TSTP Solution File: SEV422_1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEV422_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n024.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 03:09:28 EDT 2024
% Result : Theorem 31.28s 4.64s
% Output : CNFRefutation 31.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV422_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 2 17:58:21 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running TFA theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 31.28/4.64 % SZS status Started for theBenchmark.p
% 31.28/4.64 % SZS status Theorem for theBenchmark.p
% 31.28/4.64
% 31.28/4.64 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 31.28/4.64
% 31.28/4.64 ------ iProver source info
% 31.28/4.64
% 31.28/4.64 git: date: 2024-05-02 19:28:25 +0000
% 31.28/4.64 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 31.28/4.64 git: non_committed_changes: false
% 31.28/4.64
% 31.28/4.64 ------ Parsing...
% 31.28/4.64 ------ Clausification by vclausify_rel & Parsing by iProver...
% 31.28/4.64
% 31.28/4.64 ------ Preprocessing... sup_sim: 7 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 2 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
% 31.28/4.64
% 31.28/4.64 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 31.28/4.64
% 31.28/4.64 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 31.28/4.64 ------ Proving...
% 31.28/4.64 ------ Problem Properties
% 31.28/4.64
% 31.28/4.64
% 31.28/4.64 clauses 37
% 31.28/4.64 conjectures 17
% 31.28/4.64 EPR 5
% 31.28/4.64 Horn 31
% 31.28/4.64 unary 12
% 31.28/4.64 binary 20
% 31.28/4.64 lits 67
% 31.28/4.64 lits eq 26
% 31.28/4.64 fd_pure 0
% 31.28/4.64 fd_pseudo 0
% 31.28/4.64 fd_cond 2
% 31.28/4.64 fd_pseudo_cond 2
% 31.28/4.64 AC symbols 1
% 31.28/4.64
% 31.28/4.64 ------ Input Options Time Limit: Unbounded
% 31.28/4.64
% 31.28/4.64
% 31.28/4.64 ------
% 31.28/4.64 Current options:
% 31.28/4.64 ------
% 31.28/4.64
% 31.28/4.64
% 31.28/4.64
% 31.28/4.64
% 31.28/4.64 ------ Proving...
% 31.28/4.64
% 31.28/4.64
% 31.28/4.64 % SZS status Theorem for theBenchmark.p
% 31.28/4.64
% 31.28/4.64 % SZS output start CNFRefutation for theBenchmark.p
% 31.28/4.64
% 31.28/4.64 tff(f1,axiom,(
% 31.28/4.64 ! [X0 : set] : (! [X1 : element] : ~member(X1,X0) <=> empty_set = X0)),
% 31.28/4.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set)).
% 31.28/4.64
% 31.28/4.64 tff(f2,axiom,(
% 31.28/4.64 ! [X1 : element,X2 : element] : (member(X1,singleton(X2)) <=> X1 = X2)),
% 31.28/4.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)).
% 31.28/4.64
% 31.28/4.64 tff(f4,axiom,(
% 31.28/4.64 ! [X1 : element,X2 : set,X3 : set] : (member(X1,intersection(X2,X3)) <=> (member(X1,X3) & member(X1,X2)))),
% 31.28/4.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection)).
% 31.28/4.64
% 31.28/4.64 tff(f10,axiom,(
% 31.28/4.64 ! [X1 : element,X0 : set] : (empty_set = intersection(singleton(X1),X0) <=> cardinality(union(singleton(X1),X0)) = $sum(cardinality(X0),1))),
% 31.28/4.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cardinality_intersection_2)).
% 31.28/4.64
% 31.28/4.64 tff(f13,conjecture,(
% 31.28/4.64 ! [X1 : element,X6 : set,X7 : $int] : ((cardinality(X6) = X7 & ~member(X1,X6)) => $sum(X7,1) = cardinality(union(singleton(X1),X6)))),
% 31.28/4.64 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vc2)).
% 31.28/4.64
% 31.28/4.64 tff(f14,negated_conjecture,(
% 31.28/4.64 ~! [X1 : element,X6 : set,X7 : $int] : ((cardinality(X6) = X7 & ~member(X1,X6)) => $sum(X7,1) = cardinality(union(singleton(X1),X6)))),
% 31.28/4.64 inference(negated_conjecture,[],[f13])).
% 31.28/4.64
% 31.28/4.64 tff(f15,plain,(
% 31.28/4.64 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 31.28/4.64 introduced(theory_axiom_138,[])).
% 31.28/4.64
% 31.28/4.64 tff(f16,plain,(
% 31.28/4.64 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
% 31.28/4.64 introduced(theory_axiom_139,[])).
% 31.28/4.64
% 31.28/4.64 tff(f27,plain,(
% 31.28/4.64 ! [X0 : element,X1 : element] : (member(X0,singleton(X1)) <=> X0 = X1)),
% 31.28/4.64 inference(rectify,[],[f2])).
% 31.28/4.64
% 31.28/4.64 tff(f29,plain,(
% 31.28/4.64 ! [X0 : element,X1 : set,X2 : set] : (member(X0,intersection(X1,X2)) <=> (member(X0,X2) & member(X0,X1)))),
% 31.28/4.64 inference(rectify,[],[f4])).
% 31.28/4.64
% 31.28/4.64 tff(f34,plain,(
% 31.28/4.64 ! [X0 : element,X1 : set] : (empty_set = intersection(singleton(X0),X1) <=> cardinality(union(singleton(X0),X1)) = $sum(cardinality(X1),1))),
% 31.28/4.64 inference(rectify,[],[f10])).
% 31.28/4.64
% 31.28/4.64 tff(f37,plain,(
% 31.28/4.64 ~! [X0 : element,X1 : set,X2 : $int] : ((cardinality(X1) = X2 & ~member(X0,X1)) => cardinality(union(singleton(X0),X1)) = $sum(X2,1))),
% 31.28/4.64 inference(rectify,[],[f14])).
% 31.28/4.64
% 31.28/4.64 tff(f38,plain,(
% 31.28/4.64 ? [X0 : element,X1 : set,X2 : $int] : (cardinality(union(singleton(X0),X1)) != $sum(X2,1) & (cardinality(X1) = X2 & ~member(X0,X1)))),
% 31.28/4.64 inference(ennf_transformation,[],[f37])).
% 31.28/4.64
% 31.28/4.64 tff(f39,plain,(
% 31.28/4.64 ? [X0 : element,X1 : set,X2 : $int] : (cardinality(union(singleton(X0),X1)) != $sum(X2,1) & cardinality(X1) = X2 & ~member(X0,X1))),
% 31.28/4.64 inference(flattening,[],[f38])).
% 31.28/4.64
% 31.28/4.64 tff(f40,plain,(
% 31.28/4.64 ! [X0 : set] : ((! [X1 : element] : ~member(X1,X0) | empty_set != X0) & (empty_set = X0 | ? [X1 : element] : member(X1,X0)))),
% 31.28/4.64 inference(nnf_transformation,[],[f1])).
% 31.28/4.64
% 31.28/4.64 tff(f41,plain,(
% 31.28/4.64 ! [X0 : set] : ((! [X1 : element] : ~member(X1,X0) | empty_set != X0) & (empty_set = X0 | ? [X2 : element] : member(X2,X0)))),
% 31.28/4.64 inference(rectify,[],[f40])).
% 31.28/4.64
% 31.28/4.64 tff(f42,plain,(
% 31.28/4.64 ! [X0 : set] : (? [X2 : element] : member(X2,X0) => member(sK0(X0),X0))),
% 31.28/4.64 introduced(choice_axiom,[])).
% 31.28/4.64
% 31.28/4.64 tff(f43,plain,(
% 31.28/4.64 ! [X0 : set] : ((! [X1 : element] : ~member(X1,X0) | empty_set != X0) & (empty_set = X0 | member(sK0(X0),X0)))),
% 31.28/4.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f41,f42])).
% 31.28/4.64
% 31.28/4.64 tff(f44,plain,(
% 31.28/4.64 ! [X0 : element,X1 : element] : ((member(X0,singleton(X1)) | X0 != X1) & (X0 = X1 | ~member(X0,singleton(X1))))),
% 31.28/4.64 inference(nnf_transformation,[],[f27])).
% 31.28/4.64
% 31.28/4.64 tff(f45,plain,(
% 31.28/4.64 ! [X0 : element,X1 : set,X2 : set] : ((member(X0,intersection(X1,X2)) | (~member(X0,X2) | ~member(X0,X1))) & ((member(X0,X2) & member(X0,X1)) | ~member(X0,intersection(X1,X2))))),
% 31.28/4.64 inference(nnf_transformation,[],[f29])).
% 31.28/4.64
% 31.28/4.64 tff(f46,plain,(
% 31.28/4.64 ! [X0 : element,X1 : set,X2 : set] : ((member(X0,intersection(X1,X2)) | ~member(X0,X2) | ~member(X0,X1)) & ((member(X0,X2) & member(X0,X1)) | ~member(X0,intersection(X1,X2))))),
% 31.28/4.64 inference(flattening,[],[f45])).
% 31.28/4.64
% 31.28/4.64 tff(f54,plain,(
% 31.28/4.64 ! [X0 : element,X1 : set] : ((empty_set = intersection(singleton(X0),X1) | cardinality(union(singleton(X0),X1)) != $sum(cardinality(X1),1)) & (cardinality(union(singleton(X0),X1)) = $sum(cardinality(X1),1) | empty_set != intersection(singleton(X0),X1)))),
% 31.28/4.64 inference(nnf_transformation,[],[f34])).
% 31.28/4.64
% 31.28/4.64 tff(f57,plain,(
% 31.28/4.64 ? [X0 : element,X1 : set,X2 : $int] : (cardinality(union(singleton(X0),X1)) != $sum(X2,1) & cardinality(X1) = X2 & ~member(X0,X1)) => (cardinality(union(singleton(sK1),sK2)) != $sum(sK3,1) & sK3 = cardinality(sK2) & ~member(sK1,sK2))),
% 31.28/4.64 introduced(choice_axiom,[])).
% 31.28/4.64
% 31.28/4.64 tff(f58,plain,(
% 31.28/4.64 cardinality(union(singleton(sK1),sK2)) != $sum(sK3,1) & sK3 = cardinality(sK2) & ~member(sK1,sK2)),
% 31.28/4.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f39,f57])).
% 31.28/4.64
% 31.28/4.64 tff(f59,plain,(
% 31.28/4.64 ( ! [X0 : set] : (empty_set = X0 | member(sK0(X0),X0)) )),
% 31.28/4.64 inference(cnf_transformation,[],[f43])).
% 31.28/4.64
% 31.28/4.64 tff(f61,plain,(
% 31.28/4.64 ( ! [X0 : element,X1 : element] : (X0 = X1 | ~member(X0,singleton(X1))) )),
% 31.28/4.64 inference(cnf_transformation,[],[f44])).
% 31.28/4.64
% 31.28/4.64 tff(f63,plain,(
% 31.28/4.64 ( ! [X2 : set,X0 : element,X1 : set] : (member(X0,X1) | ~member(X0,intersection(X1,X2))) )),
% 31.28/4.64 inference(cnf_transformation,[],[f46])).
% 31.28/4.64
% 31.28/4.64 tff(f64,plain,(
% 31.28/4.64 ( ! [X2 : set,X0 : element,X1 : set] : (member(X0,X2) | ~member(X0,intersection(X1,X2))) )),
% 31.28/4.64 inference(cnf_transformation,[],[f46])).
% 31.28/4.64
% 31.28/4.64 tff(f78,plain,(
% 31.28/4.64 ( ! [X0 : element,X1 : set] : (cardinality(union(singleton(X0),X1)) = $sum(cardinality(X1),1) | empty_set != intersection(singleton(X0),X1)) )),
% 31.28/4.64 inference(cnf_transformation,[],[f54])).
% 31.28/4.64
% 31.28/4.64 tff(f84,plain,(
% 31.28/4.64 ~member(sK1,sK2)),
% 31.28/4.64 inference(cnf_transformation,[],[f58])).
% 31.28/4.64
% 31.28/4.64 tff(f85,plain,(
% 31.28/4.64 sK3 = cardinality(sK2)),
% 31.28/4.64 inference(cnf_transformation,[],[f58])).
% 31.28/4.64
% 31.28/4.64 tff(f86,plain,(
% 31.28/4.64 cardinality(union(singleton(sK1),sK2)) != $sum(sK3,1)),
% 31.28/4.64 inference(cnf_transformation,[],[f58])).
% 31.28/4.64
% 31.28/4.64 cnf(c_59,negated_conjecture,
% 31.28/4.64 ($sum_int($sum_int(X0_3,X1_3),X2_3) = $sum_int(X0_3,$sum_int(X1_3,X2_3))),
% 31.28/4.64 inference(cnf_transformation,[],[f16])).
% 31.28/4.64
% 31.28/4.64 cnf(c_60,negated_conjecture,
% 31.28/4.64 ($sum_int(X0_3,X1_3) = $sum_int(X1_3,X0_3)),
% 31.28/4.64 inference(cnf_transformation,[],[f15])).
% 31.28/4.64
% 31.28/4.64 cnf(c_62,negated_conjecture,
% 31.28/4.64 (X0_13 = empty_set|member(sK0(X0_13),X0_13)),
% 31.28/4.64 inference(cnf_transformation,[],[f59])).
% 31.28/4.64
% 31.28/4.64 cnf(c_64,plain,
% 31.28/4.64 (~member(X0_14,singleton(X1_14))|X0_14 = X1_14),
% 31.28/4.64 inference(cnf_transformation,[],[f61])).
% 31.28/4.64
% 31.28/4.64 cnf(c_66,plain,
% 31.28/4.64 (~member(X0_14,intersection(X0_13,X1_13))|member(X0_14,X1_13)),
% 31.28/4.64 inference(cnf_transformation,[],[f64])).
% 31.28/4.64
% 31.28/4.64 cnf(c_67,plain,
% 31.28/4.64 (~member(X0_14,intersection(X0_13,X1_13))|member(X0_14,X0_13)),
% 31.28/4.64 inference(cnf_transformation,[],[f63])).
% 31.28/4.64
% 31.28/4.64 cnf(c_81,plain,
% 31.28/4.64 (intersection(singleton(X0_14),X0_13) != empty_set|cardinality(union(singleton(X0_14),X0_13)) = $sum_int(cardinality(X0_13),1)),
% 31.28/4.64 inference(cnf_transformation,[],[f78])).
% 31.28/4.64
% 31.28/4.64 cnf(c_86,negated_conjecture,
% 31.28/4.64 (cardinality(union(singleton(sK1),sK2)) != $sum_int(sK3,1)),
% 31.28/4.64 inference(cnf_transformation,[],[f86])).
% 31.28/4.64
% 31.28/4.64 cnf(c_87,negated_conjecture,
% 31.28/4.64 (cardinality(sK2) = sK3),
% 31.28/4.64 inference(cnf_transformation,[],[f85])).
% 31.28/4.64
% 31.28/4.64 cnf(c_88,negated_conjecture,
% 31.28/4.64 (~member(sK1,sK2)),
% 31.28/4.64 inference(cnf_transformation,[],[f84])).
% 31.28/4.64
% 31.28/4.64 cnf(c_116,negated_conjecture,
% 31.28/4.64 (cardinality(union(singleton(sK1),sK2)) != $sum_int(1,sK3)),
% 31.28/4.64 inference(theory_normalisation,[status(thm)],[c_86,c_59,c_60])).
% 31.28/4.64
% 31.28/4.64 cnf(c_451,plain,
% 31.28/4.64 (cardinality(union(singleton(sK1),sK2)) != $sum_int(1,cardinality(sK2))),
% 31.28/4.64 inference(light_normalisation,[status(thm)],[c_116,c_87])).
% 31.28/4.64
% 31.28/4.64 cnf(c_41759,plain,
% 31.28/4.64 (intersection(X0_13,X1_13) = empty_set|member(sK0(intersection(X0_13,X1_13)),X0_13)),
% 31.28/4.64 inference(superposition,[status(thm)],[c_62,c_67])).
% 31.28/4.64
% 31.28/4.64 cnf(c_41760,plain,
% 31.28/4.64 (intersection(X0_13,X1_13) = empty_set|member(sK0(intersection(X0_13,X1_13)),X1_13)),
% 31.28/4.64 inference(superposition,[status(thm)],[c_62,c_66])).
% 31.28/4.64
% 31.28/4.64 cnf(c_51097,plain,
% 31.28/4.64 (sK0(intersection(singleton(X0_14),X0_13)) = X0_14|intersection(singleton(X0_14),X0_13) = empty_set),
% 31.28/4.64 inference(superposition,[status(thm)],[c_41759,c_64])).
% 31.28/4.64
% 31.28/4.64 cnf(c_51738,plain,
% 31.28/4.64 (intersection(singleton(X0_14),X0_13) = empty_set|member(X0_14,X0_13)),
% 31.28/4.64 inference(superposition,[status(thm)],[c_51097,c_41760])).
% 31.28/4.64
% 31.28/4.64 cnf(c_123951,plain,
% 31.28/4.64 (intersection(singleton(sK1),sK2) = empty_set),
% 31.28/4.64 inference(superposition,[status(thm)],[c_51738,c_88])).
% 31.28/4.64
% 31.28/4.64 cnf(c_125948,plain,
% 31.28/4.64 (cardinality(union(singleton(sK1),sK2)) = $sum_int(cardinality(sK2),1)),
% 31.28/4.64 inference(superposition,[status(thm)],[c_123951,c_81])).
% 31.28/4.64
% 31.28/4.64 cnf(c_125952,plain,
% 31.28/4.64 (cardinality(union(singleton(sK1),sK2)) = $sum_int(1,cardinality(sK2))),
% 31.28/4.64 inference(theory_normalisation,[status(thm)],[c_125948,c_59,c_60])).
% 31.28/4.64
% 31.28/4.64 cnf(c_125953,plain,
% 31.28/4.64 ($false),
% 31.28/4.64 inference(forward_subsumption_resolution,[status(thm)],[c_125952,c_451])).
% 31.28/4.64
% 31.28/4.64
% 31.28/4.64 % SZS output end CNFRefutation for theBenchmark.p
% 31.28/4.64
% 31.28/4.65
%------------------------------------------------------------------------------