%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET840-2 : 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 : 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 02:48:44 PM UTC 2026
% Result : Unsatisfiable 3.42s 6.30s
% Output : CNFRefutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 11 unt; 3 def)
% Number of atoms : 149 ( 11 equ)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 72 ( 30 ~; 42 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 73 ( 0 sgn 73 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : ~ c_lessequals(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_b))
| c_lessequals(c_Union(v_S,t_b),X0,tc_set(t_b)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_Union(X3,X2),X2)
| ~ c_in(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
fof(f5,axiom,
! [X2,X0,X1] : c_in(X0,c_insert(X0,X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f7,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f8,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f9,axiom,
! [X2,X0,X1] :
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f10,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(reorient_equations,[],[f9]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] : ~ c_lessequals(v_S,c_insert(X0,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
inference(cnf_transformation,[],[f1]) ).
tcf(c_59,negated_conjecture,
! [X0: $i] :
( c_lessequals(c_Union(v_S,t_b),X0,tc_set(t_b))
| ~ c_in(X0,v_S,tc_set(t_b)) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X3,c_Union(X1,X2),X2)
| ~ c_in(X3,X0,X2)
| ~ c_in(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[],[f5]) ).
tcf(c_64,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,[],[f7]) ).
tcf(c_65,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,[],[f8]) ).
tcf(c_66,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,[],[f10]) ).
tcf(c_153,definition,
iPr_def_10 = tc_set(t_b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_154,definition,
iPr_def_11 = c_Union(v_S,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_155,definition,
iPr_def_12 = tc_set(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_156,negated_conjecture,
! [X0: $i] :
( c_lessequals(iPr_def_11,X0,iPr_def_10)
| ~ c_in(X0,v_S,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_59,c_154,c_153]) ).
tcf(c_157,negated_conjecture,
! [X0: $i] : ~ c_lessequals(v_S,c_insert(X0,c_emptyset,iPr_def_10),iPr_def_12),
inference(demodulation,[status(thm)],[c_58,c_155]) ).
tcf(c_361,plain,
! [X0: $i] :
( c_lessequals(v_S,X0,tc_set(iPr_def_10))
| c_lessequals(iPr_def_11,c_Main_OsubsetI__1(v_S,X0,iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_64,c_156]) ).
tcf(c_362,plain,
! [X0: $i] :
( c_lessequals(v_S,X0,iPr_def_12)
| c_lessequals(iPr_def_11,c_Main_OsubsetI__1(v_S,X0,iPr_def_10),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_361,c_155]) ).
tcf(c_399,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,iPr_def_10)
| ~ c_lessequals(X0,X1,tc_set(t_b)) ),
inference(superposition,[status(thm)],[c_153,c_66]) ).
tcf(c_405,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_399,c_153]) ).
tcf(c_418,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X2,c_Union(X1,t_b),t_b)
| ~ c_in(X2,X0,t_b)
| ~ c_in(X0,X1,iPr_def_10) ),
inference(superposition,[status(thm)],[c_153,c_60]) ).
tcf(c_457,plain,
! [X0: $i] :
( c_lessequals(v_S,X0,iPr_def_12)
| ( c_Main_OsubsetI__1(v_S,X0,iPr_def_10) = iPr_def_11 )
| ~ c_lessequals(c_Main_OsubsetI__1(v_S,X0,iPr_def_10),iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_362,c_405]) ).
tcf(c_519,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,X2,tc_set(iPr_def_10))
| c_in(X0,c_Union(X1,t_b),t_b)
| ~ c_in(X0,c_Main_OsubsetI__1(X1,X2,iPr_def_10),t_b) ),
inference(superposition,[status(thm)],[c_64,c_418]) ).
tcf(c_522,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,X2,iPr_def_12)
| c_in(X0,c_Union(X1,t_b),t_b)
| ~ c_in(X0,c_Main_OsubsetI__1(X1,X2,iPr_def_10),t_b) ),
inference(light_normalisation,[status(thm)],[c_519,c_155]) ).
tcf(c_579,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,iPr_def_12)
| c_lessequals(c_Main_OsubsetI__1(X0,X1,iPr_def_10),X2,tc_set(t_b))
| c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(X0,X1,iPr_def_10),X2,t_b),c_Union(X0,t_b),t_b) ),
inference(superposition,[status(thm)],[c_64,c_522]) ).
tcf(c_580,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,iPr_def_12)
| c_lessequals(c_Main_OsubsetI__1(X0,X1,iPr_def_10),X2,iPr_def_10)
| c_in(c_Main_OsubsetI__1(c_Main_OsubsetI__1(X0,X1,iPr_def_10),X2,t_b),c_Union(X0,t_b),t_b) ),
inference(light_normalisation,[status(thm)],[c_579,c_153]) ).
tcf(c_1480,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,X1,iPr_def_12)
| c_lessequals(c_Main_OsubsetI__1(X0,X1,iPr_def_10),c_Union(X0,t_b),iPr_def_10)
| c_lessequals(c_Main_OsubsetI__1(X0,X1,iPr_def_10),c_Union(X0,t_b),tc_set(t_b)) ),
inference(superposition,[status(thm)],[c_580,c_65]) ).
tcf(c_1488,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,X1,iPr_def_12)
| c_lessequals(c_Main_OsubsetI__1(X0,X1,iPr_def_10),c_Union(X0,t_b),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_1480,c_153]) ).
tcf(c_1499,plain,
! [X0: $i] :
( c_lessequals(v_S,X0,iPr_def_12)
| c_lessequals(c_Main_OsubsetI__1(v_S,X0,iPr_def_10),iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_154,c_1488]) ).
tcf(c_1533,plain,
! [X0: $i] :
( c_lessequals(v_S,X0,iPr_def_12)
| ( c_Main_OsubsetI__1(v_S,X0,iPr_def_10) = iPr_def_11 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_457,c_1499]) ).
tcf(c_1594,plain,
! [X0: $i] : c_Main_OsubsetI__1(v_S,c_insert(X0,c_emptyset,iPr_def_10),iPr_def_10) = iPr_def_11,
inference(superposition,[status(thm)],[c_1533,c_157]) ).
tcf(c_1601,plain,
! [X0: $i] :
( c_lessequals(v_S,c_insert(X0,c_emptyset,iPr_def_10),tc_set(iPr_def_10))
| ~ c_in(iPr_def_11,c_insert(X0,c_emptyset,iPr_def_10),iPr_def_10) ),
inference(superposition,[status(thm)],[c_1594,c_65]) ).
tcf(c_1619,plain,
! [X0: $i] :
( c_lessequals(v_S,c_insert(X0,c_emptyset,iPr_def_10),iPr_def_12)
| ~ c_in(iPr_def_11,c_insert(X0,c_emptyset,iPr_def_10),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_1601,c_155]) ).
tcf(c_1620,plain,
! [X0: $i] : ~ c_in(iPr_def_11,c_insert(X0,c_emptyset,iPr_def_10),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1619,c_157]) ).
tcf(c_1685,plain,
$false,
inference(superposition,[status(thm)],[c_62,c_1620]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET840-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n020.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 12:11:10 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.42 Running first-order theorem proving
% 0.16/5.42 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
% 0.16/5.44
% 0.16/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.44
% 0.16/5.44 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 3.42/6.30 % SZS status Started for theBenchmark.p
% 3.42/6.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.42/6.30
% 3.42/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.42/6.30
% 3.42/6.30 % ------ iProver source info
% 3.42/6.30
% 3.42/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.42/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.42/6.30 % git: non_committed_changes: false
% 3.42/6.30
% 3.42/6.30 % ------ Parsing...% successful
% 3.42/6.30
% 3.42/6.30
% 3.42/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.42/6.30
% 3.42/6.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.42/6.30
% 3.42/6.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.42/6.30
% 3.42/6.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.42/6.30 % ------ Proving...
% 3.42/6.30 % ------ Problem Properties
% 3.42/6.30
% 3.42/6.30 %
% 3.42/6.30 % clauses 12
% 3.42/6.30 % conjectures 2
% 3.42/6.30 % EPR 1
% 3.42/6.30 % Horn 10
% 3.42/6.30 % unary 5
% 3.42/6.30 % binary 4
% 3.42/6.30 % lits 22
% 3.42/6.30 % lits eq 5
% 3.42/6.30 % fd_pure 0
% 3.42/6.30 % fd_pseudo 0
% 3.42/6.30 % fd_cond 0
% 3.42/6.30 % fd_pseudo_cond 2
% 3.42/6.30 % AC symbols 0
% 3.42/6.30
% 3.42/6.30 % ------ Schedule dynamic 5 is on
% 3.42/6.30
% 3.42/6.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.42/6.30
% 3.42/6.30
% 3.42/6.30 % ------
% 3.42/6.30 % Current options:
% 3.42/6.30 % ------
% 3.42/6.30
% 3.42/6.30
% 3.42/6.30 %
% 3.42/6.30
% 3.42/6.30 % ------ Proving...
% 3.42/6.30 %
% 3.42/6.30
% 3.42/6.30 % SZS status Unsatisfiable for theBenchmark.p
% 3.42/6.30
% 3.42/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.42/6.30
% 3.42/6.30
%------------------------------------------------------------------------------