TSTP Solution File: SET577+3 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET577+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n010.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 03:00:48 EDT 2024
% Result : Theorem 2.98s 1.14s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f6,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f7,conjecture,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
| member(X3,X1) ) )
=> union(X1,X2) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th18) ).
fof(f8,negated_conjecture,
~ ! [X0,X1,X2] :
( ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
| member(X3,X1) ) )
=> union(X1,X2) = X0 ),
inference(negated_conjecture,[],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
? [X0,X1,X2] :
( union(X1,X2) != X0
& ! [X3] :
( member(X3,X0)
<=> ( member(X3,X2)
| member(X3,X1) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f11]) ).
fof(f15,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f16,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) )
=> ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f20,f21]) ).
fof(f23,plain,
? [X0,X1,X2] :
( union(X1,X2) != X0
& ! [X3] :
( ( member(X3,X0)
| ( ~ member(X3,X2)
& ~ member(X3,X1) ) )
& ( member(X3,X2)
| member(X3,X1)
| ~ member(X3,X0) ) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f24,plain,
? [X0,X1,X2] :
( union(X1,X2) != X0
& ! [X3] :
( ( member(X3,X0)
| ( ~ member(X3,X2)
& ~ member(X3,X1) ) )
& ( member(X3,X2)
| member(X3,X1)
| ~ member(X3,X0) ) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
( ? [X0,X1,X2] :
( union(X1,X2) != X0
& ! [X3] :
( ( member(X3,X0)
| ( ~ member(X3,X2)
& ~ member(X3,X1) ) )
& ( member(X3,X2)
| member(X3,X1)
| ~ member(X3,X0) ) ) )
=> ( sK2 != union(sK3,sK4)
& ! [X3] :
( ( member(X3,sK2)
| ( ~ member(X3,sK4)
& ~ member(X3,sK3) ) )
& ( member(X3,sK4)
| member(X3,sK3)
| ~ member(X3,sK2) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
( sK2 != union(sK3,sK4)
& ! [X3] :
( ( member(X3,sK2)
| ( ~ member(X3,sK4)
& ~ member(X3,sK3) ) )
& ( member(X3,sK4)
| member(X3,sK3)
| ~ member(X3,sK2) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f24,f25]) ).
fof(f27,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f28,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f29,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f34,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f40,plain,
! [X0,X1] :
( X0 = X1
| member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0,X1] :
( X0 = X1
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X3] :
( member(X3,sK4)
| member(X3,sK3)
| ~ member(X3,sK2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X3] :
( member(X3,sK2)
| ~ member(X3,sK3) ),
inference(cnf_transformation,[],[f26]) ).
fof(f44,plain,
! [X3] :
( member(X3,sK2)
| ~ member(X3,sK4) ),
inference(cnf_transformation,[],[f26]) ).
fof(f45,plain,
sK2 != union(sK3,sK4),
inference(cnf_transformation,[],[f26]) ).
cnf(c_49,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf_transformation,[],[f29]) ).
cnf(c_50,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f28]) ).
cnf(c_51,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f27]) ).
cnf(c_56,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_57,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_58,plain,
( ~ member(X0,X1)
| ~ subset(X1,X2)
| member(X0,X2) ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_60,plain,
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f41]) ).
cnf(c_61,plain,
( X0 = X1
| member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_62,negated_conjecture,
union(sK3,sK4) != sK2,
inference(cnf_transformation,[],[f45]) ).
cnf(c_63,negated_conjecture,
( ~ member(X0,sK4)
| member(X0,sK2) ),
inference(cnf_transformation,[],[f44]) ).
cnf(c_64,negated_conjecture,
( ~ member(X0,sK3)
| member(X0,sK2) ),
inference(cnf_transformation,[],[f43]) ).
cnf(c_65,negated_conjecture,
( ~ member(X0,sK2)
| member(X0,sK3)
| member(X0,sK4) ),
inference(cnf_transformation,[],[f42]) ).
cnf(c_334,plain,
union(sK3,sK4) = sP0_iProver_def,
definition ).
cnf(c_335,negated_conjecture,
( ~ member(X0,sK2)
| member(X0,sK3)
| member(X0,sK4) ),
inference(demodulation,[status(thm)],[c_65]) ).
cnf(c_336,negated_conjecture,
( ~ member(X0,sK3)
| member(X0,sK2) ),
inference(demodulation,[status(thm)],[c_64]) ).
cnf(c_337,negated_conjecture,
( ~ member(X0,sK4)
| member(X0,sK2) ),
inference(demodulation,[status(thm)],[c_63]) ).
cnf(c_338,negated_conjecture,
sP0_iProver_def != sK2,
inference(demodulation,[status(thm)],[c_62,c_334]) ).
cnf(c_339,plain,
X0 = X0,
theory(equality) ).
cnf(c_341,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_544,plain,
( member(sK0(sK4,X0),sK2)
| subset(sK4,X0) ),
inference(superposition,[status(thm)],[c_57,c_337]) ).
cnf(c_546,plain,
( member(sK0(sK3,X0),sK2)
| subset(sK3,X0) ),
inference(superposition,[status(thm)],[c_57,c_336]) ).
cnf(c_562,plain,
( ~ member(X0,sK4)
| member(X0,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_334,c_49]) ).
cnf(c_572,plain,
( ~ member(X0,sK3)
| member(X0,sP0_iProver_def) ),
inference(superposition,[status(thm)],[c_334,c_50]) ).
cnf(c_617,plain,
( ~ member(X0,sP0_iProver_def)
| member(X0,sK3)
| member(X0,sK4) ),
inference(superposition,[status(thm)],[c_334,c_51]) ).
cnf(c_630,plain,
( member(sK0(sK4,X0),sP0_iProver_def)
| subset(sK4,X0) ),
inference(superposition,[status(thm)],[c_57,c_562]) ).
cnf(c_638,plain,
( member(sK0(sK3,X0),sP0_iProver_def)
| subset(sK3,X0) ),
inference(superposition,[status(thm)],[c_57,c_572]) ).
cnf(c_647,plain,
subset(sK4,sK2),
inference(superposition,[status(thm)],[c_544,c_56]) ).
cnf(c_660,plain,
subset(sK3,sK2),
inference(superposition,[status(thm)],[c_546,c_56]) ).
cnf(c_669,plain,
( sK2 != X0
| sP0_iProver_def != X0
| sP0_iProver_def = sK2 ),
inference(instantiation,[status(thm)],[c_341]) ).
cnf(c_692,plain,
( ~ member(sK1(sP0_iProver_def,sK2),sK2)
| ~ member(sK1(sP0_iProver_def,sK2),sP0_iProver_def)
| sP0_iProver_def = sK2 ),
inference(instantiation,[status(thm)],[c_60]) ).
cnf(c_693,plain,
( sP0_iProver_def = sK2
| member(sK1(sP0_iProver_def,sK2),sK2)
| member(sK1(sP0_iProver_def,sK2),sP0_iProver_def) ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_744,plain,
( X0 = sK2
| member(sK1(X0,sK2),X0)
| member(sK1(X0,sK2),sK3)
| member(sK1(X0,sK2),sK4) ),
inference(superposition,[status(thm)],[c_61,c_335]) ).
cnf(c_826,plain,
( ~ member(sK1(sP0_iProver_def,sK2),sK2)
| member(sK1(sP0_iProver_def,sK2),sK3)
| member(sK1(sP0_iProver_def,sK2),sK4) ),
inference(instantiation,[status(thm)],[c_335]) ).
cnf(c_832,plain,
( sK2 != sP0_iProver_def
| sP0_iProver_def != sP0_iProver_def
| sP0_iProver_def = sK2 ),
inference(instantiation,[status(thm)],[c_669]) ).
cnf(c_833,plain,
sP0_iProver_def = sP0_iProver_def,
inference(instantiation,[status(thm)],[c_339]) ).
cnf(c_857,plain,
subset(sK4,sP0_iProver_def),
inference(superposition,[status(thm)],[c_630,c_56]) ).
cnf(c_862,plain,
( ~ member(sK1(sP0_iProver_def,sK2),sK3)
| ~ subset(sK3,X0)
| member(sK1(sP0_iProver_def,sK2),X0) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_867,plain,
( ~ member(sK1(sP0_iProver_def,sK2),sK3)
| ~ subset(sK3,sK2)
| member(sK1(sP0_iProver_def,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_862]) ).
cnf(c_879,plain,
subset(sK3,sP0_iProver_def),
inference(superposition,[status(thm)],[c_638,c_56]) ).
cnf(c_1157,plain,
( ~ member(sK1(sP0_iProver_def,sK2),sK4)
| ~ subset(sK4,X0)
| member(sK1(sP0_iProver_def,sK2),X0) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_1162,plain,
( ~ member(sK1(sP0_iProver_def,sK2),sK4)
| ~ subset(sK4,sK2)
| member(sK1(sP0_iProver_def,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_1157]) ).
cnf(c_1724,plain,
( sK2 = sP0_iProver_def
| member(sK1(sP0_iProver_def,sK2),sK3)
| member(sK1(sP0_iProver_def,sK2),sK4) ),
inference(superposition,[status(thm)],[c_744,c_617]) ).
cnf(c_2080,plain,
( ~ member(sK1(sP0_iProver_def,sK2),sK3)
| ~ subset(sK3,sP0_iProver_def)
| member(sK1(sP0_iProver_def,sK2),sP0_iProver_def) ),
inference(instantiation,[status(thm)],[c_862]) ).
cnf(c_2139,plain,
( ~ member(sK1(sP0_iProver_def,sK2),sK4)
| ~ subset(sK4,sP0_iProver_def)
| member(sK1(sP0_iProver_def,sK2),sP0_iProver_def) ),
inference(instantiation,[status(thm)],[c_1157]) ).
cnf(c_3022,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2139,c_2080,c_1724,c_1162,c_879,c_867,c_857,c_833,c_832,c_826,c_693,c_692,c_660,c_647,c_338]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET577+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.12 % Command : run_iprover %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu May 2 20:08:04 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 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
% 2.98/1.14 % SZS status Started for theBenchmark.p
% 2.98/1.14 % SZS status Theorem for theBenchmark.p
% 2.98/1.14
% 2.98/1.14 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.98/1.14
% 2.98/1.14 ------ iProver source info
% 2.98/1.14
% 2.98/1.14 git: date: 2024-05-02 19:28:25 +0000
% 2.98/1.14 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.98/1.14 git: non_committed_changes: false
% 2.98/1.14
% 2.98/1.14 ------ Parsing...
% 2.98/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.98/1.14
% 2.98/1.14 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 2.98/1.14
% 2.98/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.98/1.14
% 2.98/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.98/1.14 ------ Proving...
% 2.98/1.14 ------ Problem Properties
% 2.98/1.14
% 2.98/1.14
% 2.98/1.14 clauses 16
% 2.98/1.14 conjectures 4
% 2.98/1.14 EPR 7
% 2.98/1.14 Horn 12
% 2.98/1.14 unary 4
% 2.98/1.14 binary 6
% 2.98/1.14 lits 34
% 2.98/1.14 lits eq 6
% 2.98/1.14 fd_pure 0
% 2.98/1.14 fd_pseudo 0
% 2.98/1.14 fd_cond 0
% 2.98/1.14 fd_pseudo_cond 3
% 2.98/1.14 AC symbols 0
% 2.98/1.14
% 2.98/1.14 ------ Schedule dynamic 5 is on
% 2.98/1.14
% 2.98/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.98/1.14
% 2.98/1.14
% 2.98/1.14 ------
% 2.98/1.14 Current options:
% 2.98/1.14 ------
% 2.98/1.14
% 2.98/1.14
% 2.98/1.14
% 2.98/1.14
% 2.98/1.14 ------ Proving...
% 2.98/1.14
% 2.98/1.14
% 2.98/1.14 % SZS status Theorem for theBenchmark.p
% 2.98/1.14
% 2.98/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.98/1.15
% 2.98/1.15
%------------------------------------------------------------------------------