%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV831-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 01:19:36 PM UTC 2026
% Result : Unsatisfiable 2.92s 1.05s
% Output : Refutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 14 unt; 0 def)
% Number of atoms : 92 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 97 ( 44 ~; 53 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-6 aty)
% Number of variables : 125 ( 125 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f87,axiom,
! [X0,X1] : c_Collect(X0,X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
fof(f407,axiom,
! [X0,X1] : c_Collect(hAPP(c_fequal(X0),X1),X0) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
fof(f452,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X0,X1,X3,X2,X6,X4)))
| ~ hBOOL(hAPP(hAPP(X6,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X0,X1,X3,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X4,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_1) ).
fof(f457,axiom,
! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X0,X1,X3,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_0) ).
fof(f461,axiom,
! [X2,X3,X0,X1,X4,X5] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X3,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X0,X1,X3,X2,X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X4,X2,X5,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_2) ).
fof(f465,axiom,
! [X0,X1] : c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv_0) ).
fof(f466,plain,
! [X0,X1] : c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) = c_Collect(hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1),X0),
inference(reorient_equations,[],[f465]) ).
fof(f496,axiom,
! [X2,X3,X0,X1] : hAPP(c_COMBK(X0,X1,X2),X3) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f500,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f501,negated_conjecture,
! [X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_COMBC(c_fequal(tc_Com_Ostate),tc_Com_Ostate,tc_Com_Ostate,tc_bool),X0),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,c_COMBK(hAPP(v_Q,X1),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f534,axiom,
! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f570,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Collect(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(superposition,[],[f500,f407]) ).
fof(f657,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),t_a),
inference(superposition,[],[f570,f87]) ).
fof(f665,plain,
! [X0,X1] : hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = c_Set_Oinsert(X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),
inference(forward_demodulation,[],[f466,f87]) ).
fof(f666,plain,
! [X0,X1] : hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = c_Collect(hAPP(c_fequal(X0),X1),X0),
inference(forward_demodulation,[],[f665,f407]) ).
fof(f667,plain,
! [X0,X1] : hAPP(c_COMBC(c_fequal(X0),X0,X0,tc_bool),X1) = hAPP(c_fequal(X0),X1),
inference(forward_demodulation,[],[f666,f87]) ).
fof(f669,plain,
! [X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_fequal(tc_Com_Ostate),X0),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,c_COMBK(hAPP(v_Q,X1),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,X1),X0)) ),
inference(superposition,[],[f501,f667]) ).
fof(f672,plain,
! [X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Collect(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_fequal(tc_Com_Ostate),X0),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,c_COMBK(hAPP(v_Q,X1),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,X1),X0)) ),
inference(forward_demodulation,[],[f669,f407]) ).
fof(f674,plain,
! [X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_fequal(tc_Com_Ostate),X0),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,c_COMBK(hAPP(v_Q,X1),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,X1),X0)) ),
inference(forward_demodulation,[],[f672,f87]) ).
fof(f841,plain,
! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Collect(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X0,X1,X3,X2))) ),
inference(forward_demodulation,[],[f457,f407]) ).
fof(f842,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X0,X1,X3,X2)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),t_a) ),
inference(forward_demodulation,[],[f841,f87]) ).
fof(f963,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Collect(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X3,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X0,X1,X3,X2,X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X4,X2,X5,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(forward_demodulation,[],[f461,f407]) ).
fof(f964,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X3,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X0,X1,X3,X2,X4,X5)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X4,X2,X5,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(forward_demodulation,[],[f963,f87]) ).
fof(f965,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Collect(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X4,X2,X5,t_a)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X3,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X0,X1,X3,X2,X4,X5))) ),
inference(forward_demodulation,[],[f964,f407]) ).
fof(f966,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(X3,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X0,X1,X3,X2,X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X4,X2,X5,t_a)),t_a) ),
inference(forward_demodulation,[],[f965,f87]) ).
fof(f1006,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Collect(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X0,X1,X3,X2,X6,X4)))
| ~ hBOOL(hAPP(hAPP(X6,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X0,X1,X3,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X4,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(forward_demodulation,[],[f452,f407]) ).
fof(f1007,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X0,X1,X3,X2,X6,X4)))
| ~ hBOOL(hAPP(hAPP(X6,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X0,X1,X3,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X4,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(forward_demodulation,[],[f1006,f87]) ).
fof(f1008,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_Collect(hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X4,t_a)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X0,X1,X3,X2,X6,X4)))
| ~ hBOOL(hAPP(hAPP(X6,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X0,X1,X3,X2))) ),
inference(forward_demodulation,[],[f1007,f407]) ).
fof(f1009,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X6,X2,X4,t_a)),t_a)
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a)),t_a)
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(X0,X1,X3,X2,X6,X4)))
| ~ hBOOL(hAPP(hAPP(X6,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(X0,X1,X3,X2))) ),
inference(forward_demodulation,[],[f1008,f87]) ).
fof(f1010,plain,
! [X2,X3,X0,X1,X4] :
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,v_c,X1,t_a)),t_a)
| hBOOL(hAPP(hAPP(c_COMBK(hAPP(v_Q,X2),tc_fun(tc_Com_Ostate,tc_bool),t_a),X3),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,X0,X1,v_c,c_COMBK(hAPP(c_fequal(tc_Com_Ostate),X4),tc_fun(tc_Com_Ostate,tc_bool),t_a),c_COMBK(hAPP(v_Q,X2),tc_fun(tc_Com_Ostate,tc_bool),t_a))))
| ~ hBOOL(hAPP(hAPP(c_COMBK(hAPP(c_fequal(tc_Com_Ostate),X4),tc_fun(tc_Com_Ostate,tc_bool),t_a),X3),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,X0,X1,v_c)))
| ~ hBOOL(hAPP(hAPP(v_P,X2),X4)) ),
inference(resolution,[],[f1009,f674]) ).
fof(f1019,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(v_Q,X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,X0,X1,v_c,c_COMBK(hAPP(c_fequal(tc_Com_Ostate),X4),tc_fun(tc_Com_Ostate,tc_bool),t_a),c_COMBK(hAPP(v_Q,X2),tc_fun(tc_Com_Ostate,tc_bool),t_a))))
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,v_c,X1,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(c_COMBK(hAPP(c_fequal(tc_Com_Ostate),X4),tc_fun(tc_Com_Ostate,tc_bool),t_a),X3),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,X0,X1,v_c)))
| ~ hBOOL(hAPP(hAPP(v_P,X2),X4)) ),
inference(forward_demodulation,[],[f1010,f496]) ).
fof(f1022,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(hAPP(v_Q,X2),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3(v_G,X0,X1,v_c,c_COMBK(hAPP(c_fequal(tc_Com_Ostate),X4),tc_fun(tc_Com_Ostate,tc_bool),t_a),c_COMBK(hAPP(v_Q,X2),tc_fun(tc_Com_Ostate,tc_bool),t_a))))
| ~ hBOOL(hAPP(hAPP(c_fequal(tc_Com_Ostate),X4),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,X0,X1,v_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X0,v_c,X1,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,X2),X4)) ),
inference(forward_demodulation,[],[f1019,f496]) ).
fof(f1023,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_fequal(tc_Com_Ostate),X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,X1,v_Q,v_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,v_c,v_Q,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_G,X1,v_Q,v_c)),X0))
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,v_c,v_Q,t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_fequal(tc_Com_Ostate),X0),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,c_COMBK(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_G,X1,v_Q,v_c)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),t_a) ),
inference(resolution,[],[f1022,f966]) ).
fof(f1024,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_fequal(tc_Com_Ostate),X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,X1,v_Q,v_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,v_c,v_Q,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_G,X1,v_Q,v_c)),X0))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(hAPP(c_fequal(tc_Com_Ostate),X0),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,c_COMBK(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_G,X1,v_Q,v_c)),tc_fun(tc_Com_Ostate,tc_bool),t_a),t_a)),t_a) ),
inference(duplicate_literal_removal,[],[f1023]) ).
fof(f1025,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1(v_G,X1,v_Q,v_c)),X0))
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X1,v_c,v_Q,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(c_fequal(tc_Com_Ostate),X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,X1,v_Q,v_c))) ),
inference(forward_subsumption_resolution,[],[f1024,f674]) ).
fof(f1030,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(c_fequal(tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c)))
| c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),t_a) ),
inference(resolution,[],[f1025,f842]) ).
fof(f1031,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(c_fequal(tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c))) ),
inference(duplicate_literal_removal,[],[f1030]) ).
fof(f1032,plain,
~ hBOOL(hAPP(hAPP(c_fequal(tc_Com_Ostate),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2(v_G,v_P,v_Q,v_c))),
inference(forward_subsumption_resolution,[],[f1031,f657]) ).
fof(f1033,plain,
$false,
inference(forward_subsumption_resolution,[],[f1032,f534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV831-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 12:35:06 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.92/1.05 % (3515107)Input is clausal, will run a generic CNF schedule.
% 2.92/1.05 % (3515117)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=45561349:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.92/1.05 % (3515118)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2010922269:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.92/1.05 % (3515116)lrs+10_1_sil=8000:sp=occurrence:random_seed=72305852:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.92/1.05 % (3515114)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3346047069:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.92/1.05 % (3515113)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=932388034:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.92/1.05 % (3515115)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4167112520:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.92/1.05 % (3515119)dis-21_1_sil=8000:lcm=predicate:random_seed=699569033: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)
% 2.92/1.05 % (3515117)Instruction limit reached!
% 2.92/1.05 % (3515117)------------------------------
% 2.92/1.05 % (3515117)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.05 % (3515117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.05 % (3515117)CaDiCaL version: 2.1.3
% 2.92/1.05 % (3515117)Termination reason: Instruction limit
% 2.92/1.05 % (3515117)Termination phase: Saturation
% 2.92/1.05 % (3515117)Time elapsed: 0.044 s
% 2.92/1.05 % (3515117)Peak memory usage: 89 MB
% 2.92/1.05 % (3515117)Instructions burned: 117 (million)
% 2.92/1.05 % (3515118)First to succeed.
% 2.92/1.05 % (3515118)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3515107"
% 2.92/1.05 % (3515119)Instruction limit reached!
% 2.92/1.05 % (3515119)------------------------------
% 2.92/1.05 % (3515119)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.05 % (3515119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.05 % (3515119)CaDiCaL version: 2.1.3
% 2.92/1.05 % (3515119)Termination reason: Instruction limit
% 2.92/1.05 % (3515119)Termination phase: Saturation
% 2.92/1.05 % (3515119)Time elapsed: 0.060 s
% 2.92/1.05 % (3515119)Peak memory usage: 88 MB
% 2.92/1.05 % (3515119)Instructions burned: 117 (million)
% 2.92/1.05 % (3515116)Instruction limit reached!
% 2.92/1.05 % (3515116)------------------------------
% 2.92/1.05 % (3515116)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.92/1.05 % (3515116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.92/1.05 % (3515116)CaDiCaL version: 2.1.3
% 2.92/1.05 % (3515116)Termination reason: Instruction limit
% 2.92/1.05 % (3515116)Termination phase: Saturation
% 2.92/1.05 % (3515116)Time elapsed: 0.070 s
% 2.92/1.05 % (3515116)Peak memory usage: 89 MB
% 2.92/1.05 % (3515116)Instructions burned: 107 (million)
% 2.92/1.05 % (3515127)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=850494194:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 2.92/1.05 % (3515129)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3183484251:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 2.92/1.05 % (3515128)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3610384652: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)
% 2.92/1.05 % (3515118)Refutation found. Thanks to Tanya!
% 2.92/1.05 % SZS status Unsatisfiable for theBenchmark
% 2.92/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 3.23/1.24 % (3515118)------------------------------
% 3.23/1.24 % (3515118)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.23/1.24 % (3515118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/1.24 % (3515118)CaDiCaL version: 2.1.3
% 3.23/1.24 % (3515118)Termination reason: Refutation
% 3.23/1.24 % (3515118)Time elapsed: 0.049 s
% 3.23/1.24 % (3515118)Peak memory usage: 89 MB
% 3.23/1.24 % (3515118)Instructions burned: 80 (million)
% 3.23/1.24 % (3515118)------------------------------
% 3.23/1.24 % (3515118)------------------------------
% 3.23/1.24 % (3515107)Success in time 0.376 s
% 3.23/1.24 % Vampire exiting
%------------------------------------------------------------------------------