%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV886-1 : 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 : n009.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 4.51s 2.20s
% Output : CNFRefutation 4.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 32 ( 25 unt; 0 def)
% Number of atoms : 43 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 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 : 16 ( 16 usr; 8 con; 0-4 aty)
% Number of variables : 31 ( 0 sgn 31 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f233,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/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
fof(f256,axiom,
! [X0] : c_Suc(X0) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
fof(f286,axiom,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f404,axiom,
! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f454,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/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
fof(f667,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/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_1) ).
fof(f700,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f701,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f703,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f704,negated_conjecture,
c_Finite__Set_Ofinite(v_G,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f705,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f823,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,[],[f667,f256]) ).
fof(f829,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,[],[f700,f256]) ).
fof(f830,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,[],[f701,f256]) ).
tcf(c_839,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,[],[f233]) ).
tcf(c_879,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,[],[f286]) ).
tcf(c_964,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,[],[f404]) ).
tcf(c_1009,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,[],[f454]) ).
tcf(c_1177,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,[],[f823]) ).
tcf(c_1203,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,[],[f829]) ).
tcf(c_1204,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,[],[f830]) ).
tcf(c_1206,negated_conjecture,
~ c_in(hAPP(v_mgt__call,v_pn),v_G,t_a),
inference(cnf_transformation,[],[f703]) ).
tcf(c_1207,negated_conjecture,
c_Finite__Set_Ofinite(v_G,t_a),
inference(cnf_transformation,[],[f704]) ).
tcf(c_1208,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,[],[f705]) ).
tcf(c_2024,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_1203,c_1009]) ).
tcf(c_4435,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_1177,c_879]) ).
tcf(c_4451,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_4435,c_1206]) ).
tcf(c_19297,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_2024,c_839]) ).
tcf(c_19298,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_19297,c_1204]) ).
tcf(c_19332,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_19298,c_964]) ).
tcf(c_19383,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_1208,c_19332]) ).
tcf(c_19385,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_19383,c_4451,c_1207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV886-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.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
% 0.10/0.37 % DateTime : Thu Sep 24 21:14:29 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 4.51/2.20 % SZS status Started for theBenchmark.p
% 4.51/2.20 % SZS status Unsatisfiable for theBenchmark.p
% 4.51/2.20
% 4.51/2.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.51/2.20
% 4.51/2.20 % ------ iProver source info
% 4.51/2.20
% 4.51/2.20 % git: date: 2026-07-19 20:42:38 +0200
% 4.51/2.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.51/2.20 % git: non_committed_changes: false
% 4.51/2.20
% 4.51/2.20 % ------ Parsing...% successful
% 4.51/2.20
% 4.51/2.20
% 4.51/2.20 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.51/2.20 % ------ Proving...
% 4.51/2.20 % ------ Problem Properties
% 4.51/2.20
% 4.51/2.20 %
% 4.51/2.20 % clauses 573
% 4.51/2.20 % conjectures 7
% 4.51/2.20 % EPR 106
% 4.51/2.20 % Horn 494
% 4.51/2.20 % unary 137
% 4.51/2.20 % binary 212
% 4.51/2.20 % lits 1333
% 4.51/2.20 % lits eq 303
% 4.51/2.20 % fd_pure 0
% 4.51/2.20 % fd_pseudo 0
% 4.51/2.20 % fd_cond 18
% 4.51/2.20 % fd_pseudo_cond 76
% 4.51/2.20 % AC symbols 0
% 4.51/2.20
% 4.51/2.20 % ------ Input Options Time Limit: Unbounded
% 4.51/2.20
% 4.51/2.20
% 4.51/2.20 % ------
% 4.51/2.20 % Current options:
% 4.51/2.20 % ------
% 4.51/2.20
% 4.51/2.20
% 4.51/2.20 %
% 4.51/2.20
% 4.51/2.20 % ------ Proving...
% 4.51/2.20 %
% 4.51/2.20
% 4.51/2.20 % SZS status Unsatisfiable for theBenchmark.p
% 4.51/2.20
% 4.51/2.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.51/2.20
% 4.51/2.20
%------------------------------------------------------------------------------