%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET839-2 : 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 : n010.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 2.11s 6.32s
% Output : CNFRefutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 10 unt; 2 def)
% Number of atoms : 157 ( 15 equ)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 78 ( 32 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 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 : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 66 ( 0 sgn 66 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,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) ).
fof(f3,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f4,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/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f5,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/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f6,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/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f7,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(reorient_equations,[],[f6]) ).
tcf(c_55,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,[],[f1]) ).
tcf(c_56,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,[],[f2]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[],[f3]) ).
tcf(c_58,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,[],[f4]) ).
tcf(c_59,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,[],[f5]) ).
tcf(c_60,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,[],[f7]) ).
tcf(c_116,definition,
iPr_def_10 = tc_set(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_117,definition,
iPr_def_11 = tc_set(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_118,negated_conjecture,
! [X0: $i,X1: $i] :
( c_lessequals(X0,X1,iPr_def_10)
| ~ c_in(X1,v_S,iPr_def_10)
| ~ c_in(X0,v_S,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_56,c_116]) ).
tcf(c_119,negated_conjecture,
! [X0: $i] : ~ c_lessequals(v_S,c_insert(X0,c_emptyset,iPr_def_10),iPr_def_11),
inference(demodulation,[status(thm)],[c_55,c_117]) ).
tcf(c_274,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X1,tc_set(iPr_def_10))
| c_lessequals(c_Main_OsubsetI__1(v_S,X1,iPr_def_10),X0,iPr_def_10)
| ~ c_in(X0,v_S,iPr_def_10) ),
inference(superposition,[status(thm)],[c_58,c_118]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X1,iPr_def_11)
| c_lessequals(c_Main_OsubsetI__1(v_S,X1,iPr_def_10),X0,iPr_def_10)
| ~ c_in(X0,v_S,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_274,c_117]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,iPr_def_10)
| ~ c_lessequals(X0,X1,tc_set(t_a)) ),
inference(superposition,[status(thm)],[c_116,c_60]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,iPr_def_10)
| ~ c_lessequals(X0,X1,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_303,c_116]) ).
tcf(c_326,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X1,iPr_def_11)
| ( c_Main_OsubsetI__1(v_S,X1,iPr_def_10) = X0 )
| ~ c_in(X0,v_S,iPr_def_10)
| ~ c_lessequals(X0,c_Main_OsubsetI__1(v_S,X1,iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_275,c_309]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X1,iPr_def_11)
| c_lessequals(v_S,X0,iPr_def_11)
| ( c_Main_OsubsetI__1(v_S,X0,iPr_def_10) = c_Main_OsubsetI__1(v_S,X1,iPr_def_10) )
| ~ c_in(c_Main_OsubsetI__1(v_S,X1,iPr_def_10),v_S,iPr_def_10)
| ~ c_in(c_Main_OsubsetI__1(v_S,X0,iPr_def_10),v_S,iPr_def_10) ),
inference(superposition,[status(thm)],[c_275,c_326]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X1,iPr_def_11)
| c_lessequals(v_S,X0,iPr_def_11)
| c_lessequals(v_S,X1,tc_set(iPr_def_10))
| ( c_Main_OsubsetI__1(v_S,X0,iPr_def_10) = c_Main_OsubsetI__1(v_S,X1,iPr_def_10) )
| ~ c_in(c_Main_OsubsetI__1(v_S,X0,iPr_def_10),v_S,iPr_def_10) ),
inference(superposition,[status(thm)],[c_58,c_341]) ).
tcf(c_360,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X1,iPr_def_11)
| c_lessequals(v_S,X0,iPr_def_11)
| ( c_Main_OsubsetI__1(v_S,X0,iPr_def_10) = c_Main_OsubsetI__1(v_S,X1,iPr_def_10) )
| ~ c_in(c_Main_OsubsetI__1(v_S,X0,iPr_def_10),v_S,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_359,c_117]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X1,iPr_def_11)
| c_lessequals(v_S,X0,iPr_def_11)
| c_lessequals(v_S,X0,tc_set(iPr_def_10))
| ( c_Main_OsubsetI__1(v_S,X0,iPr_def_10) = c_Main_OsubsetI__1(v_S,X1,iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_58,c_360]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X1,iPr_def_11)
| c_lessequals(v_S,X0,iPr_def_11)
| ( c_Main_OsubsetI__1(v_S,X0,iPr_def_10) = c_Main_OsubsetI__1(v_S,X1,iPr_def_10) ) ),
inference(light_normalisation,[status(thm)],[c_377,c_117]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,X1,iPr_def_11)
| ( c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,iPr_def_10),iPr_def_10) = c_Main_OsubsetI__1(v_S,X1,iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_378,c_119]) ).
tcf(c_409,plain,
! [X0: $i,X1: $i] : c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,iPr_def_10),iPr_def_10) = c_Main_OsubsetI__1(v_S,c_insert(X1,c_emptyset,iPr_def_10),iPr_def_10),
inference(superposition,[status(thm)],[c_394,c_119]) ).
tcf(c_426,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,c_insert(X1,c_emptyset,iPr_def_10),tc_set(iPr_def_10))
| ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,iPr_def_10),iPr_def_10),c_insert(X1,c_emptyset,iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_409,c_59]) ).
tcf(c_437,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_S,c_insert(X1,c_emptyset,iPr_def_10),iPr_def_11)
| ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,iPr_def_10),iPr_def_10),c_insert(X1,c_emptyset,iPr_def_10),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_426,c_117]) ).
tcf(c_438,plain,
! [X0: $i,X1: $i] : ~ c_in(c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,iPr_def_10),iPr_def_10),c_insert(X1,c_emptyset,iPr_def_10),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_437,c_119]) ).
tcf(c_454,plain,
$false,
inference(superposition,[status(thm)],[c_57,c_438]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET839-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.39 % Computer : n010.cluster.edu
% 0.14/5.39 % Model : x86_64 x86_64
% 0.14/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.39 % Memory : 8046.5625MB
% 0.14/5.39 % OS : Linux 6.8.0-71-generic
% 0.14/5.39 % CPULimit : 300
% 0.14/5.39 % WCLimit : 300
% 0.14/5.39 % DateTime : Thu Sep 24 12:09:51 UTC 2026
% 0.17/5.40 % CPUTime :
% 0.17/5.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.17/5.44 Running first-order theorem proving
% 0.17/5.44 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
% 0.17/5.45
% 0.17/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.17/5.45
% 0.17/5.45 % Detected problem language: tptp
% 0.17/5.46 % Proving...
% 2.11/6.32 % SZS status Started for theBenchmark.p
% 2.11/6.32 % SZS status Unsatisfiable for theBenchmark.p
% 2.11/6.32
% 2.11/6.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.11/6.32
% 2.11/6.32 % ------ iProver source info
% 2.11/6.32
% 2.11/6.32 % git: date: 2026-07-19 20:42:38 +0200
% 2.11/6.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.11/6.32 % git: non_committed_changes: false
% 2.11/6.32
% 2.11/6.32 % ------ Parsing...% successful
% 2.11/6.32
% 2.11/6.32
% 2.11/6.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.11/6.32
% 2.11/6.32 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.11/6.32
% 2.11/6.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.11/6.32
% 2.11/6.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.11/6.32 % ------ Proving...
% 2.11/6.32 % ------ Problem Properties
% 2.11/6.32
% 2.11/6.32 %
% 2.11/6.32 % clauses 8
% 2.11/6.32 % conjectures 2
% 2.11/6.32 % EPR 1
% 2.11/6.32 % Horn 7
% 2.11/6.32 % unary 4
% 2.11/6.32 % binary 2
% 2.11/6.32 % lits 14
% 2.11/6.32 % lits eq 3
% 2.11/6.32 % fd_pure 0
% 2.11/6.32 % fd_pseudo 0
% 2.11/6.32 % fd_cond 0
% 2.11/6.32 % fd_pseudo_cond 1
% 2.11/6.32 % AC symbols 0
% 2.11/6.32
% 2.11/6.32 % ------ Schedule dynamic 5 is on
% 2.11/6.32
% 2.11/6.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.11/6.32
% 2.11/6.32
% 2.11/6.32 % ------
% 2.11/6.32 % Current options:
% 2.11/6.32 % ------
% 2.11/6.32
% 2.11/6.32
% 2.11/6.32 %
% 2.11/6.32
% 2.11/6.32 % ------ Proving...
% 2.11/6.32 %
% 2.11/6.32
% 2.11/6.32 % SZS status Unsatisfiable for theBenchmark.p
% 2.11/6.32
% 2.11/6.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.11/6.32
% 2.11/6.32
%------------------------------------------------------------------------------