0.07/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command  : /export/starexec/sandbox2/solver/bin/run_iprover 120 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
0.13/0.34	% Computer : n008.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 : 960
0.13/0.34	% WCLimit  : 120
0.13/0.34	% DateTime : Wed Jul 30 16:34:19 EDT 2025
0.13/0.34	% CPUTime  : 
0.20/0.47	Running TFA theorem proving
0.20/0.48	Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core-casc.sh -l tptp -s tfa_schedule -t 120 /export/starexec/sandbox2/benchmark/theBenchmark.p
0.20/0.48	
0.20/0.48	% ======== iProver multi-core TPTP/SMT =========
0.20/0.48	
0.20/0.49	% Detected problem language: tptp
0.20/0.50	% Checking...
0.62/1.19	% Proving...
265.15/35.00	% SZS status Started for theBenchmark.p
265.15/35.00	% SZS status Theorem for theBenchmark.p
265.15/35.00	
265.15/35.00	%---------------- iProver v3.9.3 (pre CASC 2025/SMT-COMP 2025) ----------------%
265.15/35.00	
265.15/35.00	% ------  iProver source info
265.15/35.00	
265.15/35.00	% git: date: 2025-07-21 10:15:00 +0000
265.15/35.00	% git: sha1: d7ebeb21b290b8724a1e08b4c4a533d26e8c009f
265.15/35.00	% git: non_committed_changes: true
265.15/35.00	
265.15/35.00	% ------ Parsing...
265.15/35.00	% ------ Clausification by vclausify_rel  & Parsing by iProver...% 
265.15/35.00	
265.15/35.00	% ------ 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 % 
265.15/35.00	
265.15/35.00	% ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
265.15/35.00	
265.15/35.00	% ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e % 
265.15/35.00	% ------ Proving...
265.15/35.00	% ------ Problem Properties 
265.15/35.00	
265.15/35.00	% 
265.15/35.00	% clauses                               40
265.15/35.00	% conjectures                           3
265.15/35.00	% EPR                                   6
265.15/35.00	% Horn                                  34
265.15/35.00	% unary                                 14
265.15/35.00	% binary                                21
265.15/35.00	% lits                                  71
265.15/35.00	% lits eq                               28
265.15/35.00	% fd_pure                               0
265.15/35.00	% fd_pseudo                             0
265.15/35.00	% fd_cond                               2
265.15/35.00	% fd_pseudo_cond                        2
265.15/35.00	% AC symbols                            1
265.15/35.00	
265.15/35.00	% % ------ Input Options Time Limit: Unbounded
265.15/35.00	
265.15/35.00	
265.15/35.00	% % ------ 
265.15/35.00	% Current options:
265.15/35.00	% ------ 
265.15/35.00	
265.15/35.00	
265.15/35.00	% 
265.15/35.00	
265.15/35.00	% ------ Proving...
265.15/35.00	% 
265.15/35.00	
265.15/35.00	% SZS status Theorem for theBenchmark.p
265.15/35.00	
265.15/35.00	% % SZS output start CNFRefutation for theBenchmark.p
265.15/35.00	
265.15/35.00	tff(func_def_0, type, empty_set: set).
265.15/35.00	tff(pred_def_1, type, member: (element * set) > $o).
265.15/35.00	tff(pred_def_2, type, subset: (set * set) > $o).
265.15/35.00	tff(func_def_3, type, union: (set * set) > set).
265.15/35.00	tff(func_def_4, type, difference: (set * set) > set).
265.15/35.00	tff(func_def_5, type, complement: set > set).
265.15/35.00	tff(func_def_6, type, cardinality: set > $int).
265.15/35.00	tff(func_def_11, type, sK0: set > element).
265.15/35.00	tff(func_def_12, type, sK1: element).
265.15/35.00	tff(func_def_13, type, sK2: set).
265.15/35.00	tff(func_def_14, type, sK3: $int).
265.15/35.00	tff(f2,axiom,(
265.15/35.00	  ! [X2 : element,X0 : element] : (X0 = X2 <=> member(X2,singleton(X0)))),
265.15/35.00	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)).
265.15/35.00	
265.15/35.00	tff(f3,axiom,(
265.15/35.00	  ! [X3 : set] : (! [X2 : element] : ~member(X2,X3) <=> empty_set = X3)),
265.15/35.00	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set)).
265.15/35.00	
265.15/35.00	tff(f4,axiom,(
265.15/35.00	  ! [X2 : element,X3 : set] : (empty_set = intersection(singleton(X2),X3) <=> cardinality(union(singleton(X2),X3)) = $sum(cardinality(X3),1))),
265.15/35.00	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cardinality_intersection_2)).
265.15/35.00	
265.15/35.00	tff(f6,axiom,(
265.15/35.00	  ! [X2 : element,X0 : set,X1 : set] : ((member(X2,X1) & member(X2,X0)) <=> member(X2,intersection(X0,X1)))),
265.15/35.00	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection)).
265.15/35.00	
265.15/35.00	tff(f9,conjecture,(
265.15/35.00	  ! [X2 : element,X6 : set,X7 : $int] : ((~member(X2,X6) & cardinality(X6) = X7) => $sum(X7,1) = cardinality(union(singleton(X2),X6)))),
265.15/35.00	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vc2)).
265.15/35.00	
265.15/35.00	tff(f10,negated_conjecture,(
265.15/35.00	  ~! [X2 : element,X6 : set,X7 : $int] : ((~member(X2,X6) & cardinality(X6) = X7) => $sum(X7,1) = cardinality(union(singleton(X2),X6)))),
265.15/35.00	inference(negated_conjecture,[status(cth)],[f9])).
265.15/35.00	
265.15/35.00	tff(f15,plain,(
265.15/35.00	  ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
265.15/35.00	  introduced(theory_axiom_138,[])).
265.15/35.00	
265.15/35.00	tff(f16,plain,(
265.15/35.00	  ( ! [X2 : $int,X0 : $int,X1 : $int] : ($sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2)) )),
265.15/35.00	  introduced(theory_axiom_139,[])).
265.15/35.00	
265.15/35.00	tff(f20,plain,(
265.15/35.00	  ( ! [X0 : $int] : (~$less(X0,X0)) )),
265.15/35.00	  introduced(theory_axiom_145,[])).
265.15/35.00	
265.15/35.00	tff(f22,plain,(
265.15/35.00	  ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,X0) | X0 = X1) )),
265.15/35.00	  introduced(theory_axiom_147,[])).
265.15/35.00	
265.15/35.00	tff(f27,plain,(
265.15/35.00	  ! [X0 : element,X1 : element] : (X0 = X1 <=> member(X0,singleton(X1)))),
265.15/35.00	  inference(rectify,[],[f2])).
265.15/35.00	
265.15/35.00	tff(f28,plain,(
265.15/35.00	  ! [X0 : set] : (! [X1 : element] : ~member(X1,X0) <=> empty_set = X0)),
265.15/35.00	  inference(rectify,[],[f3])).
265.15/35.00	
265.15/35.00	tff(f29,plain,(
265.15/35.00	  ! [X0 : element,X1 : set] : (empty_set = intersection(singleton(X0),X1) <=> cardinality(union(singleton(X0),X1)) = $sum(cardinality(X1),1))),
265.15/35.00	  inference(rectify,[],[f4])).
265.15/35.00	
265.15/35.00	tff(f31,plain,(
265.15/35.00	  ! [X0 : element,X1 : set,X2 : set] : ((member(X0,X2) & member(X0,X1)) <=> member(X0,intersection(X1,X2)))),
265.15/35.00	  inference(rectify,[],[f6])).
265.15/35.00	
265.15/35.00	tff(f34,plain,(
265.15/35.00	  ~! [X0 : element,X1 : set,X2 : $int] : ((~member(X0,X1) & cardinality(X1) = X2) => cardinality(union(singleton(X0),X1)) = $sum(X2,1))),
265.15/35.00	  inference(rectify,[],[f10])).
265.15/35.00	
265.15/35.00	tff(f38,plain,(
265.15/35.00	  ? [X0 : element,X1 : set,X2 : $int] : (cardinality(union(singleton(X0),X1)) != $sum(X2,1) & (~member(X0,X1) & cardinality(X1) = X2))),
265.15/35.00	  inference(ennf_transformation,[],[f34])).
265.15/35.00	
265.15/35.00	tff(f39,plain,(
265.15/35.00	  ? [X0 : element,X1 : set,X2 : $int] : (cardinality(union(singleton(X0),X1)) != $sum(X2,1) & ~member(X0,X1) & cardinality(X1) = X2)),
265.15/35.00	  inference(flattening,[],[f38])).
265.15/35.00	
265.15/35.00	tff(f41,plain,(
265.15/35.00	  ! [X0 : element,X1 : element] : ((X0 = X1 | ~member(X0,singleton(X1))) & (member(X0,singleton(X1)) | X0 != X1))),
265.15/35.00	  inference(nnf_transformation,[],[f27])).
265.15/35.00	
265.15/35.00	tff(f42,plain,(
265.15/35.00	  ! [X0 : set] : ((! [X1 : element] : ~member(X1,X0) | empty_set != X0) & (empty_set = X0 | ? [X1 : element] : member(X1,X0)))),
265.15/35.00	  inference(nnf_transformation,[],[f28])).
265.15/35.00	
265.15/35.00	tff(f43,plain,(
265.15/35.00	  ! [X0 : set] : ((! [X1 : element] : ~member(X1,X0) | empty_set != X0) & (empty_set = X0 | ? [X2 : element] : member(X2,X0)))),
265.15/35.00	  inference(rectify,[],[f42])).
265.15/35.00	
265.15/35.00	tff(f44,plain,(
265.15/35.00	  ! [X0 : set] : (? [X2 : element] : member(X2,X0) => member(sK0(X0),X0))),
265.15/35.00	  introduced(choice_axiom,[])).
265.15/35.00	
265.15/35.00	tff(f45,plain,(
265.15/35.00	  ! [X0 : set] : ((! [X1 : element] : ~member(X1,X0) | empty_set != X0) & (empty_set = X0 | member(sK0(X0),X0)))),
265.15/35.00	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f43,f44])).
265.15/35.00	
265.15/35.00	tff(f46,plain,(
265.15/35.00	  ! [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)))),
265.15/35.00	  inference(nnf_transformation,[],[f29])).
265.15/35.00	
265.15/35.00	tff(f48,plain,(
265.15/35.00	  ! [X0 : element,X1 : set,X2 : set] : (((member(X0,X2) & member(X0,X1)) | ~member(X0,intersection(X1,X2))) & (member(X0,intersection(X1,X2)) | (~member(X0,X2) | ~member(X0,X1))))),
265.15/35.00	  inference(nnf_transformation,[],[f31])).
265.15/35.00	
265.15/35.00	tff(f49,plain,(
265.15/35.00	  ! [X0 : element,X1 : set,X2 : set] : (((member(X0,X2) & member(X0,X1)) | ~member(X0,intersection(X1,X2))) & (member(X0,intersection(X1,X2)) | ~member(X0,X2) | ~member(X0,X1)))),
265.15/35.00	  inference(flattening,[],[f48])).
265.15/35.00	
265.15/35.00	tff(f53,plain,(
265.15/35.00	  ? [X0 : element,X1 : set,X2 : $int] : (cardinality(union(singleton(X0),X1)) != $sum(X2,1) & ~member(X0,X1) & cardinality(X1) = X2) => (cardinality(union(singleton(sK1),sK2)) != $sum(sK3,1) & ~member(sK1,sK2) & sK3 = cardinality(sK2))),
265.15/35.00	  introduced(choice_axiom,[])).
265.15/35.00	
265.15/35.00	tff(f54,plain,(
265.15/35.00	  cardinality(union(singleton(sK1),sK2)) != $sum(sK3,1) & ~member(sK1,sK2) & sK3 = cardinality(sK2)),
265.15/35.00	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f39,f53])).
265.15/35.00	
265.15/35.00	tff(f62,plain,(
265.15/35.00	  ( ! [X0 : element,X1 : element] : (X0 = X1 | ~member(X0,singleton(X1))) )),
265.15/35.00	  inference(cnf_transformation,[],[f41])).
265.15/35.00	
265.15/35.00	tff(f63,plain,(
265.15/35.00	  ( ! [X0 : set] : (empty_set = X0 | member(sK0(X0),X0)) )),
265.15/35.00	  inference(cnf_transformation,[],[f45])).
265.15/35.00	
265.15/35.00	tff(f64,plain,(
265.15/35.00	  ( ! [X0 : set,X1 : element] : (~member(X1,X0) | empty_set != X0) )),
265.15/35.00	  inference(cnf_transformation,[],[f45])).
265.15/35.00	
265.15/35.00	tff(f65,plain,(
265.15/35.00	  ( ! [X0 : element,X1 : set] : (cardinality(union(singleton(X0),X1)) = $sum(cardinality(X1),1) | empty_set != intersection(singleton(X0),X1)) )),
265.15/35.00	  inference(cnf_transformation,[],[f46])).
265.15/35.00	
265.15/35.00	tff(f69,plain,(
265.15/35.00	  ( ! [X2 : set,X0 : element,X1 : set] : (member(X0,intersection(X1,X2)) | ~member(X0,X2) | ~member(X0,X1)) )),
265.15/35.00	  inference(cnf_transformation,[],[f49])).
265.15/35.00	
265.15/35.00	tff(f70,plain,(
265.15/35.00	  ( ! [X2 : set,X0 : element,X1 : set] : (member(X0,X1) | ~member(X0,intersection(X1,X2))) )),
265.15/35.00	  inference(cnf_transformation,[],[f49])).
265.15/35.00	
265.15/35.00	tff(f71,plain,(
265.15/35.00	  ( ! [X2 : set,X0 : element,X1 : set] : (member(X0,X2) | ~member(X0,intersection(X1,X2))) )),
265.15/35.00	  inference(cnf_transformation,[],[f49])).
265.15/35.00	
265.15/35.00	tff(f77,plain,(
265.15/35.00	  sK3 = cardinality(sK2)),
265.15/35.00	  inference(cnf_transformation,[],[f54])).
265.15/35.00	
265.15/35.00	tff(f78,plain,(
265.15/35.00	  ~member(sK1,sK2)),
265.15/35.00	  inference(cnf_transformation,[],[f54])).
265.15/35.00	
265.15/35.00	tff(f79,plain,(
265.15/35.00	  cardinality(union(singleton(sK1),sK2)) != $sum(sK3,1)),
265.15/35.00	  inference(cnf_transformation,[],[f54])).
265.15/35.00	
265.15/35.00	tff(f88,plain,(
265.15/35.00	  ( ! [X1 : element] : (~member(X1,empty_set)) )),
265.15/35.00	  inference(equality_resolution,[],[f64])).
265.15/35.00	
265.15/35.00	tcf(c_53,plain,![X0_int:$int,X1_int:$int]:  
265.15/35.00	    (X0_int = X1_int|$less(X0_int,X1_int)|$less(X1_int,X0_int)),
265.15/35.00	    inference(cnf_transformation,[],[f22])).
265.15/35.00	
265.15/35.00	tcf(c_55,plain,![X0_int:$int]:  
265.15/35.00	    (~$less(X0_int,X0_int)),
265.15/35.00	    inference(cnf_transformation,[],[f20])).
265.15/35.00	
265.15/35.00	tcf(c_59,plain,![X0_int:$int,X1_int:$int,X2_int:$int]:  
265.15/35.00	    ($sum($sum(X0_int,X1_int),X2_int) = $sum(X0_int,$sum(X1_int,X2_int))),
265.15/35.00	    inference(cnf_transformation,[],[f16])).
265.15/35.00	
265.15/35.00	tcf(c_60,plain,![X0_int:$int,X1_int:$int]:  
265.15/35.00	    ($sum(X0_int,X1_int) = $sum(X1_int,X0_int)),
265.15/35.00	    inference(cnf_transformation,[],[f15])).
265.15/35.00	
265.15/35.00	tcf(c_63,plain,![X0_element:element,X1_element:element]:  
265.15/35.00	    (~member(X0_element,singleton(X1_element))|X0_element = X1_element),
265.15/35.00	    inference(cnf_transformation,[],[f62])).
265.15/35.00	
265.15/35.00	tcf(c_65,plain,![X0_element:element]:  
265.15/35.00	    (~member(X0_element,empty_set)),
265.15/35.00	    inference(cnf_transformation,[],[f88])).
265.15/35.00	
265.15/35.00	tcf(c_66,plain,![X0_set:set]:  
265.15/35.00	    (X0_set = empty_set|member(sK0(X0_set),X0_set)),
265.15/35.00	    inference(cnf_transformation,[],[f63])).
265.15/35.00	
265.15/35.00	tcf(c_68,plain,![X0_set:set,X0_element:element]:  
265.15/35.00	    (intersection(singleton(X0_element),X0_set) != empty_set|cardinality(union(singleton(X0_element),X0_set)) = $sum(cardinality(X0_set),1)),
265.15/35.00	    inference(cnf_transformation,[],[f65])).
265.15/35.00	
265.15/35.00	tcf(c_71,plain,![X0_set:set,X0_element:element,X1_set:set]:  
265.15/35.00	    (~member(X0_element,intersection(X0_set,X1_set))|member(X0_element,X1_set)),
265.15/35.00	    inference(cnf_transformation,[],[f71])).
265.15/35.00	
265.15/35.00	tcf(c_72,plain,![X0_set:set,X0_element:element,X1_set:set]:  
265.15/35.00	    (~member(X0_element,intersection(X0_set,X1_set))|member(X0_element,X0_set)),
265.15/35.00	    inference(cnf_transformation,[],[f70])).
265.15/35.00	
265.15/35.00	tcf(c_73,plain,![X0_set:set,X0_element:element,X1_set:set]:  
265.15/35.00	    (~member(X0_element,X0_set)|~member(X0_element,X1_set)|member(X0_element,intersection(X1_set,X0_set))),
265.15/35.00	    inference(cnf_transformation,[],[f69])).
265.15/35.00	
265.15/35.00	tcf(c_79,plain, 
265.15/35.00	    (cardinality(union(singleton(sK1),sK2)) != $sum(sK3,1)),
265.15/35.00	    inference(cnf_transformation,[],[f79])).
265.15/35.00	
265.15/35.00	tcf(c_80,plain, (~member(sK1,sK2)),inference(cnf_transformation,[],[f78])).
265.15/35.00	
265.15/35.00	tcf(c_81,plain, 
265.15/35.00	    (cardinality(sK2) = sK3),
265.15/35.00	    inference(cnf_transformation,[],[f77])).
265.15/35.00	
265.15/35.00	tcf(c_117,plain,![X0_set:set,X0_element:element]:  
265.15/35.00	    (intersection(singleton(X0_element),X0_set) != empty_set|cardinality(union(singleton(X0_element),X0_set)) = $sum(1,cardinality(X0_set))),
265.15/35.00	    inference(theory_normalisation,[status(thm)],[c_68,c_59,c_60])).
265.15/35.00	
265.15/35.00	tcf(c_118,plain, 
265.15/35.00	    (cardinality(union(singleton(sK1),sK2)) != $sum(1,sK3)),
265.15/35.00	    inference(theory_normalisation,[status(thm)],[c_79,c_59,c_60])).
265.15/35.00	
265.15/35.00	tcf(c_540,plain,![X0_set:set,X0_element:element]:  
265.15/35.00	    (intersection(singleton(X0_element),X0_set) != empty_set|cardinality(union(singleton(X0_element),X0_set)) = $sum(1,cardinality(X0_set))),
265.15/35.00	    inference(prop_impl_just,[status(thm)],[c_117])).
265.15/35.00	
265.15/35.00	tcf(c_921,plain,![X0_int:$int]:  (X0_int = X0_int),theory(equality)).
265.15/35.00	
265.15/35.00	tcf(c_924,plain,![X0_int:$int,X1_int:$int,X2_int:$int]:  
265.15/35.00	    (X0_int != X1_int|X2_int != X1_int|X2_int = X0_int),
265.15/35.00	    theory(equality)).
265.15/35.00	
265.15/35.00	tcf(c_927,plain,![X0_int:$int,X1_int:$int,X2_int:$int,X3_int:$int]:  
265.15/35.00	    (X0_int != X1_int|X2_int != X3_int|$sum(X0_int,X2_int) = $sum(X1_int,X3_int)),
265.15/35.00	    theory(equality)).
265.15/35.00	
265.15/35.00	tcf(c_2524,plain,![X0_int:$int,X1_int:$int]:  
265.15/35.00	    (cardinality(union(singleton(sK1),sK2)) != X0_int|X1_int != X0_int|
265.15/35.00	    cardinality(union(singleton(sK1),sK2)) = X1_int),
265.15/35.00	    inference(instantiation,[status(thm)],[c_924])).
265.15/35.00	
265.15/35.00	tcf(c_2630,plain, (1 = 1),inference(instantiation,[status(thm)],[c_921])).
265.15/35.00	
265.15/35.00	tcf(c_2738,plain,![X0_int:$int]:  
265.15/35.00	    ($sum(1,sK3) = X0_int|$less($sum(1,sK3),X0_int)|$less(X0_int,$sum(1,sK3))),
265.15/35.00	    inference(instantiation,[status(thm)],[c_53])).
265.15/35.00	
265.15/35.00	tcf(c_2743,plain,![X0_int:$int,X1_int:$int]:  
265.15/35.00	    ($sum(1,sK3) != X0_int|X1_int != X0_int|$sum(1,sK3) = X1_int),
265.15/35.00	    inference(instantiation,[status(thm)],[c_924])).
265.15/35.00	
265.15/35.00	tcf(c_4421,plain, 
265.15/35.00	    ($sum(1,sK3) = $sum(1,sK3)|$less($sum(1,sK3),$sum(1,sK3))),
265.15/35.00	    inference(instantiation,[status(thm)],[c_2738])).
265.15/35.00	
265.15/35.00	tcf(c_4422,plain, 
265.15/35.00	    (~$less($sum(1,sK3),$sum(1,sK3))),
265.15/35.00	    inference(instantiation,[status(thm)],[c_55])).
265.15/35.00	
265.15/35.00	tcf(c_4474,plain,![X0_int:$int,X1_int:$int]:  
265.15/35.00	    (X0_int != 1|X1_int != sK3|$sum(X0_int,X1_int) = $sum(1,sK3)),
265.15/35.00	    inference(instantiation,[status(thm)],[c_927])).
265.15/35.00	
265.15/35.00	tcf(c_18737,plain,![X0_int:$int]:  
265.15/35.00	    ($sum(1,sK3) != $sum(1,sK3)|X0_int != $sum(1,sK3)|$sum(1,sK3) = X0_int),
265.15/35.00	    inference(instantiation,[status(thm)],[c_2743])).
265.15/35.00	
265.15/35.00	tcf(c_22775,plain,![X0_int:$int]:  
265.15/35.00	    (cardinality(sK2) != sK3|X0_int != 1|$sum(X0_int,cardinality(sK2)) = $sum(1,sK3)),
265.15/35.00	    inference(instantiation,[status(thm)],[c_4474])).
265.15/35.00	
265.15/35.00	tcf(c_33684,plain, 
265.15/35.00	    (intersection(singleton(sK1),sK2) != empty_set|cardinality(union(singleton(sK1),sK2)) = $sum(1,cardinality(sK2))),
265.15/35.00	    inference(instantiation,[status(thm)],[c_540])).
265.15/35.00	
265.15/35.00	tcf(c_33688,plain,![X0_int:$int]:  
265.15/35.00	    (cardinality(union(singleton(sK1),sK2)) != $sum(1,cardinality(sK2))|
265.15/35.00	    X0_int != $sum(1,cardinality(sK2))|cardinality(union(singleton(sK1),sK2)) = X0_int),
265.15/35.00	    inference(instantiation,[status(thm)],[c_2524])).
265.15/35.00	
265.15/35.00	tcf(c_37587,plain, 
265.15/35.00	    (cardinality(sK2) != sK3|1 != 1|$sum(1,cardinality(sK2)) = $sum(1,sK3)),
265.15/35.00	    inference(instantiation,[status(thm)],[c_22775])).
265.15/35.00	
265.15/35.00	tcf(c_45607,plain, 
265.15/35.00	    (cardinality(union(singleton(sK1),sK2)) != $sum(1,cardinality(sK2))|
265.15/35.00	    $sum(1,sK3) != $sum(1,cardinality(sK2))|cardinality(union(singleton(sK1),sK2)) = $sum(1,sK3)),
265.15/35.00	    inference(instantiation,[status(thm)],[c_33688])).
265.15/35.00	
265.15/35.00	tcf(c_55229,plain, 
265.15/35.00	    ($sum(1,cardinality(sK2)) != $sum(1,sK3)|$sum(1,sK3) != $sum(1,sK3)|
265.15/35.00	    $sum(1,sK3) = $sum(1,cardinality(sK2))),
265.15/35.00	    inference(instantiation,[status(thm)],[c_18737])).
265.15/35.00	
265.15/35.00	tcf(c_276183,plain,![X0_set:set,X1_set:set]:  
265.15/35.00	    (intersection(X0_set,X1_set) = empty_set|member(sK0(intersection(X0_set,X1_set)),X1_set)),
265.15/35.00	    inference(superposition,[status(thm)],[c_66,c_71])).
265.15/35.00	
265.15/35.00	tcf(c_276333,plain,![X0_set:set,X1_set:set]:  
265.15/35.00	    (intersection(X0_set,X1_set) = empty_set|member(sK0(intersection(X0_set,X1_set)),X0_set)),
265.15/35.00	    inference(superposition,[status(thm)],[c_66,c_72])).
265.15/35.00	
265.15/35.00	tcf(c_448150,plain,![X0_set:set,X0_element:element]:  
265.15/35.00	    (sK0(intersection(X0_set,singleton(X0_element))) = X0_element|intersection(X0_set,singleton(X0_element)) = empty_set),
265.15/35.00	    inference(superposition,[status(thm)],[c_276183,c_63])).
265.15/35.00	
265.15/35.00	tcf(c_612769,plain,![X0_set:set,X0_element:element]:  
265.15/35.00	    (intersection(X0_set,singleton(X0_element)) = empty_set|member(X0_element,X0_set)),
265.15/35.00	    inference(superposition,[status(thm)],[c_448150,c_276333])).
265.15/35.00	
265.15/35.00	tcf(c_753363,plain, 
265.15/35.00	    (intersection(sK2,singleton(sK1)) = empty_set),
265.15/35.00	    inference(superposition,[status(thm)],[c_612769,c_80])).
265.15/35.00	
265.15/35.00	tcf(c_753401,plain,![X0_element:element]:  
265.15/35.00	    (~member(X0_element,singleton(sK1))|~member(X0_element,sK2)|member(X0_element,empty_set)),
265.15/35.00	    inference(superposition,[status(thm)],[c_753363,c_73])).
265.15/35.00	
265.15/35.00	tcf(c_753404,plain,![X0_element:element]:  
265.15/35.00	    (~member(X0_element,singleton(sK1))|~member(X0_element,sK2)),
265.15/35.00	    inference(forward_subsumption_resolution,[status(thm)],[c_753401,c_65])).
265.15/35.00	
265.15/35.00	tcf(c_753579,plain,![X0_set:set]:  
265.15/35.00	    (~member(sK0(intersection(singleton(sK1),X0_set)),sK2)|intersection(singleton(sK1),X0_set) = empty_set),
265.15/35.00	    inference(superposition,[status(thm)],[c_276333,c_753404])).
265.15/35.00	
265.15/35.00	tcf(c_760616,plain, 
265.15/35.00	    (intersection(singleton(sK1),sK2) = empty_set),
265.15/35.00	    inference(superposition,[status(thm)],[c_276183,c_753579])).
265.15/35.00	
265.15/35.00	tcf(c_760622,plain, 
265.15/35.00	    ($false),
265.15/35.00	    inference(prop_impl_just,
265.15/35.00	              [status(thm)],
265.15/35.00	              [c_760616,c_55229,c_45607,c_37587,c_33684,c_4422,c_4421,
265.15/35.00	               c_2630,c_118,c_81])).
265.15/35.00	
265.15/35.00	
265.15/35.00	% % SZS output end CNFRefutation for theBenchmark.p
265.15/35.00	
265.15/35.00	
265.17/35.08	EOF