%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : MGT057+1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:04:22 AM UTC 2026
% Result : Theorem 0.64s 0.81s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT057+1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.02 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.07/0.34 % Computer : n003.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 7 13:31:09 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.23/0.51 start to proof:theBenchmark
% 0.54/0.80 %-------------------------------------------
% 0.54/0.80 % File :CSE---1.7
% 0.54/0.80 % Problem :theBenchmark
% 0.64/0.80 % Transform :cnf
% 0.64/0.80 % Format :tptp:raw
% 0.64/0.80 % Command :java -jar mcs_scs.jar %d %s
% 0.64/0.80
% 0.64/0.80 % Result :Theorem 0.309006s
% 0.64/0.80 % Output :CNFRefutation 0.309006s
% 0.64/0.80 %-------------------------------------------
% 0.64/0.80 %--------------------------------------------------------------------------
% 0.64/0.80 % File : MGT057+1 : TPTP v9.3.0. Released v2.4.0.
% 0.64/0.80 % Domain : Management (Organisation Theory)
% 0.64/0.80 % Problem : Conditions for a constant then increasing hazard of mortality
% 0.64/0.80 % Version : [Han98] axioms.
% 0.64/0.80 % English : In a drifting environment, an endowed organization's hazard of
% 0.64/0.80 % mortality is constant during the period of immunity; beyond the
% 0.64/0.80 % period of immunity, the hazard rises with age.
% 0.64/0.80
% 0.64/0.80 % Refs : [Kam00] Kamps (2000), Email to G. Sutcliffe
% 0.64/0.80 % : [CH00] Carroll & Hannan (2000), The Demography of Corporation
% 0.64/0.80 % : [Han98] Hannan (1998), Rethinking Age Dependence in Organizati
% 0.64/0.80 % Source : [Kam00]
% 0.64/0.80 % Names : THEOREM 6 [Han98]
% 0.64/0.80
% 0.64/0.80 % Status : Theorem
% 0.64/0.80 % Rating : 0.13 v9.3.0, 0.12 v9.0.0, 0.14 v8.2.0, 0.11 v8.1.0, 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 v6.2.0, 0.16 v6.1.0, 0.17 v6.0.0, 0.09 v5.5.0, 0.15 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.05 v3.4.0, 0.11 v3.3.0, 0.07 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.17 v2.6.0, 0.33 v2.5.0, 0.00 v2.4.0
% 0.64/0.80 % Syntax : Number of formulae : 10 ( 0 unt; 0 def)
% 0.64/0.80 % Number of atoms : 38 ( 6 equ)
% 0.64/0.80 % Maximal formula atoms : 8 ( 3 avg)
% 0.64/0.80 % Number of connectives : 31 ( 3 ~; 4 |; 14 &)
% 0.64/0.80 % ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% 0.64/0.80 % Maximal formula depth : 11 ( 6 avg)
% 0.64/0.80 % Maximal term depth : 2 ( 1 avg)
% 0.64/0.80 % Number of predicates : 8 ( 7 usr; 0 prp; 1-2 aty)
% 0.64/0.80 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.64/0.80 % Number of variables : 25 ( 25 !; 0 ?)
% 0.64/0.80 % SPC : FOF_THM_RFO_SEQ
% 0.64/0.80
% 0.64/0.80 % Comments : See MGT042+1.p for the mnemonic names.
% 0.64/0.80 %--------------------------------------------------------------------------
% 0.64/0.80 include('Axioms/MGT001+0.ax').
% 0.64/0.80 %--------------------------------------------------------------------------
% 0.64/0.80 %----Problem Axioms
% 0.64/0.80 %----An endowment provides an immunity that lasts until an
% 0.64/0.80 %----organization's age exceeds `eta'.
% 0.64/0.80 fof(definition_1,axiom,
% 0.64/0.80 ! [X] :
% 0.64/0.80 ( has_endowment(X)
% 0.64/0.80 <=> ! [T] :
% 0.64/0.80 ( organization(X)
% 0.64/0.80 & ( smaller_or_equal(age(X,T),eta)
% 0.64/0.80 => has_immunity(X,T) )
% 0.64/0.80 & ( greater(age(X,T),eta)
% 0.64/0.80 => ~ has_immunity(X,T) ) ) ) ).
% 0.64/0.80
% 0.64/0.80 %----An organization's hazard of mortality is constant during periods
% 0.64/0.80 %----in which it has immunity.
% 0.64/0.80 fof(assumption_2,axiom,
% 0.64/0.80 ! [X,T0,T] :
% 0.64/0.80 ( ( organization(X)
% 0.64/0.80 & has_immunity(X,T0)
% 0.64/0.80 & has_immunity(X,T) )
% 0.64/0.80 => hazard_of_mortality(X,T0) = hazard_of_mortality(X,T) ) ).
% 0.64/0.80
% 0.64/0.80 %----An organization's hazard of mortality is lower during periods in
% 0.64/0.80 %----which it has immunity than in periods in which it does not.
% 0.64/0.80 fof(assumption_3,axiom,
% 0.64/0.80 ! [X,T0,T] :
% 0.64/0.80 ( ( organization(X)
% 0.64/0.80 & has_immunity(X,T0)
% 0.64/0.80 & ~ has_immunity(X,T) )
% 0.64/0.80 => greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ) ).
% 0.64/0.80
% 0.64/0.80 %----Problem theorems
% 0.64/0.80 %----The obsolescence theorem for endowed organizations: In a drifting
% 0.64/0.81 %----environment, an endowed organization's hazard of mortality is
% 0.64/0.81 %----constant during the period of immunity; beyond the period of
% 0.64/0.81 %----immunity, the hazard rises with age.
% 0.64/0.81 %----From D1, A2, A3 (text says from L8,9; also needs D<, D<=).
% 0.64/0.81 %----
% 0.64/0.81 %----Text has redundant quantification over T3.
% 0.64/0.81 fof(theorem_6,conjecture,
% 0.64/0.81 ! [X,T0,T1,T2] :
% 0.64/0.81 ( ( organization(X)
% 0.64/0.81 & has_endowment(X)
% 0.64/0.81 & age(X,T0) = zero
% 0.64/0.81 & smaller_or_equal(age(X,T1),eta)
% 0.64/0.81 & greater(age(X,T2),eta)
% 0.64/0.81 & greater(eta,zero) )
% 0.64/0.81 => ( greater(hazard_of_mortality(X,T2),hazard_of_mortality(X,T1))
% 0.64/0.81 & hazard_of_mortality(X,T1) = hazard_of_mortality(X,T0) ) ) ).
% 0.64/0.81
% 0.64/0.81 %--------------------------------------------------------------------------
% 0.64/0.81 %-------------------------------------------
% 0.64/0.81 % Proof found
% 0.64/0.81 % SZS status Theorem for theBenchmark
% 0.64/0.81 % SZS output start Proof
% 0.64/0.81 %ClaNum:48(EqnAxiom:21)
% 0.64/0.81 %VarNum:106(SingletonVarNum:38)
% 0.64/0.81 %MaxLitNum:4
% 0.64/0.81 %MaxfuncDepth:2
% 0.64/0.81 %SharedTerms:20
% 0.64/0.81 %goalClause: 22 23 24 25 26 27 48
% 0.64/0.81 %singleGoalClaCount:6
% 0.64/0.81 [22]P1(a1)
% 0.64/0.81 [23]P4(a1)
% 0.64/0.81 [25]P2(a7,a6)
% 0.64/0.81 [24]E(f2(a1,a5),a6)
% 0.64/0.81 [26]P6(f2(a1,a8),a7)
% 0.64/0.81 [27]P2(f2(a1,a9),a7)
% 0.64/0.81 [48]~P2(f10(a1,a9),f10(a1,a8))+~E(f10(a1,a8),f10(a1,a5))
% 0.64/0.81 [28]~P1(x281)+P4(x281)
% 0.64/0.81 [29]~E(x291,x292)+P6(x291,x292)
% 0.64/0.81 [30]~E(x301,x302)+P3(x301,x302)
% 0.64/0.81 [32]~P7(x321,x322)+P6(x321,x322)
% 0.64/0.81 [33]~P2(x332,x331)+P7(x331,x332)
% 0.64/0.81 [34]~P2(x341,x342)+P3(x341,x342)
% 0.64/0.81 [35]~P7(x352,x351)+P2(x351,x352)
% 0.64/0.81 [38]~P2(x382,x381)+~P2(x381,x382)
% 0.64/0.81 [31]P7(x311,x312)+P2(x311,x312)+E(x311,x312)
% 0.64/0.81 [36]P7(x361,x362)+~P6(x361,x362)+E(x361,x362)
% 0.64/0.81 [37]P2(x371,x372)+~P3(x371,x372)+E(x371,x372)
% 0.64/0.81 [42]~P1(x421)+P5(x421,x422)+~P6(f2(x421,x422),a7)
% 0.64/0.81 [44]~P1(x441)+~P5(x441,x442)+~P2(f2(x441,x442),a7)
% 0.64/0.81 [39]~P2(x391,x393)+P2(x391,x392)+~P2(x393,x392)
% 0.64/0.81 [40]~P4(x401)+P1(x401)+P5(x401,f3(x401))+~P5(x401,f4(x401))
% 0.64/0.81 [43]~P4(x431)+P1(x431)+P5(x431,f3(x431))+P6(f2(x431,f4(x431)),a7)
% 0.64/0.81 [45]~P4(x451)+P1(x451)+~P5(x451,f4(x451))+P2(f2(x451,f3(x451)),a7)
% 0.64/0.81 [47]~P4(x471)+P1(x471)+P6(f2(x471,f4(x471)),a7)+P2(f2(x471,f3(x471)),a7)
% 0.64/0.81 [41]~P4(x411)+~P5(x411,x413)+~P5(x411,x412)+E(f10(x411,x412),f10(x411,x413))
% 0.64/0.81 [46]~P4(x461)+~P5(x461,x463)+P5(x461,x462)+P2(f10(x461,x462),f10(x461,x463))
% 0.64/0.81 %EqnAxiom
% 0.64/0.81 [1]E(x11,x11)
% 0.64/0.81 [2]E(x22,x21)+~E(x21,x22)
% 0.64/0.81 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.64/0.81 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.64/0.81 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.64/0.81 [6]~E(x61,x62)+E(f10(x61,x63),f10(x62,x63))
% 0.64/0.81 [7]~E(x71,x72)+E(f10(x73,x71),f10(x73,x72))
% 0.64/0.81 [8]~E(x81,x82)+E(f4(x81),f4(x82))
% 0.64/0.81 [9]~E(x91,x92)+E(f3(x91),f3(x92))
% 0.64/0.81 [10]~P1(x101)+P1(x102)+~E(x101,x102)
% 0.64/0.81 [11]~P4(x111)+P4(x112)+~E(x111,x112)
% 0.64/0.81 [12]P2(x122,x123)+~E(x121,x122)+~P2(x121,x123)
% 0.64/0.81 [13]P2(x133,x132)+~E(x131,x132)+~P2(x133,x131)
% 0.64/0.81 [14]P6(x142,x143)+~E(x141,x142)+~P6(x141,x143)
% 0.64/0.81 [15]P6(x153,x152)+~E(x151,x152)+~P6(x153,x151)
% 0.64/0.81 [16]P5(x162,x163)+~E(x161,x162)+~P5(x161,x163)
% 0.64/0.81 [17]P5(x173,x172)+~E(x171,x172)+~P5(x173,x171)
% 0.64/0.81 [18]P3(x182,x183)+~E(x181,x182)+~P3(x181,x183)
% 0.64/0.81 [19]P3(x193,x192)+~E(x191,x192)+~P3(x193,x191)
% 0.64/0.81 [20]P7(x202,x203)+~E(x201,x202)+~P7(x201,x203)
% 0.64/0.81 [21]P7(x213,x212)+~E(x211,x212)+~P7(x213,x211)
% 0.64/0.81
% 0.64/0.81 %-------------------------------------------
% 0.64/0.81 cnf(51,plain,
% 0.64/0.81 (~P2(a6,a7)),
% 0.64/0.81 inference(scs_inference,[],[25,38])).
% 0.64/0.81 cnf(53,plain,
% 0.64/0.81 (E(a6,f2(a1,a5))),
% 0.64/0.81 inference(scs_inference,[],[25,24,38,2])).
% 0.64/0.81 cnf(54,plain,
% 0.64/0.81 (P5(a1,a8)),
% 0.64/0.81 inference(scs_inference,[],[22,25,24,26,38,2,42])).
% 0.64/0.81 cnf(56,plain,
% 0.64/0.81 (~P5(a1,a9)),
% 0.64/0.81 inference(scs_inference,[],[22,25,24,26,27,38,2,42,44])).
% 0.64/0.81 cnf(58,plain,
% 0.64/0.81 (P2(f2(a1,a9),a6)),
% 0.64/0.81 inference(scs_inference,[],[22,25,24,26,27,38,2,42,44,39])).
% 0.64/0.81 cnf(61,plain,
% 0.64/0.81 (P2(a7,f2(a1,a5))),
% 0.64/0.81 inference(scs_inference,[],[22,25,24,26,27,38,2,42,44,39,12,13])).
% 0.64/0.81 cnf(83,plain,
% 0.64/0.81 (~P2(a7,f2(a1,a9))),
% 0.64/0.81 inference(scs_inference,[],[27,38])).
% 0.64/0.81 cnf(87,plain,
% 0.64/0.81 (~P2(a6,f2(a1,a9))),
% 0.64/0.81 inference(scs_inference,[],[27,51,38,35,39])).
% 0.64/0.81 cnf(89,plain,
% 0.64/0.81 (~E(a6,f2(a1,a9))),
% 0.64/0.81 inference(scs_inference,[],[25,27,51,38,35,39,13])).
% 0.64/0.81 cnf(101,plain,
% 0.64/0.81 (~P2(f2(a1,a5),a7)),
% 0.64/0.81 inference(scs_inference,[],[61,38])).
% 0.64/0.81 cnf(105,plain,
% 0.64/0.81 (P2(f2(a1,a9),f2(a1,a5))),
% 0.64/0.81 inference(scs_inference,[],[27,87,61,38,35,39])).
% 0.64/0.81 cnf(111,plain,
% 0.64/0.81 (P7(f2(a1,a5),f2(a1,a9))),
% 0.64/0.81 inference(scs_inference,[],[27,53,83,89,87,61,38,35,39,31,13,5,20])).
% 0.64/0.81 cnf(114,plain,
% 0.64/0.81 (P6(f2(a1,a8),x1141)+~E(a7,x1141)),
% 0.64/0.81 inference(scs_inference,[],[27,26,53,83,89,87,61,38,35,39,31,13,5,20,21,14,15])).
% 0.64/0.81 cnf(117,plain,
% 0.64/0.81 (P2(x1171,a6)+~E(a7,x1171)),
% 0.64/0.81 inference(scs_inference,[],[27,25,26,53,83,89,87,61,38,35,39,31,13,5,20,21,14,15,11,10,12])).
% 0.64/0.81 cnf(122,plain,
% 0.64/0.81 (~P2(f2(a1,a5),f2(a1,a9))),
% 0.64/0.81 inference(scs_inference,[],[105,38])).
% 0.64/0.81 cnf(128,plain,
% 0.64/0.81 (E(a6,a7)+P7(f2(a1,a5),a7)),
% 0.64/0.81 inference(scs_inference,[],[53,105,101,38,35,31,3])).
% 0.64/0.81 cnf(138,plain,
% 0.64/0.81 (P2(x1381,f2(a1,a5))+~E(a7,x1381)),
% 0.64/0.81 inference(scs_inference,[],[61,58,111,122,35,39,21,12])).
% 0.64/0.81 cnf(160,plain,
% 0.64/0.81 (P2(f10(a1,a9),f10(a1,a8))),
% 0.64/0.81 inference(scs_inference,[],[22,54,56,28,46])).
% 0.64/0.81 cnf(161,plain,
% 0.64/0.81 (~E(f10(a1,a8),f10(a1,a5))),
% 0.64/0.81 inference(scs_inference,[],[160,48])).
% 0.64/0.81 cnf(173,plain,
% 0.64/0.81 (P6(a6,f2(a1,a9))),
% 0.64/0.81 inference(scs_inference,[],[111,24,32,14])).
% 0.64/0.81 cnf(176,plain,
% 0.64/0.81 (~P5(a1,a5)),
% 0.64/0.81 inference(scs_inference,[],[23,161,54,53,173,7,14,41])).
% 0.64/0.81 cnf(207,plain,
% 0.64/0.81 (P3(x2071,a7)+~E(f2(a1,a9),x2071)),
% 0.64/0.81 inference(scs_inference,[],[27,34,18])).
% 0.64/0.81 cnf(208,plain,
% 0.64/0.81 (P3(f2(a1,a9),a7)),
% 0.64/0.81 inference(equality_inference,[],[207])).
% 0.64/0.81 cnf(209,plain,
% 0.64/0.81 (P3(f2(a1,a9),x2091)+~E(a7,x2091)),
% 0.64/0.81 inference(scs_inference,[],[208,19])).
% 0.64/0.81 cnf(227,plain,
% 0.64/0.81 (P6(f2(a1,a5),a7)+E(a6,a7)),
% 0.64/0.81 inference(scs_inference,[],[128,32])).
% 0.64/0.81 cnf(234,plain,
% 0.64/0.81 (E(a7,a6)+P6(f2(a1,a5),a7)),
% 0.64/0.81 inference(scs_inference,[],[227,2])).
% 0.64/0.81 cnf(237,plain,
% 0.64/0.81 (E(a7,a6)),
% 0.64/0.81 inference(scs_inference,[],[22,176,234,42])).
% 0.64/0.81 cnf(245,plain,
% 0.64/0.81 ($false),
% 0.64/0.81 inference(scs_inference,[],[237,114,117,138,209,38]),
% 0.64/0.81 ['proof']).
% 0.64/0.81 % SZS output end Proof
% 0.64/0.81 % Total time :0.309006s
%------------------------------------------------------------------------------