%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV826-1 : 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 : n006.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 18.07s 12.14s
% Output : CNFRefutation 18.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 5 unt; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 43 ( 19 ~; 24 |; 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 : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-6 aty)
% Number of variables : 39 ( 0 sgn 39 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f513,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(f514,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(f515,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(f547,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,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(f548,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(f549,negated_conjecture,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_P,X0),X1))
| hBOOL(hAPP(hAPP(v_P_H,X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tcf(c_939,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,[],[f513]) ).
tcf(c_940,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,[],[f514]) ).
tcf(c_941,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,[],[f515]) ).
tcf(c_969,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,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a),
inference(cnf_transformation,[],[f547]) ).
tcf(c_970,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,[],[f548]) ).
tcf(c_971,negated_conjecture,
! [X0: $i,X1: $i] :
( hBOOL(hAPP(hAPP(v_P_H,X0),X1))
| ~ hBOOL(hAPP(hAPP(v_P,X0),X1)) ),
inference(cnf_transformation,[],[f549]) ).
tcf(c_2529,plain,
( hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,v_P,v_Q,v_c)))
| 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(instantiation,[status(thm)],[c_940]) ).
tcf(c_3340,plain,
( hBOOL(hAPP(hAPP(v_P_H,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,v_P,v_Q,v_c)))
| ~ hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,v_P,v_Q,v_c))) ),
inference(instantiation,[status(thm)],[c_971]) ).
tcf(c_7666,plain,
! [X0: $i] :
( hBOOL(hAPP(hAPP(X0,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_G,v_P,v_Q,v_c,v_P_H,X0)))
| 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)
| ~ hBOOL(hAPP(hAPP(v_P_H,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,v_P,v_Q,v_c)))
| ~ 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,X0,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(instantiation,[status(thm)],[c_939]) ).
tcf(c_14268,plain,
( hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_G,v_P,v_Q,v_c,v_P_H,v_Q)))
| 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)
| ~ hBOOL(hAPP(hAPP(v_P_H,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2(v_G,v_P,v_Q,v_c)))
| ~ 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,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(instantiation,[status(thm)],[c_7666]) ).
tcf(c_14269,plain,
( 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)
| ~ hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1(v_G,v_P,v_Q,v_c)),v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3(v_G,v_P,v_Q,v_c,v_P_H,v_Q)))
| ~ 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,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) ),
inference(instantiation,[status(thm)],[c_941]) ).
tcf(c_14270,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_14269,c_14268,c_3340,c_2529,c_970,c_969]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV826-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.45 % Computer : n006.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Thu Sep 24 21:06:56 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 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
% 0.23/0.52
% 0.23/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.52
% 0.23/0.52 % Detected problem language: tptp
% 0.23/0.54 % Proving...
% 18.07/12.14 % SZS status Started for theBenchmark.p
% 18.07/12.14 % SZS status Unsatisfiable for theBenchmark.p
% 18.07/12.14
% 18.07/12.14 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.07/12.14
% 18.07/12.14 % ------ iProver source info
% 18.07/12.14
% 18.07/12.14 % git: date: 2026-07-19 20:42:38 +0200
% 18.07/12.14 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.07/12.14 % git: non_committed_changes: false
% 18.07/12.14
% 18.07/12.14 % ------ Parsing...% successful
% 18.07/12.14
% 18.07/12.14
% 18.07/12.14 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.07/12.14
% 18.07/12.14 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 1 0s sf_e %
% 18.07/12.14
% 18.07/12.14 % ------ Preprocessing...%
% 18.07/12.14
% 18.07/12.14 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 18.07/12.14 % ------ Proving...
% 18.07/12.14 % ------ Problem Properties
% 18.07/12.14
% 18.07/12.14 %
% 18.07/12.14 % clauses 391
% 18.07/12.14 % conjectures 3
% 18.07/12.14 % EPR 19
% 18.07/12.14 % Horn 363
% 18.07/12.14 % unary 124
% 18.07/12.14 % binary 169
% 18.07/12.14 % lits 779
% 18.07/12.14 % lits eq 238
% 18.07/12.14 % fd_pure 0
% 18.07/12.14 % fd_pseudo 0
% 18.07/12.14 % fd_cond 0
% 18.07/12.14 % fd_pseudo_cond 35
% 18.07/12.14 % AC symbols 0
% 18.07/12.14
% 18.07/12.14 % ------ Input Options Time Limit: Unbounded
% 18.07/12.14
% 18.07/12.14
% 18.07/12.14 % ------
% 18.07/12.14 % Current options:
% 18.07/12.14 % ------
% 18.07/12.14
% 18.07/12.14
% 18.07/12.14 %
% 18.07/12.14
% 18.07/12.14 % ------ Proving...
% 18.07/12.14 %
% 18.07/12.14
% 18.07/12.14 % SZS status Unsatisfiable for theBenchmark.p
% 18.07/12.14
% 18.07/12.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.07/12.14
% 18.07/12.14
%------------------------------------------------------------------------------