%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET839-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 02:48:44 PM UTC 2026
% Result : Unsatisfiable 63.40s 10.68s
% Output : CNFRefutation 63.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 13 unt; 0 def)
% Number of atoms : 111 ( 19 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 101 ( 41 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 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 : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 108 ( 0 sgn 108 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
fof(f210,axiom,
! [X2,X3,X0,X1] :
( c_in(X3,X0,X2)
| ~ c_in(X3,c_Inter(X1,X2),X2)
| ~ c_in(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-2.ax',cls_Set_OInterD_0) ).
fof(f227,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-2.ax',cls_Set_OinsertCI_1) ).
fof(f366,axiom,
! [X2,X0,X1] :
( c_in(c_Main_OInterI__1(X0,X1,X2),X1,tc_set(X2))
| c_in(X0,c_Inter(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OInterI_0) ).
fof(f368,axiom,
! [X0,X1] : c_in(X0,c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OUNIV__I_0) ).
fof(f372,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_less(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OpsubsetE_0) ).
fof(f374,axiom,
! [X2,X0,X1] :
( X0 = X1
| c_less(X0,X1,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OpsubsetI_0) ).
fof(f379,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetI_0) ).
fof(f380,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetI_1) ).
fof(f381,axiom,
! [X2,X0,X1] :
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/MSC001-0.ax',cls_Set_Osubset__antisym_0) ).
fof(f382,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(reorient_equations,[],[f381]) ).
fof(f1434,negated_conjecture,
! [X0] : ~ c_lessequals(v_S,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1435,negated_conjecture,
! [X0,X1] :
( ~ c_in(X0,v_S,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_lessequals(X0,X1,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tcf(c_1570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X3,X2)
| ~ c_in(X3,X1,tc_set(X2))
| ~ c_in(X0,c_Inter(X1,X2),X2) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_1583,plain,
! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[],[f227]) ).
tcf(c_1699,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X0,c_Inter(X1,X2),X2)
| c_in(c_Main_OInterI__1(X0,X1,X2),X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f366]) ).
tcf(c_1701,plain,
! [X0: $i,X1: $i] : c_in(X0,c_UNIV,X1),
inference(cnf_transformation,[],[f368]) ).
tcf(c_1705,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_less(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f372]) ).
tcf(c_1707,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_less(X0,X1,tc_set(X2))
| ( X0 = X1 )
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f374]) ).
tcf(c_1712,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[],[f379]) ).
tcf(c_1713,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[],[f380]) ).
tcf(c_1714,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f382]) ).
tcf(c_1999,negated_conjecture,
! [X0: $i] : ~ c_lessequals(v_S,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f1434]) ).
tcf(c_2000,negated_conjecture,
! [X0: $i,X1: $i] :
( c_lessequals(X0,X1,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(cnf_transformation,[],[f1435]) ).
tcf(c_19243,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X1,tc_set(tc_set(t_a)))
| c_lessequals(X0,c_Main_OsubsetI__1(v_S,X1,tc_set(t_a)),tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_1712,c_2000]) ).
tcf(c_19273,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X0,tc_set(tc_set(t_a)))
| ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_less(c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),X1,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_19243,c_1705]) ).
tcf(c_19351,plain,
! [X0: $i,X1: $i] : c_lessequals(X0,c_UNIV,tc_set(X1)),
inference(superposition,[status(thm)],[c_1701,c_1713]) ).
tcf(c_19769,plain,
! [X0: $i,X1: $i] :
( c_in(X1,c_Inter(v_S,t_a),t_a)
| c_lessequals(X0,c_Main_OInterI__1(X1,v_S,t_a),tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_1699,c_2000]) ).
tcf(c_20200,plain,
! [X0: $i,X1: $i] :
( c_in(X1,c_Inter(v_S,t_a),t_a)
| c_less(X0,c_Main_OInterI__1(X1,v_S,t_a),tc_set(t_a))
| ( c_Main_OInterI__1(X1,v_S,t_a) = X0 )
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_19769,c_1707]) ).
tcf(c_20459,plain,
! [X0: $i,X1: $i] :
( c_in(X1,c_Inter(v_S,t_a),t_a)
| c_lessequals(v_S,X0,tc_set(tc_set(t_a)))
| ( c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)) = c_Main_OInterI__1(X1,v_S,t_a) )
| ~ c_in(c_Main_OInterI__1(X1,v_S,t_a),v_S,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),v_S,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_20200,c_19273]) ).
tcf(c_20657,plain,
! [X0: $i,X1: $i] :
( ( X0 = c_UNIV )
| ~ c_lessequals(c_UNIV,X0,tc_set(X1)) ),
inference(superposition,[status(thm)],[c_19351,c_1714]) ).
tcf(c_20918,plain,
! [X0: $i,X1: $i] :
( c_in(X1,c_Inter(v_S,t_a),t_a)
| c_lessequals(v_S,X0,tc_set(tc_set(t_a)))
| ( c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)) = c_Main_OInterI__1(X1,v_S,t_a) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20459,c_1699,c_1712]) ).
tcf(c_20927,plain,
! [X0: $i,X1: $i] :
( c_in(X1,c_Inter(v_S,t_a),t_a)
| ( c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(t_a)) = c_Main_OInterI__1(X1,v_S,t_a) ) ),
inference(superposition,[status(thm)],[c_20918,c_1999]) ).
tcf(c_20994,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,c_Inter(v_S,t_a),tc_set(t_a))
| ( c_Main_OInterI__1(c_Main_OsubsetI__1(X0,c_Inter(v_S,t_a),t_a),v_S,t_a) = c_Main_OsubsetI__1(v_S,c_insert(X1,c_emptyset,tc_set(t_a)),tc_set(t_a)) ) ),
inference(superposition,[status(thm)],[c_20927,c_1713]) ).
tcf(c_21003,plain,
! [X0: $i] :
( ( c_Inter(v_S,t_a) = c_UNIV )
| ( c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(t_a)) = c_Main_OInterI__1(c_Main_OsubsetI__1(c_UNIV,c_Inter(v_S,t_a),t_a),v_S,t_a) ) ),
inference(superposition,[status(thm)],[c_20994,c_20657]) ).
tcf(c_21025,plain,
! [X0: $i] :
( c_lessequals(v_S,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a)))
| ( c_Inter(v_S,t_a) = c_UNIV )
| ~ c_in(c_Main_OInterI__1(c_Main_OsubsetI__1(c_UNIV,c_Inter(v_S,t_a),t_a),v_S,t_a),c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_21003,c_1713]) ).
tcf(c_21035,plain,
! [X0: $i] :
( ( c_Inter(v_S,t_a) = c_UNIV )
| ~ c_in(c_Main_OInterI__1(c_Main_OsubsetI__1(c_UNIV,c_Inter(v_S,t_a),t_a),v_S,t_a),c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(t_a)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21025,c_1999]) ).
tcf(c_21125,plain,
c_Inter(v_S,t_a) = c_UNIV,
inference(superposition,[status(thm)],[c_1583,c_21035]) ).
tcf(c_21237,plain,
! [X0: $i,X1: $i] :
( c_in(X1,X0,t_a)
| ~ c_in(X1,c_UNIV,t_a)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_21125,c_1570]) ).
tcf(c_21239,plain,
! [X0: $i,X1: $i] :
( c_in(X1,X0,t_a)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21237,c_1701]) ).
tcf(c_21248,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X1,tc_set(tc_set(t_a)))
| c_in(X0,c_Main_OsubsetI__1(v_S,X1,tc_set(t_a)),t_a) ),
inference(superposition,[status(thm)],[c_1712,c_21239]) ).
tcf(c_21263,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X1,tc_set(tc_set(t_a)))
| c_lessequals(X0,c_Main_OsubsetI__1(v_S,X1,tc_set(t_a)),tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_21248,c_1713]) ).
tcf(c_28048,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X1,tc_set(tc_set(t_a)))
| c_lessequals(X0,c_Main_OsubsetI__1(v_S,X1,tc_set(t_a)),tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_1712,c_2000]) ).
tcf(c_28062,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X1,tc_set(tc_set(t_a)))
| c_lessequals(X0,c_Main_OsubsetI__1(v_S,X1,tc_set(t_a)),tc_set(t_a)) ),
inference(global_subsumption_just,[status(thm)],[c_28048,c_21263]) ).
tcf(c_28121,plain,
! [X0: $i,X1: $i] : c_lessequals(X0,c_UNIV,tc_set(X1)),
inference(superposition,[status(thm)],[c_1701,c_1713]) ).
tcf(c_28128,plain,
! [X0: $i,X1: $i] : ~ c_less(c_UNIV,X0,tc_set(X1)),
inference(superposition,[status(thm)],[c_28121,c_1705]) ).
tcf(c_28408,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X0,tc_set(tc_set(t_a)))
| c_less(X1,c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)),tc_set(t_a))
| ( c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)) = X1 ) ),
inference(superposition,[status(thm)],[c_28062,c_1707]) ).
tcf(c_28493,plain,
! [X0: $i] :
( c_lessequals(v_S,X0,tc_set(tc_set(t_a)))
| ( c_Main_OsubsetI__1(v_S,X0,tc_set(t_a)) = c_UNIV ) ),
inference(superposition,[status(thm)],[c_28408,c_28128]) ).
tcf(c_28545,plain,
! [X0: $i] : c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(t_a)) = c_UNIV,
inference(superposition,[status(thm)],[c_28493,c_1999]) ).
tcf(c_28565,plain,
! [X0: $i] :
( c_lessequals(v_S,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(c_UNIV,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_28545,c_1713]) ).
tcf(c_28572,plain,
! [X0: $i] : ~ c_in(c_UNIV,c_insert(X0,c_emptyset,tc_set(t_a)),tc_set(t_a)),
inference(forward_subsumption_resolution,[status(thm)],[c_28565,c_1999]) ).
tcf(c_28578,plain,
$false,
inference(superposition,[status(thm)],[c_1583,c_28572]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET839-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.57 % Computer : n008.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Thu Sep 24 12:10:20 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.61 Running first-order theorem proving
% 0.15/0.62 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
% 0.15/0.63
% 0.15/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.63
% 0.15/0.63 % Detected problem language: tptp
% 0.15/0.64 % Proving...
% 63.40/10.68 % SZS status Started for theBenchmark.p
% 63.40/10.68 % SZS status Unsatisfiable for theBenchmark.p
% 63.40/10.68
% 63.40/10.68 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 63.40/10.68
% 63.40/10.68 % ------ iProver source info
% 63.40/10.68
% 63.40/10.68 % git: date: 2026-07-19 20:42:38 +0200
% 63.40/10.68 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 63.40/10.68 % git: non_committed_changes: false
% 63.40/10.68
% 63.40/10.68 % ------ Parsing...% successful
% 63.40/10.68
% 63.40/10.68
% 63.40/10.68 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 63.40/10.68
% 63.40/10.68 % ------ Preprocessing... sup_sim: 1 sf_s rm: 18 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 0 sf_s rm: 30 0s sf_e pe_s pe_e %
% 63.40/10.68
% 63.40/10.68 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 63.40/10.68
% 63.40/10.68 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 63.40/10.68 % ------ Proving...
% 63.40/10.68 % ------ Problem Properties
% 63.40/10.68
% 63.40/10.68 %
% 63.40/10.68 % clauses 297
% 63.40/10.68 % conjectures 2
% 63.40/10.68 % EPR 26
% 63.40/10.68 % Horn 270
% 63.40/10.68 % unary 76
% 63.40/10.68 % binary 173
% 63.40/10.68 % lits 566
% 63.40/10.68 % lits eq 162
% 63.40/10.68 % fd_pure 0
% 63.40/10.68 % fd_pseudo 0
% 63.40/10.68 % fd_cond 21
% 63.40/10.68 % fd_pseudo_cond 40
% 63.40/10.68 % AC symbols 0
% 63.40/10.68
% 63.40/10.68 % ------ Input Options Time Limit: Unbounded
% 63.40/10.68
% 63.40/10.68
% 63.40/10.68 % ------
% 63.40/10.68 % Current options:
% 63.40/10.68 % ------
% 63.40/10.68
% 63.40/10.68
% 63.40/10.68 %
% 63.40/10.68
% 63.40/10.68 % ------ Proving...
% 63.40/10.68 %
% 63.40/10.68
% 63.40/10.68 % SZS status Unsatisfiable for theBenchmark.p
% 63.40/10.68
% 63.40/10.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 63.40/10.68
% 63.40/10.68
%------------------------------------------------------------------------------