TSTP Solution File: SET984+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET984+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n018.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 : Mon Jun 24 14:36:46 EDT 2024
% Result : Theorem 24.53s 4.18s
% Output : CNFRefutation 24.53s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f7,axiom,
! [X0,X1] :
( empty_set = cartesian_product2(X0,X1)
<=> ( empty_set = X1
| empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(f8,axiom,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) = cartesian_product2(X2,X3)
=> ( ( X1 = X3
& X0 = X2 )
| empty_set = X1
| empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(f10,conjecture,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
=> ( ( subset(X1,X3)
& subset(X0,X2) )
| empty_set = cartesian_product2(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
=> ( ( subset(X1,X3)
& subset(X0,X2) )
| empty_set = cartesian_product2(X0,X1) ) ),
inference(negated_conjecture,[],[f10]) ).
fof(f12,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f13,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f14,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f3]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( ( X1 = X3
& X0 = X2 )
| empty_set = X1
| empty_set = X0
| cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ( X1 = X3
& X0 = X2 )
| empty_set = X1
| empty_set = X0
| cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
? [X0,X1,X2,X3] :
( ( ~ subset(X1,X3)
| ~ subset(X0,X2) )
& empty_set != cartesian_product2(X0,X1)
& subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f19,plain,
? [X0,X1,X2,X3] :
( ( ~ subset(X1,X3)
| ~ subset(X0,X2) )
& empty_set != cartesian_product2(X0,X1)
& subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f25,plain,
! [X0,X1] :
( ( empty_set = cartesian_product2(X0,X1)
| ( empty_set != X1
& empty_set != X0 ) )
& ( empty_set = X1
| empty_set = X0
| empty_set != cartesian_product2(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f26,plain,
! [X0,X1] :
( ( empty_set = cartesian_product2(X0,X1)
| ( empty_set != X1
& empty_set != X0 ) )
& ( empty_set = X1
| empty_set = X0
| empty_set != cartesian_product2(X0,X1) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
( ? [X0,X1,X2,X3] :
( ( ~ subset(X1,X3)
| ~ subset(X0,X2) )
& empty_set != cartesian_product2(X0,X1)
& subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) )
=> ( ( ~ subset(sK3,sK5)
| ~ subset(sK2,sK4) )
& empty_set != cartesian_product2(sK2,sK3)
& subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( ( ~ subset(sK3,sK5)
| ~ subset(sK2,sK4) )
& empty_set != cartesian_product2(sK2,sK3)
& subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f19,f27]) ).
fof(f29,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f31,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f14]) ).
fof(f35,plain,
! [X0,X1] :
( empty_set = X1
| empty_set = X0
| empty_set != cartesian_product2(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f36,plain,
! [X0,X1] :
( empty_set = cartesian_product2(X0,X1)
| empty_set != X0 ),
inference(cnf_transformation,[],[f26]) ).
fof(f37,plain,
! [X0,X1] :
( empty_set = cartesian_product2(X0,X1)
| empty_set != X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f38,plain,
! [X2,X3,X0,X1] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[],[f8]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| empty_set = X1
| empty_set = X0
| cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| empty_set = X1
| empty_set = X0
| cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f41,plain,
subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f28]) ).
fof(f42,plain,
empty_set != cartesian_product2(sK2,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f43,plain,
( ~ subset(sK3,sK5)
| ~ subset(sK2,sK4) ),
inference(cnf_transformation,[],[f28]) ).
fof(f44,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f12]) ).
fof(f45,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f46,plain,
! [X0] : empty_set = cartesian_product2(X0,empty_set),
inference(equality_resolution,[],[f37]) ).
fof(f47,plain,
! [X1] : empty_set = cartesian_product2(empty_set,X1),
inference(equality_resolution,[],[f36]) ).
cnf(c_49,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f29]) ).
cnf(c_51,plain,
set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f31]) ).
cnf(c_55,plain,
cartesian_product2(X0,empty_set) = empty_set,
inference(cnf_transformation,[],[f46]) ).
cnf(c_56,plain,
cartesian_product2(empty_set,X0) = empty_set,
inference(cnf_transformation,[],[f47]) ).
cnf(c_57,plain,
( cartesian_product2(X0,X1) != empty_set
| X0 = empty_set
| X1 = empty_set ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_58,plain,
set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = cartesian_product2(set_intersection2(X0,X2),set_intersection2(X1,X3)),
inference(cnf_transformation,[],[f38]) ).
cnf(c_59,plain,
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
| X0 = empty_set
| X1 = X3
| X1 = empty_set ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_60,plain,
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
| X0 = X2
| X0 = empty_set
| X1 = empty_set ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_61,negated_conjecture,
( ~ subset(sK3,sK5)
| ~ subset(sK2,sK4) ),
inference(cnf_transformation,[],[f43]) ).
cnf(c_62,negated_conjecture,
cartesian_product2(sK2,sK3) != empty_set,
inference(cnf_transformation,[],[f42]) ).
cnf(c_63,negated_conjecture,
subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f41]) ).
cnf(c_64,plain,
subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f44]) ).
cnf(c_65,plain,
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_173,plain,
cartesian_product2(sK2,sK3) = sP0_iProver_def,
definition ).
cnf(c_174,plain,
cartesian_product2(sK4,sK5) = sP1_iProver_def,
definition ).
cnf(c_175,negated_conjecture,
subset(sP0_iProver_def,sP1_iProver_def),
inference(demodulation,[status(thm)],[c_63,c_174,c_173]) ).
cnf(c_176,negated_conjecture,
sP0_iProver_def != empty_set,
inference(demodulation,[status(thm)],[c_62]) ).
cnf(c_178,plain,
X0 = X0,
theory(equality) ).
cnf(c_180,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_494,plain,
( empty_set != X0
| sP0_iProver_def != X0
| sP0_iProver_def = empty_set ),
inference(instantiation,[status(thm)],[c_180]) ).
cnf(c_584,plain,
( empty_set != sP0_iProver_def
| sP0_iProver_def != sP0_iProver_def
| sP0_iProver_def = empty_set ),
inference(instantiation,[status(thm)],[c_494]) ).
cnf(c_585,plain,
sP0_iProver_def = sP0_iProver_def,
inference(instantiation,[status(thm)],[c_178]) ).
cnf(c_6545,plain,
subset(set_intersection2(X0,X1),X1),
inference(superposition,[status(thm)],[c_49,c_64]) ).
cnf(c_6556,plain,
set_intersection2(sP0_iProver_def,sP1_iProver_def) = sP0_iProver_def,
inference(superposition,[status(thm)],[c_175,c_65]) ).
cnf(c_6579,plain,
cartesian_product2(set_intersection2(sK2,X0),set_intersection2(sK3,X1)) = set_intersection2(sP0_iProver_def,cartesian_product2(X0,X1)),
inference(superposition,[status(thm)],[c_173,c_58]) ).
cnf(c_6586,plain,
subset(cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)),cartesian_product2(X1,X3)),
inference(superposition,[status(thm)],[c_58,c_6545]) ).
cnf(c_6703,plain,
subset(cartesian_product2(set_intersection2(X0,X1),X2),cartesian_product2(X1,X2)),
inference(superposition,[status(thm)],[c_51,c_6586]) ).
cnf(c_26079,plain,
( set_intersection2(sP0_iProver_def,cartesian_product2(X0,X1)) != cartesian_product2(X2,X3)
| set_intersection2(sK2,X0) = X2
| X2 = empty_set
| X3 = empty_set ),
inference(superposition,[status(thm)],[c_6579,c_60]) ).
cnf(c_26080,plain,
( set_intersection2(sP0_iProver_def,cartesian_product2(X0,X1)) != cartesian_product2(X2,X3)
| set_intersection2(sK3,X1) = X3
| X2 = empty_set
| X3 = empty_set ),
inference(superposition,[status(thm)],[c_6579,c_59]) ).
cnf(c_26087,plain,
subset(set_intersection2(sP0_iProver_def,cartesian_product2(X0,X1)),cartesian_product2(X0,set_intersection2(sK3,X1))),
inference(superposition,[status(thm)],[c_6579,c_6703]) ).
cnf(c_26623,plain,
subset(set_intersection2(sP0_iProver_def,sP1_iProver_def),cartesian_product2(sK4,set_intersection2(sK3,sK5))),
inference(superposition,[status(thm)],[c_174,c_26087]) ).
cnf(c_26635,plain,
subset(sP0_iProver_def,cartesian_product2(sK4,set_intersection2(sK3,sK5))),
inference(light_normalisation,[status(thm)],[c_26623,c_6556]) ).
cnf(c_40884,plain,
( cartesian_product2(X0,X1) != set_intersection2(sP0_iProver_def,sP1_iProver_def)
| set_intersection2(sK2,sK4) = X0
| X0 = empty_set
| X1 = empty_set ),
inference(superposition,[status(thm)],[c_174,c_26079]) ).
cnf(c_40897,plain,
( cartesian_product2(X0,X1) != sP0_iProver_def
| set_intersection2(sK2,sK4) = X0
| X0 = empty_set
| X1 = empty_set ),
inference(light_normalisation,[status(thm)],[c_40884,c_6556]) ).
cnf(c_41009,plain,
( cartesian_product2(X0,X1) != set_intersection2(sP0_iProver_def,sP1_iProver_def)
| set_intersection2(sK3,sK5) = X1
| X0 = empty_set
| X1 = empty_set ),
inference(superposition,[status(thm)],[c_174,c_26080]) ).
cnf(c_41022,plain,
( cartesian_product2(X0,X1) != sP0_iProver_def
| set_intersection2(sK3,sK5) = X1
| X0 = empty_set
| X1 = empty_set ),
inference(light_normalisation,[status(thm)],[c_41009,c_6556]) ).
cnf(c_42842,plain,
( set_intersection2(sK2,sK4) = sK2
| empty_set = sK3
| empty_set = sK2 ),
inference(superposition,[status(thm)],[c_173,c_40897]) ).
cnf(c_43569,plain,
( set_intersection2(sK3,sK5) = sK3
| empty_set = sK3
| empty_set = sK2 ),
inference(superposition,[status(thm)],[c_173,c_41022]) ).
cnf(c_43806,plain,
( empty_set = sK3
| empty_set = sK2
| subset(sK2,sK4) ),
inference(superposition,[status(thm)],[c_42842,c_6545]) ).
cnf(c_45586,plain,
( empty_set = sK3
| empty_set = sK2
| subset(sK3,sK5) ),
inference(superposition,[status(thm)],[c_43569,c_6545]) ).
cnf(c_45648,plain,
( empty_set = sK3
| empty_set = sK2
| subset(sP0_iProver_def,cartesian_product2(sK4,sK3)) ),
inference(superposition,[status(thm)],[c_43569,c_26635]) ).
cnf(c_52907,plain,
( empty_set = sK2
| empty_set = sK3 ),
inference(global_subsumption_just,[status(thm)],[c_45648,c_61,c_43806,c_45586]) ).
cnf(c_52908,plain,
( empty_set = sK3
| empty_set = sK2 ),
inference(renaming,[status(thm)],[c_52907]) ).
cnf(c_60484,plain,
( empty_set != sP0_iProver_def
| empty_set = sK3
| empty_set = sK2 ),
inference(superposition,[status(thm)],[c_173,c_57]) ).
cnf(c_60492,plain,
( empty_set = sK3
| empty_set = sK2 ),
inference(global_subsumption_just,[status(thm)],[c_60484,c_52908]) ).
cnf(c_60498,plain,
( cartesian_product2(empty_set,sK3) = sP0_iProver_def
| empty_set = sK3 ),
inference(superposition,[status(thm)],[c_60492,c_173]) ).
cnf(c_60511,plain,
( empty_set = sK3
| empty_set = sP0_iProver_def ),
inference(demodulation,[status(thm)],[c_60498,c_56]) ).
cnf(c_60518,plain,
( cartesian_product2(sK2,empty_set) = sP0_iProver_def
| empty_set = sP0_iProver_def ),
inference(superposition,[status(thm)],[c_60511,c_173]) ).
cnf(c_60547,plain,
cartesian_product2(sK2,empty_set) = sP0_iProver_def,
inference(global_subsumption_just,[status(thm)],[c_60518,c_176,c_584,c_585,c_60518]) ).
cnf(c_60549,plain,
empty_set = sP0_iProver_def,
inference(demodulation,[status(thm)],[c_60547,c_55]) ).
cnf(c_60558,plain,
sP0_iProver_def != sP0_iProver_def,
inference(demodulation,[status(thm)],[c_176,c_60549]) ).
cnf(c_60559,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_60558]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET984+1 : TPTP v8.2.0. Released v3.2.0.
% 0.07/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jun 23 13:32:54 EDT 2024
% 0.12/0.33 % 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
% 24.53/4.18 % SZS status Started for theBenchmark.p
% 24.53/4.18 % SZS status Theorem for theBenchmark.p
% 24.53/4.18
% 24.53/4.18 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 24.53/4.18
% 24.53/4.18 ------ iProver source info
% 24.53/4.18
% 24.53/4.18 git: date: 2024-06-12 09:56:46 +0000
% 24.53/4.18 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 24.53/4.18 git: non_committed_changes: false
% 24.53/4.18
% 24.53/4.18 ------ Parsing...
% 24.53/4.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 24.53/4.18
% 24.53/4.18 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 24.53/4.18
% 24.53/4.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 24.53/4.18
% 24.53/4.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 24.53/4.18 ------ Proving...
% 24.53/4.18 ------ Problem Properties
% 24.53/4.18
% 24.53/4.18
% 24.53/4.18 clauses 19
% 24.53/4.18 conjectures 3
% 24.53/4.18 EPR 7
% 24.53/4.18 Horn 16
% 24.53/4.18 unary 14
% 24.53/4.18 binary 2
% 24.53/4.18 lits 29
% 24.53/4.18 lits eq 20
% 24.53/4.18 fd_pure 0
% 24.53/4.18 fd_pseudo 0
% 24.53/4.18 fd_cond 1
% 24.53/4.18 fd_pseudo_cond 2
% 24.53/4.18 AC symbols 0
% 24.53/4.18
% 24.53/4.18 ------ Schedule dynamic 5 is on
% 24.53/4.18
% 24.53/4.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 24.53/4.18
% 24.53/4.18
% 24.53/4.18 ------
% 24.53/4.18 Current options:
% 24.53/4.18 ------
% 24.53/4.18
% 24.53/4.18
% 24.53/4.18
% 24.53/4.18
% 24.53/4.18 ------ Proving...
% 24.53/4.18
% 24.53/4.18
% 24.53/4.18 % SZS status Theorem for theBenchmark.p
% 24.53/4.18
% 24.53/4.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.53/4.18
% 24.53/4.19
%------------------------------------------------------------------------------