%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET820-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.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 02:48:39 PM UTC 2026
% Result : Unsatisfiable 16.68s 3.24s
% Output : CNFRefutation 16.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 23 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f227,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_Set_OinsertCI_1) ).
fof(f375,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ c_in(X0,c_insert(X1,c_emptyset,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_OsingletonD__dest_0) ).
fof(f376,axiom,
! [X0,X1] : c_in(X0,c_insert(X0,c_emptyset,X1),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_OsingletonI_0) ).
fof(f1434,negated_conjecture,
v_P(v_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1435,negated_conjecture,
! [X0,X1] :
( c_in(v_x(X1),X1,tc_IntDef_Oint)
| ~ c_in(X0,X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1436,negated_conjecture,
! [X0,X1] :
( ~ v_P(v_x(X1))
| ~ c_in(X0,X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
tcf(c_1584,plain,
! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[],[f227]) ).
tcf(c_1709,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ c_in(X0,c_insert(X1,c_emptyset,X2),X2) ),
inference(cnf_transformation,[],[f375]) ).
tcf(c_1710,plain,
! [X0: $i,X1: $i] : c_in(X0,c_insert(X0,c_emptyset,X1),X1),
inference(cnf_transformation,[],[f376]) ).
tcf(c_2000,negated_conjecture,
v_P(v_a),
inference(cnf_transformation,[],[f1434]) ).
tcf(c_2001,negated_conjecture,
! [X0: $i,X1: $i] :
( c_in(v_x(X1),X1,tc_IntDef_Oint)
| ~ c_in(X0,X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[],[f1435]) ).
tcf(c_2002,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ v_P(v_x(X1))
| ~ c_in(X0,X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[],[f1436]) ).
tcf(c_3608,plain,
! [X0: $i,X1: $i] : ~ v_P(v_x(c_insert(X0,X1,tc_IntDef_Oint))),
inference(superposition,[status(thm)],[c_1584,c_2002]) ).
tcf(c_3615,plain,
! [X0: $i] : c_in(v_x(c_insert(X0,c_emptyset,tc_IntDef_Oint)),c_insert(X0,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint),
inference(superposition,[status(thm)],[c_1710,c_2001]) ).
tcf(c_5278,plain,
! [X0: $i] : v_x(c_insert(X0,c_emptyset,tc_IntDef_Oint)) = X0,
inference(superposition,[status(thm)],[c_3615,c_1709]) ).
tcf(c_5356,plain,
! [X0: $i] : ~ v_P(X0),
inference(superposition,[status(thm)],[c_5278,c_3608]) ).
tcf(c_5402,plain,
$false,
inference(superposition,[status(thm)],[c_2000,c_5356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET820-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:06:40 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 16.68/3.24 % SZS status Started for theBenchmark.p
% 16.68/3.24 % SZS status Unsatisfiable for theBenchmark.p
% 16.68/3.24
% 16.68/3.24 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 16.68/3.24
% 16.68/3.24 % ------ iProver source info
% 16.68/3.24
% 16.68/3.24 % git: date: 2026-07-19 20:42:38 +0200
% 16.68/3.24 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 16.68/3.24 % git: non_committed_changes: false
% 16.68/3.24
% 16.68/3.24 % ------ Parsing...% successful
% 16.68/3.24
% 16.68/3.24
% 16.68/3.24 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 16.68/3.24
% 16.68/3.24 % ------ Preprocessing... sup_sim: 0 sf_s rm: 18 0s sf_e sup_sim: 0 sf_s rm: 4 0s sf_e %
% 16.68/3.24
% 16.68/3.24 % ------ Preprocessing...%
% 16.68/3.24
% 16.68/3.24 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 16.68/3.24 % ------ Proving...
% 16.68/3.24 % ------ Problem Properties
% 16.68/3.24
% 16.68/3.24 %
% 16.68/3.24 % clauses 553
% 16.68/3.24 % conjectures 31
% 16.68/3.24 % EPR 285
% 16.68/3.24 % Horn 526
% 16.68/3.24 % unary 125
% 16.68/3.24 % binary 373
% 16.68/3.24 % lits 1036
% 16.68/3.24 % lits eq 157
% 16.68/3.24 % fd_pure 0
% 16.68/3.24 % fd_pseudo 0
% 16.68/3.24 % fd_cond 21
% 16.68/3.24 % fd_pseudo_cond 37
% 16.68/3.24 % AC symbols 0
% 16.68/3.24
% 16.68/3.24 % ------ Input Options Time Limit: Unbounded
% 16.68/3.24
% 16.68/3.24
% 16.68/3.24 % ------
% 16.68/3.24 % Current options:
% 16.68/3.24 % ------
% 16.68/3.24
% 16.68/3.24
% 16.68/3.24 %
% 16.68/3.24
% 16.68/3.24 % ------ Proving...
% 16.68/3.24 %
% 16.68/3.24
% 16.68/3.24 % SZS status Unsatisfiable for theBenchmark.p
% 16.68/3.24
% 16.68/3.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.68/3.24
% 16.68/3.24
%------------------------------------------------------------------------------