TSTP Solution File: SET890+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET890+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 03:01:56 EDT 2024
% Result : Theorem 3.58s 1.18s
% Output : CNFRefutation 3.58s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f6,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(f10,conjecture,
! [X0] : union(singleton(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0] : union(singleton(X0)) = X0,
inference(negated_conjecture,[],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f16,plain,
? [X0] : union(singleton(X0)) != X0,
inference(ennf_transformation,[],[f11]) ).
fof(f17,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f20,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f20,f21]) ).
fof(f23,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,[],[f14]) ).
fof(f24,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,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK1(X0,X1),X1)
& in(sK1(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f24,f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( union(X0) = X1
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ in(X2,X1) ) )
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f28,plain,
! [X0,X1] :
( ( union(X0) = X1
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(rectify,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK2(X0,X1),X3) )
| ~ in(sK2(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK2(X0,X1),X4) )
| in(sK2(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK2(X0,X1),X4) )
=> ( in(sK3(X0,X1),X0)
& in(sK2(X0,X1),sK3(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK4(X0,X5),X0)
& in(X5,sK4(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
! [X0,X1] :
( ( union(X0) = X1
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK2(X0,X1),X3) )
| ~ in(sK2(X0,X1),X1) )
& ( ( in(sK3(X0,X1),X0)
& in(sK2(X0,X1),sK3(X0,X1)) )
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK4(X0,X5),X0)
& in(X5,sK4(X0,X5)) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f28,f31,f30,f29]) ).
fof(f37,plain,
( ? [X0] : union(singleton(X0)) != X0
=> sK7 != union(singleton(sK7)) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
sK7 != union(singleton(sK7)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f16,f37]) ).
fof(f42,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f43,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f48,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f49,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f50,plain,
! [X0,X1,X5] :
( in(X5,sK4(X0,X5))
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f32]) ).
fof(f51,plain,
! [X0,X1,X5] :
( in(sK4(X0,X5),X0)
| ~ in(X5,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f32]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f60,plain,
sK7 != union(singleton(sK7)),
inference(cnf_transformation,[],[f38]) ).
fof(f63,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f44]) ).
fof(f64,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f63]) ).
fof(f65,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f43]) ).
fof(f67,plain,
! [X0,X5] :
( in(sK4(X0,X5),X0)
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f51]) ).
fof(f68,plain,
! [X0,X5] :
( in(X5,sK4(X0,X5))
| ~ in(X5,union(X0)) ),
inference(equality_resolution,[],[f50]) ).
cnf(c_50,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f42]) ).
cnf(c_55,plain,
in(X0,singleton(X0)),
inference(cnf_transformation,[],[f64]) ).
cnf(c_56,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_57,plain,
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
cnf(c_58,plain,
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
cnf(c_64,plain,
( ~ in(X0,union(X1))
| in(sK4(X1,X0),X1) ),
inference(cnf_transformation,[],[f67]) ).
cnf(c_65,plain,
( ~ in(X0,union(X1))
| in(X0,sK4(X1,X0)) ),
inference(cnf_transformation,[],[f68]) ).
cnf(c_66,plain,
( ~ in(X0,X1)
| subset(X0,union(X1)) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_70,negated_conjecture,
union(singleton(sK7)) != sK7,
inference(cnf_transformation,[],[f60]) ).
cnf(c_429,plain,
singleton(sK7) = sP0_iProver_def,
definition ).
cnf(c_430,plain,
union(sP0_iProver_def) = sP1_iProver_def,
definition ).
cnf(c_431,negated_conjecture,
sP1_iProver_def != sK7,
inference(demodulation,[status(thm)],[c_70,c_429,c_430]) ).
cnf(c_685,plain,
in(sK7,sP0_iProver_def),
inference(superposition,[status(thm)],[c_429,c_55]) ).
cnf(c_708,plain,
( ~ in(X0,sP0_iProver_def)
| subset(X0,sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_430,c_66]) ).
cnf(c_711,plain,
( ~ in(sK7,sP0_iProver_def)
| subset(sK7,sP1_iProver_def) ),
inference(instantiation,[status(thm)],[c_708]) ).
cnf(c_718,plain,
( ~ in(X0,sP0_iProver_def)
| X0 = sK7 ),
inference(superposition,[status(thm)],[c_429,c_56]) ).
cnf(c_735,plain,
subset(sK7,sP1_iProver_def),
inference(superposition,[status(thm)],[c_685,c_708]) ).
cnf(c_766,plain,
( ~ in(X0,union(sP0_iProver_def))
| sK4(sP0_iProver_def,X0) = sK7 ),
inference(superposition,[status(thm)],[c_64,c_718]) ).
cnf(c_771,plain,
( ~ in(X0,sP1_iProver_def)
| sK4(sP0_iProver_def,X0) = sK7 ),
inference(light_normalisation,[status(thm)],[c_766,c_430]) ).
cnf(c_798,plain,
( sK4(sP0_iProver_def,sK1(sP1_iProver_def,X0)) = sK7
| subset(sP1_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_58,c_771]) ).
cnf(c_879,plain,
( ~ subset(sP1_iProver_def,sK7)
| sK7 = sP1_iProver_def ),
inference(superposition,[status(thm)],[c_735,c_50]) ).
cnf(c_901,plain,
( ~ subset(sK7,sP1_iProver_def)
| ~ subset(sP1_iProver_def,sK7)
| sP1_iProver_def = sK7 ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_1017,plain,
( in(sK1(sP1_iProver_def,sK7),sP1_iProver_def)
| subset(sP1_iProver_def,sK7) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_1018,plain,
( ~ in(sK1(sP1_iProver_def,sK7),sK7)
| subset(sP1_iProver_def,sK7) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_1046,plain,
~ subset(sP1_iProver_def,sK7),
inference(global_subsumption_just,[status(thm)],[c_879,c_431,c_685,c_711,c_901]) ).
cnf(c_1846,plain,
sK4(sP0_iProver_def,sK1(sP1_iProver_def,sK7)) = sK7,
inference(superposition,[status(thm)],[c_798,c_1046]) ).
cnf(c_1949,plain,
( ~ in(sK1(sP1_iProver_def,sK7),union(sP0_iProver_def))
| in(sK1(sP1_iProver_def,sK7),sK7) ),
inference(superposition,[status(thm)],[c_1846,c_65]) ).
cnf(c_1954,plain,
( ~ in(sK1(sP1_iProver_def,sK7),sP1_iProver_def)
| in(sK1(sP1_iProver_def,sK7),sK7) ),
inference(light_normalisation,[status(thm)],[c_1949,c_430]) ).
cnf(c_1960,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1954,c_1017,c_1018,c_901,c_711,c_685,c_431]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET890+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu May 2 20:37:46 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 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
% 3.58/1.18 % SZS status Started for theBenchmark.p
% 3.58/1.18 % SZS status Theorem for theBenchmark.p
% 3.58/1.18
% 3.58/1.18 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.58/1.18
% 3.58/1.18 ------ iProver source info
% 3.58/1.18
% 3.58/1.18 git: date: 2024-05-02 19:28:25 +0000
% 3.58/1.18 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.58/1.18 git: non_committed_changes: false
% 3.58/1.18
% 3.58/1.18 ------ Parsing...
% 3.58/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.58/1.18
% 3.58/1.18 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 3.58/1.18
% 3.58/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.58/1.18
% 3.58/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.58/1.18 ------ Proving...
% 3.58/1.18 ------ Problem Properties
% 3.58/1.18
% 3.58/1.18
% 3.58/1.18 clauses 21
% 3.58/1.18 conjectures 1
% 3.58/1.18 EPR 6
% 3.58/1.18 Horn 17
% 3.58/1.18 unary 6
% 3.58/1.18 binary 7
% 3.58/1.18 lits 45
% 3.58/1.18 lits eq 13
% 3.58/1.18 fd_pure 0
% 3.58/1.18 fd_pseudo 0
% 3.58/1.18 fd_cond 0
% 3.58/1.18 fd_pseudo_cond 6
% 3.58/1.18 AC symbols 0
% 3.58/1.18
% 3.58/1.18 ------ Schedule dynamic 5 is on
% 3.58/1.18
% 3.58/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.58/1.18
% 3.58/1.18
% 3.58/1.18 ------
% 3.58/1.18 Current options:
% 3.58/1.18 ------
% 3.58/1.18
% 3.58/1.18
% 3.58/1.18
% 3.58/1.18
% 3.58/1.18 ------ Proving...
% 3.58/1.18
% 3.58/1.18
% 3.58/1.18 % SZS status Theorem for theBenchmark.p
% 3.58/1.18
% 3.58/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.58/1.18
% 3.58/1.19
%------------------------------------------------------------------------------