%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV825-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 03:24:18 PM UTC 2026
% Result : Unsatisfiable 16.45s 3.45s
% Output : CNFRefutation 16.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 45 ( 21 unt; 5 def)
% Number of atoms : 123 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 87 ( 39 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-6 aty)
% Number of variables : 117 ( 0 sgn 117 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
fof(f127,axiom,
! [X0,X1] : c_Collect(X0,X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
fof(f532,axiom,
! [X0,X1] : c_Collect(c_fequal(X0,X1),X1) = hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
fof(f533,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))) = c_Collect(c_fequal(X0,X1),X1),
inference(reorient_equations,[],[f532]) ).
fof(f566,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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))),t_a)
| ~ hBOOL(hAPP(hAPP(X6,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X1,X3,X2)))
| hBOOL(hAPP(hAPP(X4,X5),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X0,X1,X3,X2,X6,X4)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).
fof(f567,axiom,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X1,X3,X2)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).
fof(f568,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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))),t_a)
| ~ hBOOL(hAPP(hAPP(X3,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X0,X1,X3,X2,X4,X5)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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))),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).
fof(f598,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f599,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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))),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f600,negated_conjecture,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_P,X0),X2))
| hBOOL(hAPP(hAPP(v_P_H,v_Z(X0,X2,X1)),X2))
| hBOOL(hAPP(hAPP(v_Q,X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f601,negated_conjecture,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_P,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_Z(X0,X2,X1)),X1))
| hBOOL(hAPP(hAPP(v_Q,X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
tcf(c_684,plain,
! [X0: $i,X1: $i] : c_Collect(X0,X1) = X0,
inference(cnf_transformation,[],[f127]) ).
tcf(c_989,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = c_Collect(c_fequal(X1,X0),X0),
inference(cnf_transformation,[],[f533]) ).
tcf(c_1010,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( hBOOL(hAPP(hAPP(X3,X4),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X0,X5,X6,X2,X1,X3)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X2,X6,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X1,X4),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X5,X6,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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))),t_a) ),
inference(cnf_transformation,[],[f566]) ).
tcf(c_1011,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( hBOOL(hAPP(hAPP(X1,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,X1,X3,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X1,X3,X2)))
| c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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))),t_a) ),
inference(cnf_transformation,[],[f567]) ).
tcf(c_1012,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(X5,X2,X4,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)
| ~ hBOOL(hAPP(hAPP(X4,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,X5,X4,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X0,X5,X4,X2,X1,X3)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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))),t_a) ),
inference(cnf_transformation,[],[f568]) ).
tcf(c_1038,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(cnf_transformation,[],[f598]) ).
tcf(c_1039,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),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))),t_a),
inference(cnf_transformation,[],[f599]) ).
tcf(c_1040,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_P_H,v_Z(X0,X1,X2)),X1))
| ~ hBOOL(hAPP(hAPP(v_P,X0),X1)) ),
inference(cnf_transformation,[],[f600]) ).
tcf(c_1041,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_Z(X0,X1,X2)),X2)) ),
inference(cnf_transformation,[],[f601]) ).
tcf(c_3254,plain,
! [X0: $i,X1: $i] : hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))) = c_fequal(X1,X0),
inference(demodulation,[status(thm)],[c_989,c_684]) ).
tcf(c_3497,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(demodulation,[status(thm)],[c_1038,c_3254]) ).
tcf(c_3619,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a),
inference(demodulation,[status(thm)],[c_1039,c_3254]) ).
tcf(c_4177,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(X0,X3,X2,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X0,X2,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X0,X2,X3))) ),
inference(demodulation,[status(thm)],[c_1011,c_3254]) ).
tcf(c_4397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X0,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(X4,X3,X5,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| ~ hBOOL(hAPP(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X2,X0,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X2,X0,X3,X4,X5))) ),
inference(demodulation,[status(thm)],[c_1012,c_3254]) ).
tcf(c_4425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(X5,X2,X6,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a)
| hBOOL(hAPP(hAPP(X3,X4),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X0,X5,X6,X2,X1,X3)))
| ~ hBOOL(hAPP(hAPP(X1,X4),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X5,X6,X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,X3,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) ),
inference(demodulation,[status(thm)],[c_1010,c_3254]) ).
tcf(c_12592,definition,
iPr_def_10 = c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_12593,definition,
iPr_def_11 = tc_Hoare__Mirabelle_Otriple(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_12594,definition,
iPr_def_12 = c_fequal(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_12595,definition,
iPr_def_13 = c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_12596,definition,
iPr_def_14 = c_fequal(iPr_def_13,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_12597,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,iPr_def_12,t_a),
inference(demodulation,[status(thm)],[c_3619,c_12593,c_12592,c_12594]) ).
tcf(c_12598,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,iPr_def_14,t_a),
inference(demodulation,[status(thm)],[c_3497,c_12595,c_12596]) ).
tcf(c_12599,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(v_Q,X0),X2))
| ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| ~ hBOOL(hAPP(hAPP(v_Q_H,v_Z(X0,X1,X2)),X2)) ),
inference(demodulation,[status(thm)],[c_1041]) ).
tcf(c_12600,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( hBOOL(hAPP(hAPP(v_Q,X0),X2))
| hBOOL(hAPP(hAPP(v_P_H,v_Z(X0,X1,X2)),X1))
| ~ hBOOL(hAPP(hAPP(v_P,X0),X1)) ),
inference(demodulation,[status(thm)],[c_1040]) ).
tcf(c_16361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(X0,X3,X2,t_a),iPr_def_11),t_a)
| hBOOL(hAPP(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X0,X2,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X0,X2,X3))) ),
inference(light_normalisation,[status(thm)],[c_4177,c_12593]) ).
tcf(c_16462,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(X2,X3,X0,t_a),iPr_def_11),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(X4,X3,X5,t_a),iPr_def_11),t_a)
| ~ hBOOL(hAPP(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X1,X2,X0,X3)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X2,X0,X3,X4,X5))) ),
inference(light_normalisation,[status(thm)],[c_4397,c_12593]) ).
tcf(c_16527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X2,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(X3,X5,X4,t_a),iPr_def_11),t_a)
| hBOOL(hAPP(hAPP(X6,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X2,X3,X4,X5,X0,X6)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X2,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(X0,X5,X6,t_a),iPr_def_11),t_a)
| ~ hBOOL(hAPP(hAPP(X0,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X2,X3,X4,X5))) ),
inference(light_normalisation,[status(thm)],[c_4425,c_12593]) ).
tcf(c_16543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(X4,X6,X5,t_a),iPr_def_11),t_a)
| hBOOL(hAPP(hAPP(v_Q,X1),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X3,X4,X5,X6,X0,v_Q_H)))
| ~ hBOOL(hAPP(hAPP(v_P,X1),X2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(X0,X6,v_Q_H,t_a),iPr_def_11),t_a)
| ~ hBOOL(hAPP(hAPP(X0,v_Z(X1,X2,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X3,X4,X5,X6,X0,v_Q_H))),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X3,X4,X5,X6))) ),
inference(superposition,[status(thm)],[c_16527,c_12599]) ).
tcf(c_16627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X1,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(X2,X4,X3,t_a),iPr_def_11),t_a)
| hBOOL(hAPP(hAPP(v_Q,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(X1,X2,X3,X4,v_P_H,v_Q_H)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,X4,v_Q_H,t_a),iPr_def_11),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,X0),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X1,X2,X3,X4))) ),
inference(superposition,[status(thm)],[c_12600,c_16543]) ).
tcf(c_16674,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(X1,X2,v_Q,t_a),iPr_def_11),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,X2,v_Q_H,t_a),iPr_def_11),t_a)
| ~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(X0,X1,v_Q,X2)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(X0,X1,v_Q,X2))) ),
inference(superposition,[status(thm)],[c_16627,c_16462]) ).
tcf(c_16685,plain,
! [X0: $i,X1: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(v_P,X1,v_Q,t_a),iPr_def_11),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,X1,v_Q_H,t_a),iPr_def_11),t_a) ),
inference(superposition,[status(thm)],[c_16361,c_16674]) ).
tcf(c_17123,plain,
! [X0: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a),iPr_def_11),t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,c_fequal(iPr_def_13,iPr_def_11),t_a) ),
inference(superposition,[status(thm)],[c_12595,c_16685]) ).
tcf(c_17124,plain,
! [X0: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(X0,iPr_def_12,t_a)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X0,iPr_def_14,t_a) ),
inference(light_normalisation,[status(thm)],[c_17123,c_12592,c_12594,c_12596]) ).
tcf(c_17238,plain,
c_Hoare__Mirabelle_Ohoare__derivs(v_G,iPr_def_12,t_a),
inference(superposition,[status(thm)],[c_12598,c_17124]) ).
tcf(c_17239,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_17238,c_12597]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV825-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.44 % Computer : n010.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Thu Sep 24 21:07:29 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.22/0.51 Running first-order theorem proving
% 0.22/0.51 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.52
% 0.22/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.22/0.52
% 0.22/0.52 % Detected problem language: tptp
% 0.22/0.54 % Proving...
% 16.45/3.45 % SZS status Started for theBenchmark.p
% 16.45/3.45 % SZS status Unsatisfiable for theBenchmark.p
% 16.45/3.45
% 16.45/3.45 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 16.45/3.45
% 16.45/3.45 % ------ iProver source info
% 16.45/3.45
% 16.45/3.45 % git: date: 2026-07-19 20:42:38 +0200
% 16.45/3.45 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 16.45/3.45 % git: non_committed_changes: false
% 16.45/3.45
% 16.45/3.45 % ------ Parsing...% successful
% 16.45/3.45
% 16.45/3.45
% 16.45/3.45 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 16.45/3.45
% 16.45/3.45 % ------ Preprocessing... sup_sim: 67 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 16.45/3.45
% 16.45/3.45 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 16.45/3.45
% 16.45/3.45 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 16.45/3.45 % ------ Proving...
% 16.45/3.45 % ------ Problem Properties
% 16.45/3.45
% 16.45/3.45 %
% 16.45/3.45 % clauses 398
% 16.45/3.45 % conjectures 2
% 16.45/3.45 % EPR 21
% 16.45/3.45 % Horn 368
% 16.45/3.45 % unary 131
% 16.45/3.45 % binary 171
% 16.45/3.45 % lits 783
% 16.45/3.45 % lits eq 247
% 16.45/3.45 % fd_pure 0
% 16.45/3.45 % fd_pseudo 0
% 16.45/3.45 % fd_cond 0
% 16.45/3.45 % fd_pseudo_cond 38
% 16.45/3.45 % AC symbols 0
% 16.45/3.45
% 16.45/3.45 % ------ Schedule dynamic 5 is on
% 16.45/3.45
% 16.45/3.45 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 16.45/3.45
% 16.45/3.45
% 16.45/3.45 % ------
% 16.45/3.45 % Current options:
% 16.45/3.45 % ------
% 16.45/3.45
% 16.45/3.45
% 16.45/3.45 %
% 16.45/3.45
% 16.45/3.45 % ------ Proving...
% 16.45/3.45 %
% 16.45/3.45
% 16.45/3.45 % SZS status Unsatisfiable for theBenchmark.p
% 16.45/3.45
% 16.45/3.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.45/3.45
% 16.45/3.45
%------------------------------------------------------------------------------