TSTP Solution File: SET901+1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SET901+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n009.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 14:31:37 EDT 2023
% Result : Theorem 193.83s 194.27s
% Output : CNFRefutation 193.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET901+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.10/0.31 % Computer : n009.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat Aug 26 12:26:50 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.53 start to proof:theBenchmark
% 193.76/194.26 %-------------------------------------------
% 193.76/194.26 % File :CSE---1.6
% 193.76/194.26 % Problem :theBenchmark
% 193.76/194.26 % Transform :cnf
% 193.76/194.26 % Format :tptp:raw
% 193.76/194.26 % Command :java -jar mcs_scs.jar %d %s
% 193.76/194.26
% 193.76/194.26 % Result :Theorem 193.240000s
% 193.76/194.26 % Output :CNFRefutation 193.240000s
% 193.76/194.26 %-------------------------------------------
% 193.83/194.27 %------------------------------------------------------------------------------
% 193.83/194.27 % File : SET901+1 : TPTP v8.1.2. Released v3.2.0.
% 193.83/194.27 % Domain : Set theory
% 193.83/194.27 % Problem : Basic properties of sets, theorem 42
% 193.83/194.27 % Version : [Urb06] axioms : Especial.
% 193.83/194.27 % English : subset(A,unordered_pair(B,C)) <=> ~ ( A != empty_set &
% 193.83/194.27 % A != singleton(B) & A != singleton(C) & A != unordered_pair(B,C) )
% 193.83/194.27
% 193.83/194.27 % Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% 193.83/194.27 % : [Urb06] Urban (2006), Email to G. Sutcliffe
% 193.83/194.27 % Source : [Urb06]
% 193.83/194.27 % Names : zfmisc_1__t42_zfmisc_1 [Urb06]
% 193.83/194.27
% 193.83/194.27 % Status : Theorem
% 193.83/194.27 % Rating : 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.13 v6.0.0, 0.09 v5.5.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.00 v4.1.0, 0.04 v4.0.1, 0.09 v4.0.0, 0.08 v3.7.0, 0.00 v3.4.0, 0.05 v3.3.0, 0.07 v3.2.0
% 193.83/194.27 % Syntax : Number of formulae : 7 ( 5 unt; 0 def)
% 193.83/194.27 % Number of atoms : 15 ( 9 equ)
% 193.83/194.27 % Maximal formula atoms : 5 ( 2 avg)
% 193.83/194.27 % Number of connectives : 19 ( 11 ~; 0 |; 6 &)
% 193.83/194.27 % ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% 193.83/194.27 % Maximal formula depth : 10 ( 5 avg)
% 193.83/194.27 % Maximal term depth : 2 ( 1 avg)
% 193.83/194.27 % Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% 193.83/194.27 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% 193.83/194.27 % Number of variables : 12 ( 10 !; 2 ?)
% 193.83/194.27 % SPC : FOF_THM_RFO_SEQ
% 193.83/194.27
% 193.83/194.27 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% 193.83/194.27 % library, www.mizar.org
% 193.83/194.27 %------------------------------------------------------------------------------
% 193.83/194.27 fof(commutativity_k2_tarski,axiom,
% 193.83/194.27 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
% 193.83/194.27
% 193.83/194.27 fof(reflexivity_r1_tarski,axiom,
% 193.83/194.27 ! [A,B] : subset(A,A) ).
% 193.83/194.27
% 193.83/194.27 fof(fc1_xboole_0,axiom,
% 193.83/194.27 empty(empty_set) ).
% 193.83/194.27
% 193.83/194.27 fof(rc1_xboole_0,axiom,
% 193.83/194.27 ? [A] : empty(A) ).
% 193.83/194.27
% 193.83/194.27 fof(rc2_xboole_0,axiom,
% 193.83/194.27 ? [A] : ~ empty(A) ).
% 193.83/194.27
% 193.83/194.27 fof(t42_zfmisc_1,conjecture,
% 193.83/194.27 ! [A,B,C] :
% 193.83/194.27 ( subset(A,unordered_pair(B,C))
% 193.83/194.27 <=> ~ ( A != empty_set
% 193.83/194.27 & A != singleton(B)
% 193.83/194.27 & A != singleton(C)
% 193.83/194.27 & A != unordered_pair(B,C) ) ) ).
% 193.83/194.27
% 193.83/194.27 fof(l46_zfmisc_1,axiom,
% 193.83/194.27 ! [A,B,C] :
% 193.83/194.27 ( subset(A,unordered_pair(B,C))
% 193.83/194.27 <=> ~ ( A != empty_set
% 193.83/194.27 & A != singleton(B)
% 193.83/194.27 & A != singleton(C)
% 193.83/194.27 & A != unordered_pair(B,C) ) ) ).
% 193.83/194.27
% 193.83/194.27 %------------------------------------------------------------------------------
% 193.83/194.27 %-------------------------------------------
% 193.83/194.27 % Proof found
% 193.83/194.27 % SZS status Theorem for theBenchmark
% 193.83/194.27 % SZS output start Proof
% 193.83/194.27 %ClaNum:24(EqnAxiom:9)
% 193.83/194.27 %VarNum:37(SingletonVarNum:18)
% 193.83/194.27 %MaxLitNum:5
% 193.83/194.27 %MaxfuncDepth:1
% 193.83/194.27 %SharedTerms:22
% 193.83/194.27 %goalClause: 18 19 20 21 23
% 193.83/194.27 [10]P1(a1)
% 193.83/194.27 [11]P1(a2)
% 193.83/194.27 [14]~P1(a4)
% 193.83/194.27 [12]P2(x121,x121)
% 193.83/194.27 [13]E(f3(x131,x132),f3(x132,x131))
% 193.83/194.27 [19]~E(a1,a6)+~P2(a6,f3(a7,a8))
% 193.83/194.27 [20]~P2(a6,f3(a7,a8))+~E(f5(a7),a6)
% 193.83/194.27 [21]~P2(a6,f3(a7,a8))+~E(f5(a8),a6)
% 193.83/194.27 [23]~E(f3(a7,a8),a6)+~P2(a6,f3(a7,a8))
% 193.83/194.27 [15]~E(x151,a1)+P2(x151,f3(x152,x153))
% 193.83/194.27 [16]~E(x161,f5(x163))+P2(x161,f3(x162,x163))
% 193.83/194.27 [17]~E(x171,f5(x172))+P2(x171,f3(x172,x173))
% 193.83/194.27 [22]P2(x221,f3(x222,x223))+~E(x221,f3(x222,x223))
% 193.83/194.27 [18]E(a1,a6)+P2(a6,f3(a7,a8))+E(f5(a7),a6)+E(f5(a8),a6)+E(f3(a7,a8),a6)
% 193.83/194.27 [24]E(x241,f3(x243,x242))+~P2(x241,f3(x243,x242))+E(x241,a1)+E(x241,f5(x242))+E(x241,f5(x243))
% 193.83/194.27 %EqnAxiom
% 193.83/194.27 [1]E(x11,x11)
% 193.83/194.27 [2]E(x22,x21)+~E(x21,x22)
% 193.83/194.27 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 193.83/194.27 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 193.83/194.27 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 193.83/194.27 [6]~E(x61,x62)+E(f5(x61),f5(x62))
% 193.83/194.27 [7]~P1(x71)+P1(x72)+~E(x71,x72)
% 193.83/194.27 [8]P2(x82,x83)+~E(x81,x82)+~P2(x81,x83)
% 193.83/194.27 [9]P2(x93,x92)+~E(x91,x92)+~P2(x93,x91)
% 193.83/194.27
% 193.83/194.27 %-------------------------------------------
% 193.84/194.28 cnf(47,plain,
% 193.84/194.28 (~E(a6,a1)+~E(a1,a6)),
% 193.84/194.28 inference(scs_inference,[],[15,19])).
% 193.84/194.28 cnf(48,plain,
% 193.84/194.28 (~E(a6,a1)),
% 193.84/194.28 inference(scs_inference,[],[47,2])).
% 193.84/194.28 cnf(49,plain,
% 193.84/194.28 (~E(a1,a6)),
% 193.84/194.28 inference(scs_inference,[],[48,2])).
% 193.84/194.28 cnf(50,plain,
% 193.84/194.28 (E(f3(a7,a8),a6)+P2(a6,f3(a7,a8))+E(f5(a7),a6)+E(f5(a8),a6)),
% 193.84/194.28 inference(scs_inference,[],[49,18])).
% 193.84/194.28 cnf(54,plain,
% 193.84/194.28 (~E(x541,a6)+~E(a1,x541)),
% 193.84/194.28 inference(scs_inference,[],[49,3])).
% 193.84/194.28 cnf(55,plain,
% 193.84/194.28 (~E(x551,a1)+~E(x551,a6)),
% 193.84/194.28 inference(scs_inference,[],[49,3,2])).
% 193.84/194.28 cnf(57,plain,
% 193.84/194.28 (~E(a6,x571)+~E(a1,x571)),
% 193.84/194.28 inference(scs_inference,[],[54,2])).
% 193.84/194.28 cnf(58,plain,
% 193.84/194.28 (~E(a6,x581)+~E(x581,a1)),
% 193.84/194.28 inference(scs_inference,[],[55,2])).
% 193.84/194.28 cnf(63,plain,
% 193.84/194.28 (~E(a1,f3(x631,x632))+~E(a6,f3(x632,x631))),
% 193.84/194.28 inference(scs_inference,[],[13,57,3])).
% 193.84/194.28 cnf(75,plain,
% 193.84/194.28 (~E(f3(x751,x752),a6)+~E(a1,f3(x752,x751))),
% 193.84/194.28 inference(scs_inference,[],[63,2])).
% 193.84/194.28 cnf(202,plain,
% 193.84/194.28 (E(a6,f3(a7,a8))+E(f5(a8),a6)+E(f5(a7),a6)+P2(a6,f3(a7,a8))),
% 193.84/194.28 inference(scs_inference,[],[2,50])).
% 193.84/194.28 cnf(246,plain,
% 193.84/194.28 (E(f5(x2461),a6)+E(a6,f5(x2462))+E(a6,f3(x2462,x2461))+~P2(a6,f3(x2462,x2461))),
% 193.84/194.28 inference(scs_inference,[],[48,2,24])).
% 193.84/194.28 cnf(250,plain,
% 193.84/194.28 (E(f5(x2501),a6)+~P2(a6,f3(x2501,x2502))+E(a6,f3(x2501,x2502))+E(f5(x2502),a6)),
% 193.84/194.28 inference(scs_inference,[],[2,246])).
% 193.84/194.28 cnf(252,plain,
% 193.84/194.28 (E(f3(x2521,x2522),a6)+~P2(a6,f3(x2521,x2522))+E(f5(x2522),a6)+E(a6,f5(x2521))),
% 193.84/194.28 inference(scs_inference,[],[2,246])).
% 193.84/194.28 cnf(254,plain,
% 193.84/194.28 (E(f3(x2541,x2542),a6)+E(f5(x2542),a6)+~P2(a6,f3(x2541,x2542))+E(f5(x2541),a6)),
% 193.84/194.28 inference(scs_inference,[],[2,250])).
% 193.84/194.28 cnf(262,plain,
% 193.84/194.28 (E(a6,f5(x2621))+E(f5(x2622),a6)+E(f3(x2622,x2621),a6)+~P2(a6,f3(x2622,x2621))),
% 193.84/194.28 inference(scs_inference,[],[2,254])).
% 193.84/194.28 cnf(832,plain,
% 193.84/194.28 (~E(a1,f5(x8321))+~P2(a6,f3(x8321,x8322))+E(f3(x8321,x8322),a6)+E(a6,f5(x8322))),
% 193.84/194.28 inference(scs_inference,[],[54,262])).
% 193.84/194.28 cnf(1039,plain,
% 193.84/194.28 (~E(a1,x10391)+P2(x10391,f3(x10392,x10393))),
% 193.84/194.28 inference(scs_inference,[],[15,2])).
% 193.84/194.28 cnf(1040,plain,
% 193.84/194.28 (P2(a1,f3(x10401,x10402))),
% 193.84/194.28 inference(equality_inference,[],[1039])).
% 193.84/194.28 cnf(1076,plain,
% 193.84/194.28 (~E(f5(a8),a6)+~E(a6,f5(a8))),
% 193.84/194.28 inference(scs_inference,[],[16,21])).
% 193.84/194.28 cnf(1078,plain,
% 193.84/194.28 (~E(f5(a8),a6)),
% 193.84/194.28 inference(scs_inference,[],[1076,2])).
% 193.84/194.28 cnf(1079,plain,
% 193.84/194.28 (E(f5(a7),a6)+E(f3(a7,a8),a6)+P2(a6,f3(a7,a8))),
% 193.84/194.28 inference(scs_inference,[],[1078,50])).
% 193.84/194.28 cnf(1085,plain,
% 193.84/194.28 (E(f5(a7),a6)+E(a6,f3(a7,a8))+P2(a6,f3(a7,a8))),
% 193.84/194.28 inference(scs_inference,[],[1078,202])).
% 193.84/194.28 cnf(1105,plain,
% 193.84/194.28 (~E(a6,f5(a8))),
% 193.84/194.28 inference(scs_inference,[],[1078,2])).
% 193.84/194.28 cnf(1106,plain,
% 193.84/194.28 (~E(x11061,a6)+~E(f5(a8),x11061)),
% 193.84/194.28 inference(scs_inference,[],[1078,2,3])).
% 193.84/194.28 cnf(1145,plain,
% 193.84/194.28 (~E(x11451,f5(a8))+~E(a6,x11451)),
% 193.84/194.28 inference(scs_inference,[],[1105,3])).
% 193.84/194.28 cnf(1952,plain,
% 193.84/194.28 (~E(a1,f5(x19521))+~P2(a6,f3(x19521,a8))+E(f3(x19521,a8),a6)),
% 193.84/194.28 inference(scs_inference,[],[1105,832])).
% 193.84/194.28 cnf(1955,plain,
% 193.84/194.28 (~E(f5(x19551),a1)+E(f3(x19551,a8),a6)+~P2(a6,f3(x19551,a8))),
% 193.84/194.28 inference(scs_inference,[],[1952,2])).
% 193.84/194.28 cnf(1957,plain,
% 193.84/194.28 (~P2(a6,f3(a7,a8))+~E(f5(a7),a1)),
% 193.84/194.28 inference(scs_inference,[],[1955,23])).
% 193.84/194.28 cnf(1962,plain,
% 193.84/194.28 (~E(a1,f5(a7))+~P2(a6,f3(a7,a8))),
% 193.84/194.28 inference(scs_inference,[],[1957,2])).
% 193.84/194.28 cnf(2084,plain,
% 193.84/194.28 (~E(a6,x20841)+~E(f5(a8),x20841)),
% 193.84/194.28 inference(scs_inference,[],[1106,2])).
% 193.84/194.28 cnf(2086,plain,
% 193.84/194.28 (~E(f5(a8),f3(x20861,x20862))+~E(a6,f3(x20862,x20861))),
% 193.84/194.28 inference(scs_inference,[],[13,2084,3])).
% 193.84/194.28 cnf(2088,plain,
% 193.84/194.28 (~E(f3(x20881,x20882),f5(a8))+~E(a6,f3(x20882,x20881))),
% 193.84/194.28 inference(scs_inference,[],[2086,2])).
% 193.84/194.28 cnf(2101,plain,
% 193.84/194.28 (~E(x21011,f5(a8))+~E(x21011,a6)),
% 193.84/194.28 inference(scs_inference,[],[1106,2])).
% 193.84/194.28 cnf(2106,plain,
% 193.84/194.28 (~E(f3(x21061,x21062),f5(a8))+~E(f3(x21062,x21061),a6)),
% 193.84/194.28 inference(scs_inference,[],[13,2101,3])).
% 193.84/194.28 cnf(2109,plain,
% 193.84/194.28 (~E(f5(a8),f3(x21091,x21092))+~E(f3(x21092,x21091),a6)),
% 193.84/194.28 inference(scs_inference,[],[2106,2])).
% 193.84/194.28 cnf(3865,plain,
% 193.84/194.28 (P2(a6,f3(x38651,x38652))+~P2(a6,f3(x38652,a8))+E(f3(x38652,a8),a6)),
% 193.84/194.28 inference(scs_inference,[],[1078,16,252])).
% 193.84/194.28 cnf(3874,plain,
% 193.84/194.28 (P2(a6,f3(x38741,x38742))+E(f3(x38741,a8),a6)+~P2(a6,f3(x38741,a8))),
% 193.84/194.28 inference(scs_inference,[],[13,3865,9])).
% 193.84/194.28 cnf(3876,plain,
% 193.84/194.28 (~P2(a6,f3(a7,a8))+P2(a6,f3(a7,x38761))),
% 193.84/194.28 inference(scs_inference,[],[3874,23])).
% 193.84/194.28 cnf(3878,plain,
% 193.84/194.28 (~P2(a6,f3(a8,a7))+P2(a6,f3(a7,x38781))),
% 193.84/194.28 inference(scs_inference,[],[13,3876,9])).
% 193.84/194.28 cnf(3886,plain,
% 193.84/194.28 (~E(a6,f3(a8,a7))+P2(a6,f3(a7,x38861))),
% 193.84/194.28 inference(scs_inference,[],[3878,22])).
% 193.84/194.28 cnf(3888,plain,
% 193.84/194.28 (~E(f3(a8,a7),a6)+P2(a6,f3(a7,x38881))),
% 193.84/194.28 inference(scs_inference,[],[3886,2])).
% 193.84/194.28 cnf(3891,plain,
% 193.84/194.28 (~E(f3(a7,a8),a6)+P2(a6,f3(a7,x38911))),
% 193.84/194.28 inference(scs_inference,[],[13,3888,3])).
% 193.84/194.28 cnf(4050,plain,
% 193.84/194.28 (~E(f5(a7),a6)+~E(a6,f5(a7))),
% 193.84/194.28 inference(scs_inference,[],[20,17])).
% 193.84/194.28 cnf(4060,plain,
% 193.84/194.28 (~E(f5(a7),a6)),
% 193.84/194.28 inference(scs_inference,[],[4050,2])).
% 193.84/194.28 cnf(4081,plain,
% 193.84/194.28 (E(f3(a7,a8),a6)+P2(a6,f3(a7,a8))),
% 193.84/194.28 inference(scs_inference,[],[4060,1079])).
% 193.84/194.28 cnf(4086,plain,
% 193.84/194.28 (E(a6,f3(a7,a8))+P2(a6,f3(a7,a8))),
% 193.84/194.28 inference(scs_inference,[],[4060,1085])).
% 193.84/194.28 cnf(4107,plain,
% 193.84/194.28 (~E(a6,f5(a7))),
% 193.84/194.28 inference(scs_inference,[],[4060,2])).
% 193.84/194.28 cnf(4153,plain,
% 193.84/194.28 (~E(f3(a7,a8),a6)+E(f3(a7,a7),a6)),
% 193.84/194.28 inference(scs_inference,[],[4107,4060,262,3891])).
% 193.84/194.28 cnf(4177,plain,
% 193.84/194.28 (~E(x41771,f5(a7))+~E(a6,x41771)),
% 193.84/194.28 inference(scs_inference,[],[4107,3])).
% 193.84/194.28 cnf(4190,plain,
% 193.84/194.28 (E(a6,f3(a7,a8))),
% 193.84/194.28 inference(scs_inference,[],[4107,1078,246,4081,4086])).
% 193.84/194.28 cnf(4261,plain,
% 193.84/194.28 ($false),
% 193.84/194.28 inference(scs_inference,[],[4190,1040,12,13,2086,1145,63,57,58,22,2,9,8,3,4153,4177,2088,2106,2109,1962,1957,75,55,23]),
% 193.84/194.29 ['proof']).
% 193.84/194.29 % SZS output end Proof
% 193.84/194.29 % Total time :193.240000s
%------------------------------------------------------------------------------