1_filter,U_192,U_193)
| ~ leq(U_192,n5)
| ~ leq(n0,U_192) )
| ~ leq(U_193,pred(pv57))
| ~ leq(n0,U_193) )
& ! [U_191,U_190] :
( a_select3(id_ds1_filter,U_191,U_190) = a_select3(id_ds1_filter,U_190,U_191)
| ~ gt(pv57,U_191)
| ~ leq(U_190,n5)
| ~ leq(U_191,n5)
| ~ leq(n0,U_190)
| ~ leq(n0,U_191) )
& ! [U_189,U_188] :
( a_select3(id_ds1_filter,U_189,U_188) = a_select3(id_ds1_filter,U_188,U_189)
| ~ gt(pv58,U_188)
| U_189 != pv57
| ~ leq(U_188,n5)
| ~ leq(U_189,n5)
| ~ leq(n0,U_188)
| ~ leq(n0,U_189) )
& ! [U_187,U_186] :
( a_select3(pminus_ds1_filter,U_187,U_186) = a_select3(pminus_ds1_filter,U_186,U_187)
| ~ leq(U_186,n5)
| ~ leq(U_187,n5)
| ~ leq(n0,U_186)
| ~ leq(n0,U_187) )
& ! [U_185,U_184] :
( a_select3(r_ds1_filter,U_185,U_184) = a_select3(r_ds1_filter,U_184,U_185)
| ~ leq(U_184,n2)
| ~ leq(U_185,n2)
| ~ leq(n0,U_184)
| ~ leq(n0,U_185) )
& ! [U_183,U_182] :
( a_select3(q_ds1_filter,U_183,U_182) = a_select3(q_ds1_filter,U_182,U_183)
| ~ leq(U_182,n5)
| ~ leq(U_183,n5)
| ~ leq(n0,U_182)
| ~ leq(n0,U_183) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5) ),
inference(variable_rename,[status(thm)],[f_53_2]) ).
fof(f_53_4,negated_conjecture,
( ? [U_194] :
( a_select3(id_ds1_filter,sK28,U_194) != a_select3(id_ds1_filter,U_194,sK28)
& pv57 != sK28
& ( U_194 != sK28
| pv57 != U_194 )
& leq(U_194,n5)
& leq(n0,U_194) )
& leq(sK28,pred(pv57))
& leq(n0,sK28)
& ! [U_193] :
( ! [U_192] :
( a_select3(id_ds1_filter,U_193,U_192) = a_select3(id_ds1_filter,U_192,U_193)
| ~ leq(U_192,n5)
| ~ leq(n0,U_192) )
| ~ leq(U_193,pred(pv57))
| ~ leq(n0,U_193) )
& ! [U_191,U_190] :
( a_select3(id_ds1_filter,U_191,U_190) = a_select3(id_ds1_filter,U_190,U_191)
| ~ gt(pv57,U_191)
| ~ leq(U_190,n5)
| ~ leq(U_191,n5)
| ~ leq(n0,U_190)
| ~ leq(n0,U_191) )
& ! [U_189,U_188] :
( a_select3(id_ds1_filter,U_189,U_188) = a_select3(id_ds1_filter,U_188,U_189)
| ~ gt(pv58,U_188)
| U_189 != pv57
| ~ leq(U_188,n5)
| ~ leq(U_189,n5)
| ~ leq(n0,U_188)
| ~ leq(n0,U_189) )
& ! [U_187,U_186] :
( a_select3(pminus_ds1_filter,U_187,U_186) = a_select3(pminus_ds1_filter,U_186,U_187)
| ~ leq(U_186,n5)
| ~ leq(U_187,n5)
| ~ leq(n0,U_186)
| ~ leq(n0,U_187) )
& ! [U_185,U_184] :
( a_select3(r_ds1_filter,U_185,U_184) = a_select3(r_ds1_filter,U_184,U_185)
| ~ leq(U_184,n2)
| ~ leq(U_185,n2)
| ~ leq(n0,U_184)
| ~ leq(n0,U_185) )
& ! [U_183,U_182] :
( a_select3(q_ds1_filter,U_183,U_182) = a_select3(q_ds1_filter,U_182,U_183)
| ~ leq(U_182,n5)
| ~ leq(U_183,n5)
| ~ leq(n0,U_182)
| ~ leq(n0,U_183) )
& 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,[sK28]),skolemize(U_195,sK28)],[f_53_3]) ).
fof(f_53_5,negated_conjecture,
( a_select3(id_ds1_filter,sK28,sK29) != a_select3(id_ds1_filter,sK29,sK28)
& pv57 != sK28
& ( sK29 != sK28
| pv57 != sK29 )
& leq(sK29,n5)
& leq(n0,sK29)
& leq(sK28,pred(pv57))
& leq(n0,sK28)
& ! [U_193] :
( ! [U_192] :
( a_select3(id_ds1_filter,U_193,U_192) = a_select3(id_ds1_filter,U_192,U_193)
| ~ leq(U_192,n5)
| ~ leq(n0,U_192) )
| ~ leq(U_193,pred(pv57))
| ~ leq(n0,U_193) )
& ! [U_191,U_190] :
( a_select3(id_ds1_filter,U_191,U_190) = a_select3(id_ds1_filter,U_190,U_191)
| ~ gt(pv57,U_191)
| ~ leq(U_190,n5)
| ~ leq(U_191,n5)
| ~ leq(n0,U_190)
| ~ leq(n0,U_191) )
& ! [U_189,U_188] :
( a_select3(id_ds1_filter,U_189,U_188) = a_select3(id_ds1_filter,U_188,U_189)
| ~ gt(pv58,U_188)
| U_189 != pv57
| ~ leq(U_188,n5)
| ~ leq(U_189,n5)
| ~ leq(n0,U_188)
| ~ leq(n0,U_189) )
& ! [U_187,U_186] :
( a_select3(pminus_ds1_filter,U_187,U_186) = a_select3(pminus_ds1_filter,U_186,U_187)
| ~ leq(U_186,n5)
| ~ leq(U_187,n5)
| ~ leq(n0,U_186)
| ~ leq(n0,U_187) )
& ! [U_185,U_184] :
( a_select3(r_ds1_filter,U_185,U_184) = a_select3(r_ds1_filter,U_184,U_185)
| ~ leq(U_184,n2)
| ~ leq(U_185,n2)
| ~ leq(n0,U_184)
| ~ leq(n0,U_185) )
& ! [U_183,U_182] :
( a_select3(q_ds1_filter,U_183,U_182) = a_select3(q_ds1_filter,U_182,U_183)
| ~ leq(U_182,n5)
| ~ leq(U_183,n5)
| ~ leq(n0,U_182)
| ~ leq(n0,U_183) )
& 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,[sK29]),skolemize(U_194,sK29)],[f_53_4]) ).
fof(f_53_6,negated_conjecture,
( a_select3(id_ds1_filter,sK28,sK29) != a_select3(id_ds1_filter,sK29,sK28)
& pv57 != sK28
& ( sK29 != sK28
| pv57 != sK29 )
& leq(sK29,n5)
& leq(n0,sK29)
& leq(sK28,pred(pv57))
& leq(n0,sK28)
& ! [U_192,U_193] :
( a_select3(id_ds1_filter,U_193,U_192) = a_select3(id_ds1_filter,U_192,U_193)
| ~ leq(U_192,n5)
| ~ leq(n0,U_192)
| ~ leq(U_193,pred(pv57))
| ~ leq(n0,U_193) )
& ! [U_190,U_191] :
( a_select3(id_ds1_filter,U_191,U_190) = a_select3(id_ds1_filter,U_190,U_191)
| ~ gt(pv57,U_191)
| ~ leq(U_190,n5)
| ~ leq(U_191,n5)
| ~ leq(n0,U_190)
| ~ leq(n0,U_191) )
& ! [U_188,U_189] :
( a_select3(id_ds1_filter,U_189,U_188) = a_select3(id_ds1_filter,U_188,U_189)
| ~ gt(pv58,U_188)
| U_189 != pv57
| ~ leq(U_188,n5)
| ~ leq(U_189,n5)
| ~ leq(n0,U_188)
| ~ leq(n0,U_189) )
& ! [U_186,U_187] :
( a_select3(pminus_ds1_filter,U_187,U_186) = a_select3(pminus_ds1_filter,U_186,U_187)
| ~ leq(U_186,n5)
| ~ leq(U_187,n5)
| ~ leq(n0,U_186)
| ~ leq(n0,U_187) )
& ! [U_185,U_184] :
( a_select3(r_ds1_filter,U_185,U_184) = a_select3(r_ds1_filter,U_184,U_185)
| ~ leq(U_184,n2)
| ~ leq(U_185,n2)
| ~ leq(n0,U_184)
| ~ leq(n0,U_185) )
& ! [U_182,U_183] :
( a_select3(q_ds1_filter,U_183,U_182) = a_select3(q_ds1_filter,U_182,U_183)
| ~ leq(U_182,n5)
| ~ leq(U_183,n5)
| ~ leq(n0,U_182)
| ~ leq(n0,U_183) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5) ),
inference(definitional_conversion,[status(esa)],[f_53_5]) ).
cnf(f_53_18,negated_conjecture,
( a_select3(id_ds1_filter,U_193,U_192) = a_select3(id_ds1_filter,U_192,U_193)
| ~ leq(U_192,n5)
| ~ leq(n0,U_192)
| ~ leq(U_193,pred(pv57))
| ~ leq(n0,U_193) ),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_19,negated_conjecture,
leq(n0,sK28),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_20,negated_conjecture,
leq(sK28,pred(pv57)),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_21,negated_conjecture,
leq(n0,sK29),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_22,negated_conjecture,
leq(sK29,n5),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(f_53_25,negated_conjecture,
a_select3(id_ds1_filter,sK28,sK29) != a_select3(id_ds1_filter,sK29,sK28),
inference(clausify,[status(thm)],[f_53_6]) ).
cnf(t1,plain,
a_select3(id_ds1_filter,sK28,sK29) != a_select3(id_ds1_filter,sK29,sK28),
inference(start,[status(thm),parent(0:0)],[f_53_25]) ).
cnf(t2,plain,
( ~ leq(sK28,pred(pv57))
| ~ leq(n0,sK29)
| ~ leq(sK29,n5)
| ~ leq(n0,sK28)
| a_select3(id_ds1_filter,sK28,sK29) = a_select3(id_ds1_filter,sK29,sK28) ),
inference(extension,[status(thm),parent(t1:1)],[f_53_18]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
leq(n0,sK28),
inference(extension,[status(thm),parent(t2:2)],[f_53_19]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
leq(sK29,n5),
inference(extension,[status(thm),parent(t2:3)],[f_53_22]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
leq(n0,sK29),
inference(extension,[status(thm),parent(t2:4)],[f_53_21]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
leq(sK28,pred(pv57)),
inference(extension,[status(thm),parent(t2:5)],[f_53_20]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV221+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.57 % Computer : n008.cluster.edu
% 0.10/10.57 % Model : x86_64 x86_64
% 0.10/10.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.57 % Memory : 8046.5625MB
% 0.10/10.57 % OS : Linux 6.8.0-71-generic
% 0.10/10.57 % CPULimit : 300
% 0.10/10.57 % WCLimit : 300
% 0.10/10.57 % DateTime : Sun Sep 20 03:11:07 UTC 2026
% 0.10/10.57 % CPUTime :
% 2.45/12.90 % SZS status Theorem for theBenchmark
% 2.45/12.90 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------