TSTP Solution File: SEU110+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU110+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 03:04:32 EDT 2024
% Result : Theorem 3.90s 1.18s
% Output : CNFRefutation 3.90s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f8,axiom,
! [X0,X1] :
( preboolean(X1)
=> ( finite_subsets(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(f9,axiom,
! [X0] : preboolean(finite_subsets(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f26,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f27,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> subset(finite_subsets(X0),finite_subsets(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> subset(finite_subsets(X0),finite_subsets(X1)) ),
inference(negated_conjecture,[],[f27]) ).
fof(f52,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f53,plain,
! [X0,X1] :
( ( finite_subsets(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) )
| ~ preboolean(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f58,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f59,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
? [X0,X1] :
( ~ subset(finite_subsets(X0),finite_subsets(X1))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f69,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f70,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f70,f71]) ).
fof(f73,plain,
! [X0,X1] :
( ( ( finite_subsets(X0) = X1
| ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) )
& ( ( finite(X2)
& subset(X2,X0) )
| ~ in(X2,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(nnf_transformation,[],[f53]) ).
fof(f74,plain,
! [X0,X1] :
( ( ( finite_subsets(X0) = X1
| ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) )
& ( ( finite(X2)
& subset(X2,X0) )
| ~ in(X2,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ( ( finite_subsets(X0) = X1
| ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ finite(X3)
| ~ subset(X3,X0) )
& ( ( finite(X3)
& subset(X3,X0) )
| ~ in(X3,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) )
=> ( ( ~ finite(sK1(X0,X1))
| ~ subset(sK1(X0,X1),X0)
| ~ in(sK1(X0,X1),X1) )
& ( ( finite(sK1(X0,X1))
& subset(sK1(X0,X1),X0) )
| in(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0,X1] :
( ( ( finite_subsets(X0) = X1
| ( ( ~ finite(sK1(X0,X1))
| ~ subset(sK1(X0,X1),X0)
| ~ in(sK1(X0,X1),X1) )
& ( ( finite(sK1(X0,X1))
& subset(sK1(X0,X1),X0) )
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ finite(X3)
| ~ subset(X3,X0) )
& ( ( finite(X3)
& subset(X3,X0) )
| ~ in(X3,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f75,f76]) ).
fof(f98,plain,
( ? [X0,X1] :
( ~ subset(finite_subsets(X0),finite_subsets(X1))
& subset(X0,X1) )
=> ( ~ subset(finite_subsets(sK12),finite_subsets(sK13))
& subset(sK12,sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
( ~ subset(finite_subsets(sK12),finite_subsets(sK13))
& subset(sK12,sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f60,f98]) ).
fof(f109,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f110,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f111,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| finite_subsets(X0) != X1
| ~ preboolean(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f112,plain,
! [X3,X0,X1] :
( finite(X3)
| ~ in(X3,X1)
| finite_subsets(X0) != X1
| ~ preboolean(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f113,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ finite(X3)
| ~ subset(X3,X0)
| finite_subsets(X0) != X1
| ~ preboolean(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f117,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f152,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f153,plain,
subset(sK12,sK13),
inference(cnf_transformation,[],[f99]) ).
fof(f154,plain,
~ subset(finite_subsets(sK12),finite_subsets(sK13)),
inference(cnf_transformation,[],[f99]) ).
fof(f163,plain,
! [X3,X0] :
( in(X3,finite_subsets(X0))
| ~ finite(X3)
| ~ subset(X3,X0)
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[],[f113]) ).
fof(f164,plain,
! [X3,X0] :
( finite(X3)
| ~ in(X3,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[],[f112]) ).
fof(f165,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[],[f111]) ).
cnf(c_56,plain,
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
cnf(c_57,plain,
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_62,plain,
( ~ subset(X0,X1)
| ~ preboolean(finite_subsets(X1))
| ~ finite(X0)
| in(X0,finite_subsets(X1)) ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_63,plain,
( ~ in(X0,finite_subsets(X1))
| ~ preboolean(finite_subsets(X1))
| finite(X0) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_64,plain,
( ~ in(X0,finite_subsets(X1))
| ~ preboolean(finite_subsets(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_65,plain,
preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f117]) ).
cnf(c_100,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X0)
| subset(X2,X1) ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_101,negated_conjecture,
~ subset(finite_subsets(sK12),finite_subsets(sK13)),
inference(cnf_transformation,[],[f154]) ).
cnf(c_102,negated_conjecture,
subset(sK12,sK13),
inference(cnf_transformation,[],[f153]) ).
cnf(c_318,plain,
( ~ in(X0,finite_subsets(X1))
| finite(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_63,c_65]) ).
cnf(c_319,plain,
( ~ subset(X0,X1)
| ~ finite(X0)
| in(X0,finite_subsets(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_62,c_65]) ).
cnf(c_320,plain,
( ~ in(X0,finite_subsets(X1))
| subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_64,c_65]) ).
cnf(c_1178,plain,
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(prop_impl_just,[status(thm)],[c_320]) ).
cnf(c_1179,plain,
( ~ in(X0,finite_subsets(X1))
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_1178]) ).
cnf(c_1184,plain,
( finite(X0)
| ~ in(X0,finite_subsets(X1)) ),
inference(prop_impl_just,[status(thm)],[c_318]) ).
cnf(c_1185,plain,
( ~ in(X0,finite_subsets(X1))
| finite(X0) ),
inference(renaming,[status(thm)],[c_1184]) ).
cnf(c_2021,plain,
finite_subsets(sK12) = sP0_iProver_def,
definition ).
cnf(c_2022,plain,
finite_subsets(sK13) = sP1_iProver_def,
definition ).
cnf(c_2023,negated_conjecture,
subset(sK12,sK13),
inference(demodulation,[status(thm)],[c_102]) ).
cnf(c_2024,negated_conjecture,
~ subset(sP0_iProver_def,sP1_iProver_def),
inference(demodulation,[status(thm)],[c_101,c_2022,c_2021]) ).
cnf(c_2972,plain,
( ~ in(X0,sP0_iProver_def)
| finite(X0) ),
inference(superposition,[status(thm)],[c_2021,c_1185]) ).
cnf(c_3001,plain,
( finite(sK0(sP0_iProver_def,X0))
| subset(sP0_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_57,c_2972]) ).
cnf(c_3201,plain,
( ~ subset(X0,sK12)
| subset(X0,sK13) ),
inference(superposition,[status(thm)],[c_2023,c_100]) ).
cnf(c_3233,plain,
( ~ subset(X0,sK13)
| ~ finite(X0)
| in(X0,sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_2022,c_319]) ).
cnf(c_3722,plain,
( subset(sK0(finite_subsets(X0),X1),X0)
| subset(finite_subsets(X0),X1) ),
inference(superposition,[status(thm)],[c_57,c_1179]) ).
cnf(c_4177,plain,
( subset(sK0(finite_subsets(sK12),X0),sK13)
| subset(finite_subsets(sK12),X0) ),
inference(superposition,[status(thm)],[c_3722,c_3201]) ).
cnf(c_4189,plain,
( subset(sK0(sP0_iProver_def,X0),sK13)
| subset(sP0_iProver_def,X0) ),
inference(light_normalisation,[status(thm)],[c_4177,c_2021]) ).
cnf(c_12109,plain,
( ~ finite(sK0(sP0_iProver_def,X0))
| in(sK0(sP0_iProver_def,X0),sP1_iProver_def)
| subset(sP0_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_4189,c_3233]) ).
cnf(c_14170,plain,
( in(sK0(sP0_iProver_def,X0),sP1_iProver_def)
| subset(sP0_iProver_def,X0) ),
inference(global_subsumption_just,[status(thm)],[c_12109,c_3001,c_12109]) ).
cnf(c_14181,plain,
subset(sP0_iProver_def,sP1_iProver_def),
inference(superposition,[status(thm)],[c_14170,c_56]) ).
cnf(c_14184,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_14181,c_2024]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU110+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 17:41:26 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.90/1.18 % SZS status Started for theBenchmark.p
% 3.90/1.18 % SZS status Theorem for theBenchmark.p
% 3.90/1.18
% 3.90/1.18 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.90/1.18
% 3.90/1.18 ------ iProver source info
% 3.90/1.18
% 3.90/1.18 git: date: 2024-05-02 19:28:25 +0000
% 3.90/1.18 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.90/1.18 git: non_committed_changes: false
% 3.90/1.18
% 3.90/1.18 ------ Parsing...
% 3.90/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.90/1.18
% 3.90/1.18 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e
% 3.90/1.18
% 3.90/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.90/1.18
% 3.90/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.90/1.18 ------ Proving...
% 3.90/1.18 ------ Problem Properties
% 3.90/1.18
% 3.90/1.18
% 3.90/1.18 clauses 53
% 3.90/1.18 conjectures 2
% 3.90/1.18 EPR 22
% 3.90/1.18 Horn 44
% 3.90/1.18 unary 22
% 3.90/1.18 binary 20
% 3.90/1.18 lits 99
% 3.90/1.18 lits eq 7
% 3.90/1.18 fd_pure 0
% 3.90/1.18 fd_pseudo 0
% 3.90/1.18 fd_cond 1
% 3.90/1.18 fd_pseudo_cond 4
% 3.90/1.18 AC symbols 0
% 3.90/1.18
% 3.90/1.18 ------ Schedule dynamic 5 is on
% 3.90/1.18
% 3.90/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.90/1.18
% 3.90/1.18
% 3.90/1.18 ------
% 3.90/1.18 Current options:
% 3.90/1.18 ------
% 3.90/1.18
% 3.90/1.18
% 3.90/1.18
% 3.90/1.18
% 3.90/1.18 ------ Proving...
% 3.90/1.18
% 3.90/1.18
% 3.90/1.18 % SZS status Theorem for theBenchmark.p
% 3.90/1.18
% 3.90/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.90/1.18
% 3.90/1.18
%------------------------------------------------------------------------------