%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ062-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 : Tue Sep 29 12:31:26 PM UTC 2026
% Result : Unsatisfiable 16.58s 3.27s
% Output : Refutation 17.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 47
% Syntax : Number of formulae : 168 ( 101 unt; 29 def)
% Number of atoms : 258 ( 102 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 175 ( 85 ~; 86 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-3 aty)
% Number of functors : 49 ( 49 usr; 36 con; 0-4 aty)
% Number of variables : 90 ( 0 sgn 90 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f190,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1))
| c_in(X2,X0,X1)
| c_Finite__Set_Ocard(c_insert(X2,X0,X1),X1) = c_Suc(c_Finite__Set_Ocard(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
fof(f1630,axiom,
! [X2,X0,X1] : c_Relation_OImage(c_Relation_Odiag(X0,X1),X2,X1,X1) = c_inter(X0,X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
fof(f1871,axiom,
! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_Suc(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
fof(f1872,plain,
! [X0] : c_Suc(X0) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),
inference(reorient_equations,[],[f1871]) ).
fof(f1958,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_inter(X1,X2,X3),X3)
| c_in(X0,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
fof(f1959,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X0,X1,X2)
| ~ c_in(X0,X3,X2)
| c_in(X0,c_inter(X3,X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
fof(f2005,axiom,
! [X0,X1] : c_union(c_emptyset,X0,X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
fof(f2010,axiom,
! [X2,X3,X0,X1] : c_union(c_insert(X0,X1,X2),X3,X2) = c_insert(X0,c_union(X1,X3,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
fof(f2011,axiom,
! [X2,X3,X0,X1] : c_union(X0,c_insert(X1,X2,X3),X3) = c_insert(X1,c_union(X0,X2,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
fof(f2051,axiom,
! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f2167,axiom,
! [X2,X0,X1] :
( ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_inter(X2,X0,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
fof(f2251,axiom,
! [X0,X1] : c_in(X0,c_insert(X0,c_emptyset,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
fof(f3319,axiom,
! [X0] :
( ~ c_in(X0,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat)))
| c_in(X0,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Mutil_Otiling__domino__finite_0) ).
fof(f3322,negated_conjecture,
c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3323,negated_conjecture,
c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3324,negated_conjecture,
c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) = c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3325,plain,
c_emptyset = c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)),
inference(reorient_equations,[],[f3324]) ).
fof(f3326,negated_conjecture,
c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3327,negated_conjecture,
c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f3328,negated_conjecture,
c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f3345,plain,
! [X2,X0,X1] :
( c_Finite__Set_Ocard(c_insert(X2,X0,X1),X1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X0,X1),tc_nat),tc_nat)
| c_in(X2,X0,X1)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1)) ),
inference(definition_unfolding,[],[f190,f1872]) ).
fof(f3509,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,c_Relation_OImage(c_Relation_Odiag(X1,X3),X2,X3,X3),X3)
| c_in(X0,X2,X3) ),
inference(definition_unfolding,[],[f1958,f1630]) ).
fof(f3510,plain,
! [X2,X3,X0,X1] :
( c_in(X0,c_Relation_OImage(c_Relation_Odiag(X3,X2),X1,X2,X2),X2)
| ~ c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(definition_unfolding,[],[f1959,f1630]) ).
fof(f3542,plain,
! [X2,X0,X1] :
( c_in(c_Relation_OImage(c_Relation_Odiag(X2,X1),X0,X1,X1),c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1)) ),
inference(definition_unfolding,[],[f2167,f1630]) ).
fof(f3557,plain,
c_Finite__Set_Ocard(c_Relation_OImage(c_Relation_Odiag(c_Mutil_Ocoloured(c_0),tc_prod(tc_nat,tc_nat)),v_t,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_Relation_OImage(c_Relation_Odiag(c_Mutil_Ocoloured(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)),tc_prod(tc_nat,tc_nat)),v_t,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
inference(definition_unfolding,[],[f3323,f1630,f1630,f1872]) ).
fof(f3558,plain,
c_emptyset = c_Relation_OImage(c_Relation_Odiag(v_a,tc_prod(tc_nat,tc_nat)),v_t,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),
inference(definition_unfolding,[],[f3325,f1630]) ).
fof(f3559,plain,
c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_Relation_Odiag(c_Mutil_Ocoloured(c_0),tc_prod(tc_nat,tc_nat)),v_a,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),
inference(definition_unfolding,[],[f3326,f1630]) ).
fof(f3560,plain,
c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_Relation_Odiag(c_Mutil_Ocoloured(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)),tc_prod(tc_nat,tc_nat)),v_a,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),
inference(definition_unfolding,[],[f3327,f1630,f1872]) ).
fof(f3561,plain,
c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_Relation_OImage(c_Relation_Odiag(c_Mutil_Ocoloured(c_0),tc_prod(tc_nat,tc_nat)),v_t,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_Relation_OImage(c_Relation_Odiag(c_Mutil_Ocoloured(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)),tc_prod(tc_nat,tc_nat)),v_t,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
inference(definition_unfolding,[],[f3328,f1630,f1630,f1872]) ).
fof(f3562,definition,
sF0 = tc_prod(tc_nat,tc_nat),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f3563,plain,
tc_prod(tc_nat,tc_nat) = sF0,
inference(reorient_equations,[],[f3562]) ).
fof(f3564,definition,
sF1 = c_Mutil_Otiling(c_Mutil_Odomino,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f3565,plain,
c_Mutil_Otiling(c_Mutil_Odomino,sF0) = sF1,
inference(reorient_equations,[],[f3564]) ).
fof(f3566,definition,
sF2 = tc_set(sF0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f3567,plain,
tc_set(sF0) = sF2,
inference(reorient_equations,[],[f3566]) ).
fof(f3568,plain,
c_in(v_t,sF1,sF2),
inference(definition_folding,[],[f3322,f3567,f3563,f3565,f3563]) ).
fof(f3569,definition,
sF3 = c_Mutil_Ocoloured(c_0),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f3570,plain,
c_Mutil_Ocoloured(c_0) = sF3,
inference(reorient_equations,[],[f3569]) ).
fof(f3571,definition,
sF4 = c_Relation_Odiag(sF3,sF0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f3572,plain,
c_Relation_Odiag(sF3,sF0) = sF4,
inference(reorient_equations,[],[f3571]) ).
fof(f3573,definition,
sF5 = c_Relation_OImage(sF4,v_t,sF0,sF0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f3574,plain,
c_Relation_OImage(sF4,v_t,sF0,sF0) = sF5,
inference(reorient_equations,[],[f3573]) ).
fof(f3575,definition,
sF6 = c_Finite__Set_Ocard(sF5,sF0),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f3576,plain,
c_Finite__Set_Ocard(sF5,sF0) = sF6,
inference(reorient_equations,[],[f3575]) ).
fof(f3577,definition,
sF7 = c_SetInterval_OatMost(c_0,tc_nat),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f3578,plain,
c_SetInterval_OatMost(c_0,tc_nat) = sF7,
inference(reorient_equations,[],[f3577]) ).
fof(f3579,definition,
sF8 = c_Finite__Set_Ocard(sF7,tc_nat),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f3580,plain,
c_Finite__Set_Ocard(sF7,tc_nat) = sF8,
inference(reorient_equations,[],[f3579]) ).
fof(f3581,definition,
sF9 = c_Mutil_Ocoloured(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f3582,plain,
c_Mutil_Ocoloured(sF8) = sF9,
inference(reorient_equations,[],[f3581]) ).
fof(f3583,definition,
sF10 = c_Relation_Odiag(sF9,sF0),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f3584,plain,
c_Relation_Odiag(sF9,sF0) = sF10,
inference(reorient_equations,[],[f3583]) ).
fof(f3585,definition,
sF11 = c_Relation_OImage(sF10,v_t,sF0,sF0),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f3586,plain,
c_Relation_OImage(sF10,v_t,sF0,sF0) = sF11,
inference(reorient_equations,[],[f3585]) ).
fof(f3587,definition,
sF12 = c_Finite__Set_Ocard(sF11,sF0),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f3588,plain,
c_Finite__Set_Ocard(sF11,sF0) = sF12,
inference(reorient_equations,[],[f3587]) ).
fof(f3589,plain,
sF6 = sF12,
inference(definition_folding,[],[f3557,f3588,f3563,f3586,f3563,f3563,f3584,f3563,f3582,f3580,f3578,f3576,f3563,f3574,f3563,f3563,f3572,f3563,f3570]) ).
fof(f3590,definition,
sF13 = c_Relation_Odiag(v_a,sF0),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f3591,plain,
c_Relation_Odiag(v_a,sF0) = sF13,
inference(reorient_equations,[],[f3590]) ).
fof(f3592,definition,
sF14 = c_Relation_OImage(sF13,v_t,sF0,sF0),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f3593,plain,
c_Relation_OImage(sF13,v_t,sF0,sF0) = sF14,
inference(reorient_equations,[],[f3592]) ).
fof(f3594,plain,
c_emptyset = sF14,
inference(definition_folding,[],[f3558,f3593,f3563,f3563,f3591,f3563]) ).
fof(f3595,definition,
sF15 = c_Pair(v_i,v_j,tc_nat,tc_nat),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f3596,plain,
c_Pair(v_i,v_j,tc_nat,tc_nat) = sF15,
inference(reorient_equations,[],[f3595]) ).
fof(f3597,definition,
sF16 = c_insert(sF15,c_emptyset,sF0),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f3598,plain,
c_insert(sF15,c_emptyset,sF0) = sF16,
inference(reorient_equations,[],[f3597]) ).
fof(f3599,definition,
sF17 = c_Relation_OImage(sF4,v_a,sF0,sF0),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f3600,plain,
c_Relation_OImage(sF4,v_a,sF0,sF0) = sF17,
inference(reorient_equations,[],[f3599]) ).
fof(f3601,plain,
sF16 = sF17,
inference(definition_folding,[],[f3559,f3600,f3563,f3563,f3572,f3563,f3570,f3598,f3563,f3596]) ).
fof(f3602,definition,
sF18 = c_Pair(v_m,v_n,tc_nat,tc_nat),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f3603,plain,
c_Pair(v_m,v_n,tc_nat,tc_nat) = sF18,
inference(reorient_equations,[],[f3602]) ).
fof(f3604,definition,
sF19 = c_insert(sF18,c_emptyset,sF0),
introduced(definition,[new_symbols(definition,[sF19])],[function_definition]) ).
fof(f3605,plain,
c_insert(sF18,c_emptyset,sF0) = sF19,
inference(reorient_equations,[],[f3604]) ).
fof(f3606,definition,
sF20 = c_Relation_OImage(sF10,v_a,sF0,sF0),
introduced(definition,[new_symbols(definition,[sF20])],[function_definition]) ).
fof(f3607,plain,
c_Relation_OImage(sF10,v_a,sF0,sF0) = sF20,
inference(reorient_equations,[],[f3606]) ).
fof(f3608,plain,
sF19 = sF20,
inference(definition_folding,[],[f3560,f3607,f3563,f3563,f3584,f3563,f3582,f3580,f3578,f3605,f3563,f3603]) ).
fof(f3609,definition,
sF21 = c_insert(sF15,sF5,sF0),
introduced(definition,[new_symbols(definition,[sF21])],[function_definition]) ).
fof(f3610,plain,
c_insert(sF15,sF5,sF0) = sF21,
inference(reorient_equations,[],[f3609]) ).
fof(f3611,definition,
sF22 = c_Finite__Set_Ocard(sF21,sF0),
introduced(definition,[new_symbols(definition,[sF22])],[function_definition]) ).
fof(f3612,plain,
c_Finite__Set_Ocard(sF21,sF0) = sF22,
inference(reorient_equations,[],[f3611]) ).
fof(f3613,definition,
sF23 = c_insert(sF18,sF11,sF0),
introduced(definition,[new_symbols(definition,[sF23])],[function_definition]) ).
fof(f3614,plain,
c_insert(sF18,sF11,sF0) = sF23,
inference(reorient_equations,[],[f3613]) ).
fof(f3615,definition,
sF24 = c_Finite__Set_Ocard(sF23,sF0),
introduced(definition,[new_symbols(definition,[sF24])],[function_definition]) ).
fof(f3616,plain,
c_Finite__Set_Ocard(sF23,sF0) = sF24,
inference(reorient_equations,[],[f3615]) ).
fof(f3617,plain,
sF22 != sF24,
inference(definition_folding,[],[f3561,f3616,f3563,f3614,f3563,f3586,f3563,f3563,f3584,f3563,f3582,f3580,f3578,f3603,f3612,f3563,f3610,f3563,f3574,f3563,f3563,f3572,f3563,f3570,f3596]) ).
fof(f3632,plain,
! [X2,X3,X0,X1] : c_union(c_insert(X0,X1,X2),X3,X2) = c_union(X1,c_insert(X0,X3,X2),X2),
inference(forward_demodulation,[],[f2010,f2011]) ).
fof(f3767,plain,
! [X0] :
( c_in(X0,c_Finite__Set_OFinites,tc_set(sF0))
| ~ c_in(X0,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) ),
inference(backward_demodulation,[],[f3319,f3563]) ).
fof(f3772,plain,
sF6 = c_Finite__Set_Ocard(sF11,sF0),
inference(forward_demodulation,[],[f3588,f3589]) ).
fof(f3773,plain,
c_emptyset = c_Relation_OImage(sF13,v_t,sF0,sF0),
inference(forward_demodulation,[],[f3593,f3594]) ).
fof(f3774,plain,
sF16 = c_Relation_OImage(sF4,v_a,sF0,sF0),
inference(forward_demodulation,[],[f3600,f3601]) ).
fof(f3775,plain,
sF19 = c_Relation_OImage(sF10,v_a,sF0,sF0),
inference(forward_demodulation,[],[f3607,f3608]) ).
fof(f3818,plain,
! [X0] :
( c_in(X0,c_Finite__Set_OFinites,sF2)
| ~ c_in(X0,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) ),
inference(forward_demodulation,[],[f3767,f3567]) ).
fof(f3833,plain,
! [X0] :
( ~ c_in(X0,c_Mutil_Otiling(c_Mutil_Odomino,sF0),tc_set(sF0))
| c_in(X0,c_Finite__Set_OFinites,sF2) ),
inference(forward_demodulation,[],[f3818,f3563]) ).
fof(f3839,plain,
! [X0] :
( ~ c_in(X0,c_Mutil_Otiling(c_Mutil_Odomino,sF0),sF2)
| c_in(X0,c_Finite__Set_OFinites,sF2) ),
inference(forward_demodulation,[],[f3833,f3567]) ).
fof(f3842,plain,
! [X0] :
( c_in(X0,c_Finite__Set_OFinites,sF2)
| ~ c_in(X0,sF1,sF2) ),
inference(forward_demodulation,[],[f3839,f3565]) ).
fof(f3852,plain,
! [X0,X1] :
( ~ c_in(X0,c_Relation_OImage(sF10,X1,sF0,sF0),sF0)
| c_in(X0,X1,sF0) ),
inference(superposition,[],[f3509,f3584]) ).
fof(f3853,plain,
! [X0,X1] :
( ~ c_in(X0,c_Relation_OImage(sF4,X1,sF0,sF0),sF0)
| c_in(X0,X1,sF0) ),
inference(superposition,[],[f3509,f3572]) ).
fof(f3917,plain,
c_in(sF15,sF16,sF0),
inference(superposition,[],[f2251,f3598]) ).
fof(f3918,plain,
c_in(sF18,sF19,sF0),
inference(superposition,[],[f2251,f3605]) ).
fof(f3930,plain,
! [X0] :
( c_Finite__Set_Ocard(c_insert(X0,sF5,sF0),sF0) = c_Finite__Set_Ocard(c_SetInterval_OatMost(sF6,tc_nat),tc_nat)
| c_in(X0,sF5,sF0)
| ~ c_in(sF5,c_Finite__Set_OFinites,tc_set(sF0)) ),
inference(superposition,[],[f3345,f3576]) ).
fof(f3931,plain,
! [X0] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(sF6,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_insert(X0,sF11,sF0),sF0)
| c_in(X0,sF11,sF0)
| ~ c_in(sF11,c_Finite__Set_OFinites,tc_set(sF0)) ),
inference(superposition,[],[f3345,f3772]) ).
fof(f3942,plain,
! [X0] :
( ~ c_in(sF11,c_Finite__Set_OFinites,sF2)
| c_Finite__Set_Ocard(c_SetInterval_OatMost(sF6,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_insert(X0,sF11,sF0),sF0)
| c_in(X0,sF11,sF0) ),
inference(forward_demodulation,[],[f3931,f3567]) ).
fof(f3943,plain,
! [X0] :
( ~ c_in(sF5,c_Finite__Set_OFinites,sF2)
| c_Finite__Set_Ocard(c_insert(X0,sF5,sF0),sF0) = c_Finite__Set_Ocard(c_SetInterval_OatMost(sF6,tc_nat),tc_nat)
| c_in(X0,sF5,sF0) ),
inference(forward_demodulation,[],[f3930,f3567]) ).
fof(f3962,definition,
( spl25_7
<=> ! [X0] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(sF6,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_insert(X0,sF11,sF0),sF0)
| c_in(X0,sF11,sF0) ) ),
introduced(definition,[new_symbols(definition,[spl25_7])],[avatar_definition]) ).
fof(f3963,plain,
( ! [X0] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(sF6,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_insert(X0,sF11,sF0),sF0)
| c_in(X0,sF11,sF0) )
| ~ spl25_7 ),
inference(avatar_component_clause,[],[f3962]) ).
fof(f3965,definition,
( spl25_8
<=> c_in(sF11,c_Finite__Set_OFinites,sF2) ),
introduced(definition,[new_symbols(definition,[spl25_8])],[avatar_definition]) ).
fof(f3967,plain,
( ~ c_in(sF11,c_Finite__Set_OFinites,sF2)
| spl25_8 ),
inference(avatar_component_clause,[],[f3965]) ).
fof(f3968,plain,
( spl25_7
| ~ spl25_8 ),
inference(avatar_split_clause,[],[f3942,f3965,f3962]) ).
fof(f3970,definition,
( spl25_9
<=> ! [X0] :
( c_Finite__Set_Ocard(c_insert(X0,sF5,sF0),sF0) = c_Finite__Set_Ocard(c_SetInterval_OatMost(sF6,tc_nat),tc_nat)
| c_in(X0,sF5,sF0) ) ),
introduced(definition,[new_symbols(definition,[spl25_9])],[avatar_definition]) ).
fof(f3971,plain,
( ! [X0] :
( c_Finite__Set_Ocard(c_insert(X0,sF5,sF0),sF0) = c_Finite__Set_Ocard(c_SetInterval_OatMost(sF6,tc_nat),tc_nat)
| c_in(X0,sF5,sF0) )
| ~ spl25_9 ),
inference(avatar_component_clause,[],[f3970]) ).
fof(f3973,definition,
( spl25_10
<=> c_in(sF5,c_Finite__Set_OFinites,sF2) ),
introduced(definition,[new_symbols(definition,[spl25_10])],[avatar_definition]) ).
fof(f3975,plain,
( ~ c_in(sF5,c_Finite__Set_OFinites,sF2)
| spl25_10 ),
inference(avatar_component_clause,[],[f3973]) ).
fof(f3976,plain,
( spl25_9
| ~ spl25_10 ),
inference(avatar_split_clause,[],[f3943,f3973,f3970]) ).
fof(f3997,plain,
! [X0] :
( c_in(X0,v_a,sF0)
| ~ c_in(X0,sF19,sF0) ),
inference(superposition,[],[f3852,f3775]) ).
fof(f3998,plain,
! [X0] :
( c_in(X0,v_t,sF0)
| ~ c_in(X0,sF11,sF0) ),
inference(superposition,[],[f3852,f3586]) ).
fof(f4019,plain,
! [X0] :
( c_in(X0,v_a,sF0)
| ~ c_in(X0,sF16,sF0) ),
inference(superposition,[],[f3853,f3774]) ).
fof(f4020,plain,
! [X0] :
( c_in(X0,v_t,sF0)
| ~ c_in(X0,sF5,sF0) ),
inference(superposition,[],[f3853,f3574]) ).
fof(f4026,plain,
! [X0,X1] :
( c_in(X0,c_Relation_OImage(sF13,X1,sF0,sF0),sF0)
| ~ c_in(X0,v_a,sF0)
| ~ c_in(X0,X1,sF0) ),
inference(superposition,[],[f3510,f3591]) ).
fof(f4243,plain,
! [X0] :
( c_in(X0,c_emptyset,sF0)
| ~ c_in(X0,v_a,sF0)
| ~ c_in(X0,v_t,sF0) ),
inference(superposition,[],[f4026,f3773]) ).
fof(f4245,plain,
! [X0] :
( ~ c_in(X0,v_a,sF0)
| ~ c_in(X0,v_t,sF0) ),
inference(forward_subsumption_resolution,[],[f4243,f2051]) ).
fof(f4246,plain,
! [X0] :
( ~ c_in(X0,sF16,sF0)
| ~ c_in(X0,v_t,sF0) ),
inference(resolution,[],[f4245,f4019]) ).
fof(f4247,plain,
! [X0] :
( ~ c_in(X0,sF19,sF0)
| ~ c_in(X0,v_t,sF0) ),
inference(resolution,[],[f4245,f3997]) ).
fof(f4248,plain,
~ c_in(sF15,v_t,sF0),
inference(resolution,[],[f4246,f3917]) ).
fof(f4249,plain,
~ c_in(sF18,v_t,sF0),
inference(resolution,[],[f4247,f3918]) ).
fof(f5126,plain,
~ c_in(sF18,sF11,sF0),
inference(resolution,[],[f4249,f3998]) ).
fof(f5135,plain,
~ c_in(sF15,sF5,sF0),
inference(resolution,[],[f4248,f4020]) ).
fof(f5764,plain,
! [X0] : c_union(c_emptyset,c_insert(sF15,X0,sF0),sF0) = c_union(sF16,X0,sF0),
inference(superposition,[],[f3632,f3598]) ).
fof(f5769,plain,
! [X0] : c_union(c_emptyset,c_insert(sF18,X0,sF0),sF0) = c_union(sF19,X0,sF0),
inference(superposition,[],[f3632,f3605]) ).
fof(f5785,plain,
! [X0] : c_insert(sF18,X0,sF0) = c_union(sF19,X0,sF0),
inference(forward_demodulation,[],[f5769,f2005]) ).
fof(f5786,plain,
! [X0] : c_insert(sF15,X0,sF0) = c_union(sF16,X0,sF0),
inference(forward_demodulation,[],[f5764,f2005]) ).
fof(f5811,plain,
sF23 = c_union(sF19,sF11,sF0),
inference(backward_demodulation,[],[f3614,f5785]) ).
fof(f5835,plain,
sF21 = c_union(sF16,sF5,sF0),
inference(backward_demodulation,[],[f3610,f5786]) ).
fof(f11024,plain,
! [X0] :
( c_in(c_Relation_OImage(sF10,X0,sF0,sF0),c_Finite__Set_OFinites,tc_set(sF0))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(sF0)) ),
inference(superposition,[],[f3542,f3584]) ).
fof(f11025,plain,
! [X0] :
( c_in(c_Relation_OImage(sF4,X0,sF0,sF0),c_Finite__Set_OFinites,tc_set(sF0))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(sF0)) ),
inference(superposition,[],[f3542,f3572]) ).
fof(f11045,plain,
! [X0] :
( c_in(c_Relation_OImage(sF4,X0,sF0,sF0),c_Finite__Set_OFinites,sF2)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(sF0)) ),
inference(forward_demodulation,[],[f11025,f3567]) ).
fof(f11046,plain,
! [X0] :
( c_in(c_Relation_OImage(sF10,X0,sF0,sF0),c_Finite__Set_OFinites,sF2)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(sF0)) ),
inference(forward_demodulation,[],[f11024,f3567]) ).
fof(f11048,plain,
! [X0] :
( c_in(c_Relation_OImage(sF4,X0,sF0,sF0),c_Finite__Set_OFinites,sF2)
| ~ c_in(X0,c_Finite__Set_OFinites,sF2) ),
inference(forward_demodulation,[],[f11045,f3567]) ).
fof(f11049,plain,
! [X0] :
( c_in(c_Relation_OImage(sF10,X0,sF0,sF0),c_Finite__Set_OFinites,sF2)
| ~ c_in(X0,c_Finite__Set_OFinites,sF2) ),
inference(forward_demodulation,[],[f11046,f3567]) ).
fof(f11057,plain,
( c_in(sF5,c_Finite__Set_OFinites,sF2)
| ~ c_in(v_t,c_Finite__Set_OFinites,sF2) ),
inference(superposition,[],[f11048,f3574]) ).
fof(f11061,plain,
( ~ c_in(v_t,c_Finite__Set_OFinites,sF2)
| spl25_10 ),
inference(forward_subsumption_resolution,[],[f11057,f3975]) ).
fof(f11063,plain,
( ~ c_in(v_t,sF1,sF2)
| spl25_10 ),
inference(resolution,[],[f11061,f3842]) ).
fof(f11065,plain,
( $false
| spl25_10 ),
inference(forward_subsumption_resolution,[],[f11063,f3568]) ).
fof(f11066,plain,
spl25_10,
inference(avatar_contradiction_clause,[],[f11065]) ).
fof(f11172,plain,
( c_in(sF11,c_Finite__Set_OFinites,sF2)
| ~ c_in(v_t,c_Finite__Set_OFinites,sF2) ),
inference(superposition,[],[f11049,f3586]) ).
fof(f11176,plain,
( ~ c_in(v_t,c_Finite__Set_OFinites,sF2)
| spl25_8 ),
inference(forward_subsumption_resolution,[],[f11172,f3967]) ).
fof(f11177,plain,
( ~ c_in(v_t,sF1,sF2)
| spl25_8 ),
inference(resolution,[],[f11176,f3842]) ).
fof(f11179,plain,
( $false
| spl25_8 ),
inference(forward_subsumption_resolution,[],[f11177,f3568]) ).
fof(f11180,plain,
spl25_8,
inference(avatar_contradiction_clause,[],[f11179]) ).
fof(f11191,plain,
( c_Finite__Set_Ocard(c_SetInterval_OatMost(sF6,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_union(sF19,sF11,sF0),sF0)
| c_in(sF18,sF11,sF0)
| ~ spl25_7 ),
inference(superposition,[],[f3963,f5785]) ).
fof(f11204,plain,
( c_Finite__Set_Ocard(c_SetInterval_OatMost(sF6,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_union(sF19,sF11,sF0),sF0)
| ~ spl25_7 ),
inference(forward_subsumption_resolution,[],[f11191,f5126]) ).
fof(f11208,plain,
( c_Finite__Set_Ocard(sF23,sF0) = c_Finite__Set_Ocard(c_SetInterval_OatMost(sF6,tc_nat),tc_nat)
| ~ spl25_7 ),
inference(forward_demodulation,[],[f11204,f5811]) ).
fof(f11218,plain,
( sF24 = c_Finite__Set_Ocard(c_SetInterval_OatMost(sF6,tc_nat),tc_nat)
| ~ spl25_7 ),
inference(forward_demodulation,[],[f11208,f3616]) ).
fof(f11220,plain,
( ! [X0] :
( sF24 = c_Finite__Set_Ocard(c_insert(X0,sF5,sF0),sF0)
| c_in(X0,sF5,sF0) )
| ~ spl25_7
| ~ spl25_9 ),
inference(backward_demodulation,[],[f3971,f11218]) ).
fof(f11344,plain,
( sF24 = c_Finite__Set_Ocard(c_union(sF16,sF5,sF0),sF0)
| c_in(sF15,sF5,sF0)
| ~ spl25_7
| ~ spl25_9 ),
inference(superposition,[],[f11220,f5786]) ).
fof(f11361,plain,
( sF24 = c_Finite__Set_Ocard(c_union(sF16,sF5,sF0),sF0)
| ~ spl25_7
| ~ spl25_9 ),
inference(forward_subsumption_resolution,[],[f11344,f5135]) ).
fof(f11363,plain,
( c_Finite__Set_Ocard(sF21,sF0) = sF24
| ~ spl25_7
| ~ spl25_9 ),
inference(forward_demodulation,[],[f11361,f5835]) ).
fof(f11377,plain,
( sF22 = sF24
| ~ spl25_7
| ~ spl25_9 ),
inference(forward_demodulation,[],[f11363,f3612]) ).
fof(f11378,plain,
( $false
| ~ spl25_7
| ~ spl25_9 ),
inference(forward_subsumption_resolution,[],[f11377,f3617]) ).
fof(f11379,plain,
( ~ spl25_7
| ~ spl25_9 ),
inference(avatar_contradiction_clause,[],[f11378]) ).
cnf(s6,plain,
( spl25_7
| ~ spl25_8 ),
inference(sat_conversion,[],[f3968]) ).
cnf(s7,plain,
( spl25_9
| ~ spl25_10 ),
inference(sat_conversion,[],[f3976]) ).
cnf(s209,plain,
spl25_10,
inference(sat_conversion,[],[f11066]) ).
cnf(s212,plain,
spl25_8,
inference(sat_conversion,[],[f11180]) ).
cnf(s219,plain,
( ~ spl25_7
| ~ spl25_9 ),
inference(sat_conversion,[],[f11379]) ).
cnf(s233,plain,
spl25_9,
inference(rat,[],[s7,s209]) ).
cnf(s234,plain,
~ spl25_7,
inference(rat,[],[s219,s233]) ).
cnf(s235,plain,
$false,
inference(rat,[],[s6,s212,s234]) ).
fof(f11380,plain,
$false,
inference(avatar_sat_refutation,[],[s235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ062-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 22:36:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.12/2.40 % (1841968)Input is clausal, will run a generic CNF schedule.
% 10.12/2.40 % (1842007)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=433431244:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 10.12/2.40 % (1842008)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1249619979:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 10.12/2.40 % (1842010)lrs+10_1_sil=8000:sp=occurrence:random_seed=2718418113:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 10.12/2.40 % (1842012)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3118507014:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 10.12/2.40 % (1842011)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=330718546:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 10.12/2.40 % (1842009)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2097298207:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 10.12/2.40 % (1842013)dis-21_1_sil=8000:lcm=predicate:random_seed=1675710284:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 10.12/2.40 % (1842013)Instruction limit reached!
% 10.12/2.40 % (1842013)------------------------------
% 10.12/2.40 % (1842013)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.12/2.40 % (1842013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.12/2.40 % (1842013)CaDiCaL version: 2.1.3
% 10.12/2.40 % (1842013)Termination reason: Instruction limit
% 10.12/2.40 % (1842013)Termination phase: Saturation
% 10.12/2.40 % (1842013)Time elapsed: 0.063 s
% 10.12/2.40 % (1842013)Peak memory usage: 90 MB
% 10.12/2.40 % (1842013)Instructions burned: 118 (million)
% 10.12/2.40 % (1842011)Instruction limit reached!
% 10.12/2.40 % (1842011)------------------------------
% 10.12/2.40 % (1842011)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.12/2.40 % (1842011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.12/2.40 % (1842011)CaDiCaL version: 2.1.3
% 10.12/2.40 % (1842011)Termination reason: Instruction limit
% 10.12/2.40 % (1842011)Termination phase: Saturation
% 10.12/2.40 % (1842011)Time elapsed: 0.070 s
% 10.12/2.40 % (1842011)Peak memory usage: 90 MB
% 10.12/2.40 % (1842011)Instructions burned: 114 (million)
% 10.12/2.40 % (1842010)Instruction limit reached!
% 10.12/2.40 % (1842010)------------------------------
% 10.12/2.40 % (1842010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.12/2.40 % (1842010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.12/2.40 % (1842010)CaDiCaL version: 2.1.3
% 10.12/2.40 % (1842010)Termination reason: Instruction limit
% 10.12/2.40 % (1842010)Termination phase: Saturation
% 10.12/2.40 % (1842010)Time elapsed: 0.071 s
% 10.12/2.40 % (1842010)Peak memory usage: 91 MB
% 10.12/2.40 % (1842010)Instructions burned: 107 (million)
% 10.12/2.40 % (1842012)Instruction limit reached!
% 10.12/2.40 % (1842012)------------------------------
% 10.12/2.40 % (1842012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.12/2.40 % (1842012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.12/2.40 % (1842012)CaDiCaL version: 2.1.3
% 10.12/2.40 % (1842012)Termination reason: Instruction limit
% 10.12/2.40 % (1842012)Termination phase: Saturation
% 10.12/2.40 % (1842012)Time elapsed: 0.108 s
% 10.12/2.40 % (1842012)Peak memory usage: 91 MB
% 10.12/2.40 % (1842012)Instructions burned: 180 (million)
% 10.12/2.40 % (1842023)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1220120038:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 10.12/2.40 % (1842021)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2260503879:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 10.12/2.40 % (1842022)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3186011010:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 10.12/2.40 % (1842024)lrs+10_64_to=lpo:sil=8000:random_seed=3641083109:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 10.12/2.40 % (1842021)Instruction limit reached!
% 16.58/3.27 % (1842021)------------------------------
% 16.58/3.27 % (1842021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842021)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842021)Termination reason: Instruction limit
% 16.58/3.27 % (1842021)Termination phase: Saturation
% 16.58/3.27 % (1842021)Time elapsed: 0.088 s
% 16.58/3.27 % (1842021)Peak memory usage: 91 MB
% 16.58/3.27 % (1842021)Instructions burned: 143 (million)
% 16.58/3.27 % (1842022)Instruction limit reached!
% 16.58/3.27 % (1842022)------------------------------
% 16.58/3.27 % (1842022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842022)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842022)Termination reason: Instruction limit
% 16.58/3.27 % (1842022)Termination phase: Saturation
% 16.58/3.27 % (1842022)Time elapsed: 0.106 s
% 16.58/3.27 % (1842022)Peak memory usage: 92 MB
% 16.58/3.27 % (1842022)Instructions burned: 189 (million)
% 16.58/3.27 % (1842024)Instruction limit reached!
% 16.58/3.27 % (1842024)------------------------------
% 16.58/3.27 % (1842024)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842024)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842024)Termination reason: Instruction limit
% 16.58/3.27 % (1842024)Termination phase: Saturation
% 16.58/3.27 % (1842024)Time elapsed: 0.072 s
% 16.58/3.27 % (1842024)Peak memory usage: 91 MB
% 16.58/3.27 % (1842024)Instructions burned: 127 (million)
% 16.58/3.27 % (1842023)Instruction limit reached!
% 16.58/3.27 % (1842023)------------------------------
% 16.58/3.27 % (1842023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842023)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842023)Termination reason: Instruction limit
% 16.58/3.27 % (1842023)Termination phase: Saturation
% 16.58/3.27 % (1842023)Time elapsed: 0.128 s
% 16.58/3.27 % (1842023)Peak memory usage: 92 MB
% 16.58/3.27 % (1842023)Instructions burned: 219 (million)
% 16.58/3.27 % (1842029)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1768139155:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 16.58/3.27 % (1842030)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2074281378:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 16.58/3.27 % (1842031)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=401202008:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 16.58/3.27 % (1842032)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=3811858824:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2994 on theBenchmark for (2994ds/106Mi)
% 16.58/3.27 % (1842032)Instruction limit reached!
% 16.58/3.27 % (1842032)------------------------------
% 16.58/3.27 % (1842032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842032)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842032)Termination reason: Instruction limit
% 16.58/3.27 % (1842032)Termination phase: Saturation
% 16.58/3.27 % (1842032)Time elapsed: 0.060 s
% 16.58/3.27 % (1842032)Peak memory usage: 90 MB
% 16.58/3.27 % (1842032)Instructions burned: 107 (million)
% 16.58/3.27 % (1842030)Instruction limit reached!
% 16.58/3.27 % (1842030)------------------------------
% 16.58/3.27 % (1842030)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842030)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842030)Termination reason: Instruction limit
% 16.58/3.27 % (1842030)Termination phase: Saturation
% 16.58/3.27 % (1842030)Time elapsed: 0.083 s
% 16.58/3.27 % (1842030)Peak memory usage: 92 MB
% 16.58/3.27 % (1842030)Instructions burned: 158 (million)
% 16.58/3.27 % (1842029)Instruction limit reached!
% 16.58/3.27 % (1842029)------------------------------
% 16.58/3.27 % (1842029)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842029)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842029)Termination reason: Instruction limit
% 16.58/3.27 % (1842029)Termination phase: Saturation
% 16.58/3.27 % (1842029)Time elapsed: 0.111 s
% 16.58/3.27 % (1842029)Peak memory usage: 92 MB
% 16.58/3.27 % (1842029)Instructions burned: 195 (million)
% 16.58/3.27 % (1842037)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=3493508719:i=107_2992 on theBenchmark for (2992ds/107Mi)
% 16.58/3.27 % (1842038)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=3807960134:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2992 on theBenchmark for (2992ds/242Mi)
% 16.58/3.27 % (1842039)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=1783631464:cond=fast:i=5208:av=off_2992 on theBenchmark for (2992ds/5208Mi)
% 16.58/3.27 % (1842037)Instruction limit reached!
% 16.58/3.27 % (1842037)------------------------------
% 16.58/3.27 % (1842037)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842037)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842037)Termination reason: Instruction limit
% 16.58/3.27 % (1842037)Termination phase: Saturation
% 16.58/3.27 % (1842037)Time elapsed: 0.065 s
% 16.58/3.27 % (1842037)Peak memory usage: 92 MB
% 16.58/3.27 % (1842037)Instructions burned: 107 (million)
% 16.58/3.27 % (1842038)Instruction limit reached!
% 16.58/3.27 % (1842038)------------------------------
% 16.58/3.27 % (1842038)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842038)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842038)Termination reason: Instruction limit
% 16.58/3.27 % (1842038)Termination phase: Saturation
% 16.58/3.27 % (1842038)Time elapsed: 0.131 s
% 16.58/3.27 % (1842038)Peak memory usage: 91 MB
% 16.58/3.27 % (1842038)Instructions burned: 243 (million)
% 16.58/3.27 % (1842043)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=3587037091:i=134:sd=2:doe=on:ss=axioms:sgt=14_2990 on theBenchmark for (2990ds/134Mi)
% 16.58/3.27 % (1842044)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=4206928017:i=499:bd=all_2989 on theBenchmark for (2989ds/499Mi)
% 16.58/3.27 % (1842043)Instruction limit reached!
% 16.58/3.27 % (1842043)------------------------------
% 16.58/3.27 % (1842043)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842043)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842043)Termination reason: Instruction limit
% 16.58/3.27 % (1842043)Termination phase: Saturation
% 16.58/3.27 % (1842043)Time elapsed: 0.089 s
% 16.58/3.27 % (1842043)Peak memory usage: 91 MB
% 16.58/3.27 % (1842043)Instructions burned: 135 (million)
% 16.58/3.27 % (1842047)lrs+10_64_to=lpo:sil=8000:prc=on:sp=reverse_frequency:nwc=5:alpa=false:flr=on:random_seed=159068388:i=191:fgj=on:bd=all_2988 on theBenchmark for (2988ds/191Mi)
% 16.58/3.27 % (1842044)Instruction limit reached!
% 16.58/3.27 % (1842044)------------------------------
% 16.58/3.27 % (1842044)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842044)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842044)Termination reason: Instruction limit
% 16.58/3.27 % (1842044)Termination phase: Saturation
% 16.58/3.27 % (1842044)Time elapsed: 0.279 s
% 16.58/3.27 % (1842044)Peak memory usage: 97 MB
% 16.58/3.27 % (1842044)Instructions burned: 499 (million)
% 16.58/3.27 % (1842047)Instruction limit reached!
% 16.58/3.27 % (1842047)------------------------------
% 16.58/3.27 % (1842047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842047)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842047)Termination reason: Instruction limit
% 16.58/3.27 % (1842047)Termination phase: Saturation
% 16.58/3.27 % (1842047)Time elapsed: 0.112 s
% 16.58/3.27 % (1842047)Peak memory usage: 92 MB
% 16.58/3.27 % (1842047)Instructions burned: 192 (million)
% 16.58/3.27 % (1842049)lrs-11_32_anc=all:sil=8000:spb=goal_then_units:sac=on:random_seed=1039208213:i=264:kws=precedence:fsr=off_2985 on theBenchmark for (2985ds/264Mi)
% 16.58/3.27 % (1842050)lrs-22_64_to=lpo:sil=8000:sp=const_frequency:urr=ec_only:nwc=4:flr=on:random_seed=1979880835:cond=on:i=156:bs=on:gtg=exists_all:er=known_2985 on theBenchmark for (2985ds/156Mi)
% 16.58/3.27 % (1842050)Instruction limit reached!
% 16.58/3.27 % (1842050)------------------------------
% 16.58/3.27 % (1842050)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842050)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842050)Termination reason: Instruction limit
% 16.58/3.27 % (1842050)Termination phase: Saturation
% 16.58/3.27 % (1842050)Time elapsed: 0.083 s
% 16.58/3.27 % (1842050)Peak memory usage: 91 MB
% 16.58/3.27 % (1842050)Instructions burned: 157 (million)
% 16.58/3.27 % (1842049)Instruction limit reached!
% 16.58/3.27 % (1842049)------------------------------
% 16.58/3.27 % (1842049)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842049)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842049)Termination reason: Instruction limit
% 16.58/3.27 % (1842049)Termination phase: Saturation
% 16.58/3.27 % (1842049)Time elapsed: 0.127 s
% 16.58/3.27 % (1842049)Peak memory usage: 93 MB
% 16.58/3.27 % (1842049)Instructions burned: 265 (million)
% 16.58/3.27 % (1842053)lrs-1010_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:sp=reverse_frequency:spb=units:lcm=predicate:urr=on:s2agt=8:updr=off:random_seed=3880326030:i=3256:kws=precedence:bd=preordered:av=off_2983 on theBenchmark for (2983ds/3256Mi)
% 16.58/3.27 % (1842054)dis+1003_128_sil=8000:tgt=full:fd=off:random_seed=468888742:i=537:av=off:ss=included_2983 on theBenchmark for (2983ds/537Mi)
% 16.58/3.27 % (1842054)Instruction limit reached!
% 16.58/3.27 % (1842054)------------------------------
% 16.58/3.27 % (1842054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842054)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842054)Termination reason: Instruction limit
% 16.58/3.27 % (1842054)Termination phase: Saturation
% 16.58/3.27 % (1842054)Time elapsed: 0.303 s
% 16.58/3.27 % (1842054)Peak memory usage: 92 MB
% 16.58/3.27 % (1842054)Instructions burned: 537 (million)
% 16.58/3.27 % (1842009)First to succeed.
% 16.58/3.27 % (1842009)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1841968"
% 16.58/3.27 % (1842057)ott+1010_32_to=lpo:sil=8000:urr=on:nwc=4:random_seed=446189875:i=180:bd=preordered:av=off_2979 on theBenchmark for (2979ds/180Mi)
% 16.58/3.27 % (1842057)Instruction limit reached!
% 16.58/3.27 % (1842057)------------------------------
% 16.58/3.27 % (1842057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.58/3.27 % (1842057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.58/3.27 % (1842057)CaDiCaL version: 2.1.3
% 16.58/3.27 % (1842057)Termination reason: Instruction limit
% 16.58/3.27 % (1842057)Termination phase: Saturation
% 16.58/3.27 % (1842057)Time elapsed: 0.103 s
% 16.58/3.27 % (1842057)Peak memory usage: 91 MB
% 16.58/3.27 % (1842057)Instructions burned: 180 (million)
% 16.58/3.27 % (1842009)Refutation found. Thanks to Tanya!
% 16.58/3.27 % SZS status Unsatisfiable for theBenchmark
% 16.58/3.27 % SZS output start Proof for theBenchmark
% See solution above
% 17.18/3.46 % (1842009)------------------------------
% 17.18/3.46 % (1842009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 17.18/3.46 % (1842009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 17.18/3.46 % (1842009)CaDiCaL version: 2.1.3
% 17.18/3.46 % (1842009)Termination reason: Refutation
% 17.18/3.46 % (1842009)Time elapsed: 1.918 s
% 17.18/3.46 % (1842009)Peak memory usage: 156 MB
% 17.18/3.46 % (1842009)Instructions burned: 3017 (million)
% 17.18/3.46 % (1842009)------------------------------
% 17.18/3.46 % (1842009)------------------------------
% 17.18/3.46 % (1841968)Success in time 2.411 s
% 17.18/3.46 % Vampire exiting
%------------------------------------------------------------------------------