TSTP Solution File: SET921+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET921+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n015.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 03:02:00 EDT 2024
% Result : Theorem 0.46s 1.14s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<=> ( X0 != X2
& in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<=> ( X0 != X2
& in(X0,X1) ) ),
inference(negated_conjecture,[],[f6]) ).
fof(f9,plain,
? [X0,X1,X2] :
( in(X0,set_difference(X1,singleton(X2)))
<~> ( X0 != X2
& in(X0,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,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,[],[f2]) ).
fof(f11,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,[],[f10]) ).
fof(f12,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(f13,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])],[f11,f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( ~ in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) )
| in(sK1(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ( ( in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( ~ in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) )
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f16,f17]) ).
fof(f23,plain,
? [X0,X1,X2] :
( ( X0 = X2
| ~ in(X0,X1)
| ~ in(X0,set_difference(X1,singleton(X2))) )
& ( ( X0 != X2
& in(X0,X1) )
| in(X0,set_difference(X1,singleton(X2))) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f24,plain,
? [X0,X1,X2] :
( ( X0 = X2
| ~ in(X0,X1)
| ~ in(X0,set_difference(X1,singleton(X2))) )
& ( ( X0 != X2
& in(X0,X1) )
| in(X0,set_difference(X1,singleton(X2))) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
( ? [X0,X1,X2] :
( ( X0 = X2
| ~ in(X0,X1)
| ~ in(X0,set_difference(X1,singleton(X2))) )
& ( ( X0 != X2
& in(X0,X1) )
| in(X0,set_difference(X1,singleton(X2))) ) )
=> ( ( sK4 = sK6
| ~ in(sK4,sK5)
| ~ in(sK4,set_difference(sK5,singleton(sK6))) )
& ( ( sK4 != sK6
& in(sK4,sK5) )
| in(sK4,set_difference(sK5,singleton(sK6))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
( ( sK4 = sK6
| ~ in(sK4,sK5)
| ~ in(sK4,set_difference(sK5,singleton(sK6))) )
& ( ( sK4 != sK6
& in(sK4,sK5) )
| in(sK4,set_difference(sK5,singleton(sK6))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f24,f25]) ).
fof(f28,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f13]) ).
fof(f29,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f13]) ).
fof(f32,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f18]) ).
fof(f40,plain,
( in(sK4,sK5)
| in(sK4,set_difference(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
( sK4 != sK6
| in(sK4,set_difference(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
( sK4 = sK6
| ~ in(sK4,sK5)
| ~ in(sK4,set_difference(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f29]) ).
fof(f44,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f43]) ).
fof(f45,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f28]) ).
fof(f46,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f34]) ).
fof(f47,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f33]) ).
fof(f48,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f32]) ).
cnf(c_52,plain,
in(X0,singleton(X0)),
inference(cnf_transformation,[],[f44]) ).
cnf(c_53,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_57,plain,
( ~ in(X0,X1)
| in(X0,set_difference(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f46]) ).
cnf(c_58,plain,
( ~ in(X0,set_difference(X1,X2))
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f47]) ).
cnf(c_59,plain,
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
cnf(c_62,negated_conjecture,
( ~ in(sK4,set_difference(sK5,singleton(sK6)))
| ~ in(sK4,sK5)
| sK4 = sK6 ),
inference(cnf_transformation,[],[f42]) ).
cnf(c_63,negated_conjecture,
( sK4 != sK6
| in(sK4,set_difference(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f41]) ).
cnf(c_64,negated_conjecture,
( in(sK4,set_difference(sK5,singleton(sK6)))
| in(sK4,sK5) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_89,plain,
in(sK4,sK5),
inference(backward_subsumption_resolution,[status(thm)],[c_64,c_59]) ).
cnf(c_218,plain,
( ~ in(sK4,set_difference(sK5,singleton(sK6)))
| sK4 = sK6 ),
inference(prop_impl_just,[status(thm)],[c_62,c_89]) ).
cnf(c_400,plain,
singleton(sK6) = sP0_iProver_def,
definition ).
cnf(c_401,plain,
set_difference(sK5,sP0_iProver_def) = sP1_iProver_def,
definition ).
cnf(c_402,negated_conjecture,
( sK4 != sK6
| in(sK4,sP1_iProver_def) ),
inference(demodulation,[status(thm)],[c_63,c_400,c_401]) ).
cnf(c_613,plain,
in(sK6,sP0_iProver_def),
inference(superposition,[status(thm)],[c_400,c_52]) ).
cnf(c_622,plain,
( ~ in(sK4,sP1_iProver_def)
| sK4 = sK6 ),
inference(light_normalisation,[status(thm)],[c_218,c_400,c_401]) ).
cnf(c_632,plain,
( ~ in(X0,sP0_iProver_def)
| X0 = sK6 ),
inference(superposition,[status(thm)],[c_400,c_53]) ).
cnf(c_635,plain,
( ~ in(sK4,sP0_iProver_def)
| sK4 = sK6 ),
inference(instantiation,[status(thm)],[c_632]) ).
cnf(c_647,plain,
( ~ in(X0,sP0_iProver_def)
| ~ in(X0,sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_401,c_58]) ).
cnf(c_657,plain,
( ~ in(X0,sK5)
| in(X0,sP0_iProver_def)
| in(X0,sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_401,c_57]) ).
cnf(c_667,plain,
( ~ in(sK4,sK5)
| in(sK4,sP0_iProver_def)
| in(sK4,sP1_iProver_def) ),
inference(instantiation,[status(thm)],[c_657]) ).
cnf(c_685,plain,
~ in(sK6,sP1_iProver_def),
inference(superposition,[status(thm)],[c_613,c_647]) ).
cnf(c_692,plain,
( in(sK4,sP0_iProver_def)
| in(sK4,sP1_iProver_def) ),
inference(superposition,[status(thm)],[c_89,c_657]) ).
cnf(c_695,plain,
in(sK4,sP1_iProver_def),
inference(global_subsumption_just,[status(thm)],[c_692,c_89,c_402,c_635,c_667]) ).
cnf(c_697,plain,
sK4 = sK6,
inference(backward_subsumption_resolution,[status(thm)],[c_622,c_695]) ).
cnf(c_698,plain,
~ in(sK4,sP1_iProver_def),
inference(demodulation,[status(thm)],[c_685,c_697]) ).
cnf(c_705,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_698,c_695]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET921+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.12 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu May 2 20:53:51 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.46/1.14 % SZS status Started for theBenchmark.p
% 0.46/1.14 % SZS status Theorem for theBenchmark.p
% 0.46/1.14
% 0.46/1.14 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.46/1.14
% 0.46/1.14 ------ iProver source info
% 0.46/1.14
% 0.46/1.14 git: date: 2024-05-02 19:28:25 +0000
% 0.46/1.14 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.46/1.14 git: non_committed_changes: false
% 0.46/1.14
% 0.46/1.14 ------ Parsing...
% 0.46/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.46/1.14
% 0.46/1.14 ------ 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
% 0.46/1.14
% 0.46/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.46/1.14
% 0.46/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.46/1.14 ------ Proving...
% 0.46/1.14 ------ Problem Properties
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 clauses 17
% 0.46/1.14 conjectures 1
% 0.46/1.14 EPR 4
% 0.46/1.14 Horn 12
% 0.46/1.14 unary 5
% 0.46/1.14 binary 6
% 0.46/1.14 lits 36
% 0.46/1.14 lits eq 13
% 0.46/1.14 fd_pure 0
% 0.46/1.14 fd_pseudo 0
% 0.46/1.14 fd_cond 0
% 0.46/1.14 fd_pseudo_cond 5
% 0.46/1.14 AC symbols 0
% 0.46/1.14
% 0.46/1.14 ------ Schedule dynamic 5 is on
% 0.46/1.14
% 0.46/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 ------
% 0.46/1.14 Current options:
% 0.46/1.14 ------
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 ------ Proving...
% 0.46/1.14
% 0.46/1.14
% 0.46/1.14 % SZS status Theorem for theBenchmark.p
% 0.46/1.14
% 0.46/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.46/1.14
% 0.46/1.14
%------------------------------------------------------------------------------