%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV885-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n020.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 03:24:24 PM UTC 2026
% Result : Unsatisfiable 10.78s 7.76s
% Output : CNFRefutation 10.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 38 ( 28 unt; 0 def)
% Number of atoms : 54 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 17 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 44 ( 0 sgn 44 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
fof(f31,plain,
! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),
inference(reorient_equations,[],[f30]) ).
fof(f76,axiom,
! [X0] : c_Suc(X0) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
fof(f151,axiom,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f1029,axiom,
! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f1108,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
fof(f1216,axiom,
! [X2,X3,X0,X1,X4] :
( ~ c_Finite__Set_Ofinite(X3,X4)
| ~ c_lessequals(X0,c_Set_Oimage(X2,X3,X4,X1),tc_fun(X1,tc_bool))
| c_Finite__Set_Ofinite(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__surj_0) ).
fof(f1224,axiom,
! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_in(X0,X1,X2)
| c_Finite__Set_Ocard(c_Set_Oinsert(X0,X1,X2),X2) = c_Suc(c_Finite__Set_Ocard(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert__if_1) ).
fof(f1263,negated_conjecture,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1264,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1265,negated_conjecture,
c_lessequals(c_Suc(v_na),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1266,negated_conjecture,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_Suc(v_na),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1268,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f1269,negated_conjecture,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f1442,plain,
! [X2,X0,X1] :
( ~ c_Finite__Set_Ofinite(X1,X2)
| c_in(X0,X1,X2)
| c_Finite__Set_Ocard(c_Set_Oinsert(X0,X1,X2),X2) = c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(X1,X2),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1224,f76]) ).
fof(f1448,plain,
c_lessequals(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
inference(definition_unfolding,[],[f1265,f76]) ).
fof(f1449,plain,
c_Finite__Set_Ocard(v_G,t_a) = c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1266,f76]) ).
tcf(c_1190,plain,
! [X0: $i,X1: $i,X2: $i] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
inference(cnf_transformation,[],[f31]) ).
tcf(c_1276,plain,
! [X0: $i,X1: $i] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),
inference(cnf_transformation,[],[f151]) ).
tcf(c_1892,plain,
! [X0: $i,X1: $i] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) = X1,
inference(cnf_transformation,[],[f1029]) ).
tcf(c_1959,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) = X1 )
| ~ c_lessequals(X0,X1,tc_nat) ),
inference(cnf_transformation,[],[f1108]) ).
tcf(c_2050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_Finite__Set_Ofinite(X0,X4)
| ~ c_Finite__Set_Ofinite(X2,X3)
| ~ c_lessequals(X0,c_Set_Oimage(X1,X2,X3,X4),tc_fun(X4,tc_bool)) ),
inference(cnf_transformation,[],[f1216]) ).
tcf(c_2058,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X2,X0,X1)
| ( c_HOL_Oplus__class_Oplus(c_Finite__Set_Ocard(X0,X1),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Finite__Set_Ocard(c_Set_Oinsert(X2,X0,X1),X1) )
| ~ c_Finite__Set_Ofinite(X0,X1) ),
inference(cnf_transformation,[],[f1442]) ).
tcf(c_2090,negated_conjecture,
c_Finite__Set_Ofinite(v_U,tc_Com_Opname),
inference(cnf_transformation,[],[f1263]) ).
tcf(c_2091,negated_conjecture,
c_lessequals(v_G,c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),tc_fun(t_a,tc_bool)),
inference(cnf_transformation,[],[f1264]) ).
tcf(c_2092,negated_conjecture,
c_lessequals(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),tc_nat),
inference(cnf_transformation,[],[f1448]) ).
tcf(c_2093,negated_conjecture,
c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(v_G,t_a),
inference(cnf_transformation,[],[f1449]) ).
tcf(c_2095,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
inference(cnf_transformation,[],[f1268]) ).
tcf(c_2096,negated_conjecture,
c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) != c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a),
inference(cnf_transformation,[],[f1269]) ).
tcf(c_3028,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(superposition,[status(thm)],[c_2092,c_1959]) ).
tcf(c_4468,plain,
( c_Finite__Set_Ofinite(v_G,t_a)
| ~ c_Finite__Set_Ofinite(v_U,tc_Com_Opname) ),
inference(superposition,[status(thm)],[c_2091,c_2050]) ).
tcf(c_6391,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X2,X0,X1)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(X0,X1),tc_nat) = c_Finite__Set_Ocard(c_Set_Oinsert(X2,X0,X1),X1) )
| ~ c_Finite__Set_Ofinite(X0,X1) ),
inference(demodulation,[status(thm)],[c_2058,c_1276]) ).
tcf(c_6405,plain,
( ( c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat) )
| ~ c_Finite__Set_Ofinite(v_G,t_a) ),
inference(superposition,[status(thm)],[c_6391,c_2095]) ).
tcf(c_21016,plain,
c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(demodulation,[status(thm)],[c_3028,c_1190]) ).
tcf(c_21017,plain,
c_HOL_Oplus__class_Oplus(v_na,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),
inference(light_normalisation,[status(thm)],[c_21016,c_2093]) ).
tcf(c_21071,plain,
c_HOL_Ominus__class_Ominus(c_Finite__Set_Ocard(c_Set_Oimage(v_mgt__call,v_U,tc_Com_Opname,t_a),t_a),v_na,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat),
inference(superposition,[status(thm)],[c_21017,c_1892]) ).
tcf(c_21090,plain,
c_Finite__Set_Ocard(c_Set_Oinsert(hAPP(v_mgt__call,v_pn),v_G,t_a),t_a) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Finite__Set_Ocard(v_G,t_a),tc_nat),
inference(demodulation,[status(thm)],[c_2096,c_21071]) ).
tcf(c_21092,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_21090,c_6405,c_4468,c_2090]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV885-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.39 % Computer : n020.cluster.edu
% 0.09/5.39 % Model : x86_64 x86_64
% 0.09/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.39 % Memory : 8046.5625MB
% 0.09/5.39 % OS : Linux 6.8.0-71-generic
% 0.09/5.39 % CPULimit : 300
% 0.09/5.39 % WCLimit : 300
% 0.09/5.39 % DateTime : Thu Sep 24 21:14:24 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.43 Running first-order theorem proving
% 0.14/5.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/5.44
% 0.14/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.44
% 0.14/5.44 % Detected problem language: tptp
% 0.14/5.45 % Proving...
% 10.78/7.76 % SZS status Started for theBenchmark.p
% 10.78/7.76 % SZS status Unsatisfiable for theBenchmark.p
% 10.78/7.76
% 10.78/7.76 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.78/7.76
% 10.78/7.76 % ------ iProver source info
% 10.78/7.76
% 10.78/7.76 % git: date: 2026-07-19 20:42:38 +0200
% 10.78/7.76 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.78/7.76 % git: non_committed_changes: false
% 10.78/7.76
% 10.78/7.76 % ------ Parsing...% successful
% 10.78/7.76
% 10.78/7.76
% 10.78/7.76 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 10.78/7.76 % ------ Proving...
% 10.78/7.76 % ------ Problem Properties
% 10.78/7.76
% 10.78/7.76 %
% 10.78/7.76 % clauses 986
% 10.78/7.76 % conjectures 7
% 10.78/7.76 % EPR 127
% 10.78/7.76 % Horn 868
% 10.78/7.76 % unary 226
% 10.78/7.76 % binary 376
% 10.78/7.76 % lits 2296
% 10.78/7.76 % lits eq 544
% 10.78/7.76 % fd_pure 0
% 10.78/7.76 % fd_pseudo 0
% 10.78/7.76 % fd_cond 31
% 10.78/7.76 % fd_pseudo_cond 102
% 10.78/7.76 % AC symbols 0
% 10.78/7.76
% 10.78/7.76 % ------ Input Options Time Limit: Unbounded
% 10.78/7.76
% 10.78/7.76
% 10.78/7.76 % ------
% 10.78/7.76 % Current options:
% 10.78/7.76 % ------
% 10.78/7.76
% 10.78/7.76
% 10.78/7.76 %
% 10.78/7.76
% 10.78/7.76 % ------ Proving...
% 10.78/7.76 %
% 10.78/7.76
% 10.78/7.76 % SZS status Unsatisfiable for theBenchmark.p
% 10.78/7.76
% 10.78/7.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.78/7.76
%------------------------------------------------------------------------------