TSTP Solution File: SET635+3 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET635+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.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 : Thu Aug 31 15:08:49 EDT 2023
% Result : Theorem 3.78s 1.16s
% Output : CNFRefutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 33 unt; 0 def)
% Number of atoms : 62 ( 43 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 11 |; 6 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn; 43 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).
fof(f3,axiom,
! [X0] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_empty_set) ).
fof(f4,axiom,
! [X0,X1,X2] : difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection_and_union) ).
fof(f5,axiom,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_and_intersection) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f9,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f11,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f16,conjecture,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),intersection(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th117) ).
fof(f17,negated_conjecture,
~ ! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),intersection(X0,X2)),
inference(negated_conjecture,[],[f16]) ).
fof(f19,plain,
? [X0,X1,X2] : intersection(X0,difference(X1,X2)) != difference(intersection(X0,X1),intersection(X0,X2)),
inference(ennf_transformation,[],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ( difference(X0,X1) = empty_set
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| difference(X0,X1) != empty_set ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f25,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f26,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f25]) ).
fof(f35,plain,
( ? [X0,X1,X2] : intersection(X0,difference(X1,X2)) != difference(intersection(X0,X1),intersection(X0,X2))
=> intersection(sK2,difference(sK3,sK4)) != difference(intersection(sK2,sK3),intersection(sK2,sK4)) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
intersection(sK2,difference(sK3,sK4)) != difference(intersection(sK2,sK3),intersection(sK2,sK4)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f19,f35]) ).
fof(f39,plain,
! [X0,X1] :
( difference(X0,X1) = empty_set
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f41,plain,
! [X2,X0,X1] : difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
inference(cnf_transformation,[],[f4]) ).
fof(f42,plain,
! [X2,X0,X1] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f52,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f54,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f63,plain,
intersection(sK2,difference(sK3,sK4)) != difference(intersection(sK2,sK3),intersection(sK2,sK4)),
inference(cnf_transformation,[],[f36]) ).
fof(f65,plain,
! [X1] : subset(X1,X1),
inference(equality_resolution,[],[f49]) ).
cnf(c_50,plain,
( ~ subset(X0,X1)
| difference(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_52,plain,
union(X0,empty_set) = X0,
inference(cnf_transformation,[],[f40]) ).
cnf(c_53,plain,
union(difference(X0,X1),difference(X0,X2)) = difference(X0,intersection(X1,X2)),
inference(cnf_transformation,[],[f41]) ).
cnf(c_54,plain,
intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
inference(cnf_transformation,[],[f42]) ).
cnf(c_63,plain,
subset(X0,X0),
inference(cnf_transformation,[],[f65]) ).
cnf(c_64,plain,
union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f52]) ).
cnf(c_66,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f54]) ).
cnf(c_73,negated_conjecture,
difference(intersection(sK2,sK3),intersection(sK2,sK4)) != intersection(sK2,difference(sK3,sK4)),
inference(cnf_transformation,[],[f63]) ).
cnf(c_295,plain,
intersection(sK2,difference(sK3,intersection(sK2,sK4))) != intersection(sK2,difference(sK3,sK4)),
inference(demodulation,[status(thm)],[c_73,c_54]) ).
cnf(c_941,plain,
union(empty_set,X0) = X0,
inference(superposition,[status(thm)],[c_52,c_64]) ).
cnf(c_996,plain,
difference(X0,X0) = empty_set,
inference(superposition,[status(thm)],[c_63,c_50]) ).
cnf(c_1001,plain,
difference(X0,intersection(X0,X1)) = union(empty_set,difference(X0,X1)),
inference(superposition,[status(thm)],[c_996,c_53]) ).
cnf(c_1062,plain,
intersection(X0,difference(X1,X2)) = difference(intersection(X1,X0),X2),
inference(superposition,[status(thm)],[c_66,c_54]) ).
cnf(c_1236,plain,
difference(X0,intersection(X0,X1)) = difference(X0,X1),
inference(demodulation,[status(thm)],[c_1001,c_941]) ).
cnf(c_2594,plain,
intersection(X0,difference(X1,X2)) = intersection(X1,difference(X0,X2)),
inference(superposition,[status(thm)],[c_1062,c_54]) ).
cnf(c_6893,plain,
intersection(X0,difference(X1,intersection(X0,X2))) = intersection(X1,difference(X0,X2)),
inference(superposition,[status(thm)],[c_1236,c_2594]) ).
cnf(c_7065,plain,
intersection(sK2,difference(sK3,sK4)) != intersection(sK3,difference(sK2,sK4)),
inference(demodulation,[status(thm)],[c_295,c_6893]) ).
cnf(c_7066,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7065,c_2594]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET635+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n011.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 : Sat Aug 26 12:28:54 EDT 2023
% 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 --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.78/1.16 % SZS status Started for theBenchmark.p
% 3.78/1.16 % SZS status Theorem for theBenchmark.p
% 3.78/1.16
% 3.78/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.78/1.16
% 3.78/1.16 ------ iProver source info
% 3.78/1.16
% 3.78/1.16 git: date: 2023-05-31 18:12:56 +0000
% 3.78/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.78/1.16 git: non_committed_changes: false
% 3.78/1.16 git: last_make_outside_of_git: false
% 3.78/1.16
% 3.78/1.16 ------ Parsing...
% 3.78/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.78/1.16
% 3.78/1.16 ------ Preprocessing... sup_sim: 1 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
% 3.78/1.16
% 3.78/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.78/1.16
% 3.78/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.78/1.16 ------ Proving...
% 3.78/1.16 ------ Problem Properties
% 3.78/1.16
% 3.78/1.16
% 3.78/1.16 clauses 23
% 3.78/1.16 conjectures 0
% 3.78/1.16 EPR 4
% 3.78/1.16 Horn 20
% 3.78/1.16 unary 9
% 3.78/1.16 binary 8
% 3.78/1.16 lits 43
% 3.78/1.16 lits eq 11
% 3.78/1.16 fd_pure 0
% 3.78/1.16 fd_pseudo 0
% 3.78/1.16 fd_cond 0
% 3.78/1.16 fd_pseudo_cond 3
% 3.78/1.16 AC symbols 0
% 3.78/1.16
% 3.78/1.16 ------ Schedule dynamic 5 is on
% 3.78/1.16
% 3.78/1.16 ------ no conjectures: strip conj schedule
% 3.78/1.16
% 3.78/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.78/1.16
% 3.78/1.16
% 3.78/1.16 ------
% 3.78/1.16 Current options:
% 3.78/1.16 ------
% 3.78/1.16
% 3.78/1.16
% 3.78/1.16
% 3.78/1.16
% 3.78/1.16 ------ Proving...
% 3.78/1.16
% 3.78/1.16
% 3.78/1.16 % SZS status Theorem for theBenchmark.p
% 3.78/1.16
% 3.78/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.78/1.17
% 3.78/1.17
%------------------------------------------------------------------------------