TSTP Solution File: HAL004+1 by SRASS---0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SRASS---0.1
% Problem : HAL004+1 : TPTP v5.0.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : SRASS -q2 -a 0 10 10 10 -i3 -n60 %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Wed Dec 29 07:25:21 EST 2010
% Result : Theorem 5.53s
% Output : Solution 5.53s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Reading problem from /tmp/SystemOnTPTP24173/HAL004+1.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM ...
% found
% SZS status THM for /tmp/SystemOnTPTP24173/HAL004+1.tptp
% SZS output start Solution for /tmp/SystemOnTPTP24173/HAL004+1.tptp
% TreeLimitedRun: ----------------------------------------------------------
% TreeLimitedRun: /home/graph/tptp/Systems/EP---1.2/eproof --print-statistics -xAuto -tAuto --cpu-limit=60 --proof-time-unlimited --memory-limit=Auto --tstp-in --tstp-out /tmp/SRASS.s.p
% TreeLimitedRun: CPU time limit is 60s
% TreeLimitedRun: WC time limit is 120s
% TreeLimitedRun: PID is 24269
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.00 WC
% PrfWatch: 1.92 CPU 2.01 WC
% # Preprocessing time : 0.014 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% PrfWatch: 3.91 CPU 4.01 WC
% # SZS output start CNFRefutation.
% fof(1, axiom,surjection(beta),file('/tmp/SRASS.s.p', beta_surjection)).
% fof(4, axiom,surjection(h),file('/tmp/SRASS.s.p', h_surjection)).
% fof(5, axiom,![X1]:![X2]:![X3]:((surjection(X1)&morphism(X1,X2,X3))=>![X4]:(element(X4,X3)=>?[X5]:(element(X5,X2)&apply(X1,X5)=X4))),file('/tmp/SRASS.s.p', surjection_properties)).
% fof(7, axiom,morphism(delta,e,r),file('/tmp/SRASS.s.p', delta_morphism)).
% fof(8, axiom,morphism(g,b,e),file('/tmp/SRASS.s.p', g_morphism)).
% fof(9, axiom,commute(beta,h,g,delta),file('/tmp/SRASS.s.p', beta_h_g_delta_commute)).
% fof(10, axiom,![X1]:![X2]:![X3]:(morphism(X1,X2,X3)=>(![X6]:(element(X6,X2)=>element(apply(X1,X6),X3))&apply(X1,zero(X2))=zero(X3))),file('/tmp/SRASS.s.p', morphism)).
% fof(13, axiom,![X9]:![X10]:![X11]:![X12]:![X2]:![X13]:![X14]:![X3]:(((((commute(X9,X10,X11,X12)&morphism(X9,X2,X13))&morphism(X10,X13,X3))&morphism(X11,X2,X14))&morphism(X12,X14,X3))=>![X5]:(element(X5,X2)=>apply(X10,apply(X9,X5))=apply(X12,apply(X11,X5)))),file('/tmp/SRASS.s.p', commute_properties)).
% fof(15, axiom,![X1]:![X2]:![X3]:(morphism(X1,X2,X3)=>![X7]:![X8]:((element(X7,X2)&element(X8,X2))=>apply(X1,subtract(X2,X7,X8))=subtract(X3,apply(X1,X7),apply(X1,X8)))),file('/tmp/SRASS.s.p', subtract_distribution)).
% fof(16, axiom,morphism(h,c,r),file('/tmp/SRASS.s.p', h_morphism)).
% fof(17, axiom,morphism(beta,b,c),file('/tmp/SRASS.s.p', beta_morphism)).
% fof(18, axiom,![X2]:![X7]:![X8]:((element(X7,X2)&element(X8,X2))=>subtract(X2,X7,subtract(X2,X7,X8))=X8),file('/tmp/SRASS.s.p', subtract_cancellation)).
% fof(19, axiom,![X2]:![X7]:![X8]:((element(X7,X2)&element(X8,X2))=>element(subtract(X2,X7,X8),X2)),file('/tmp/SRASS.s.p', subtract_in_domain)).
% fof(20, axiom,![X15]:![X16]:![X2]:![X17]:![X3]:(((exact(X15,X16)&morphism(X15,X2,X17))&morphism(X16,X17,X3))=>![X18]:((element(X18,X17)&apply(X16,X18)=zero(X3))<=>?[X5]:(element(X5,X2)&apply(X15,X5)=X18))),file('/tmp/SRASS.s.p', exact_properties)).
% fof(23, axiom,![X2]:![X6]:(element(X6,X2)=>subtract(X2,X6,X6)=zero(X2)),file('/tmp/SRASS.s.p', subtract_to_0)).
% fof(24, axiom,exact(alpha,beta),file('/tmp/SRASS.s.p', alpha_beta_exact)).
% fof(26, axiom,morphism(alpha,a,b),file('/tmp/SRASS.s.p', alpha_morphism)).
% fof(31, conjecture,![X19]:(element(X19,e)=>?[X20]:?[X21]:((((element(X20,r)&apply(delta,X19)=X20)&element(X21,b))&apply(h,apply(beta,X21))=X20)&apply(delta,apply(g,X21))=X20)),file('/tmp/SRASS.s.p', lemma3)).
% fof(32, negated_conjecture,~(![X19]:(element(X19,e)=>?[X20]:?[X21]:((((element(X20,r)&apply(delta,X19)=X20)&element(X21,b))&apply(h,apply(beta,X21))=X20)&apply(delta,apply(g,X21))=X20))),inference(assume_negation,[status(cth)],[31])).
% cnf(33,plain,(surjection(beta)),inference(split_conjunct,[status(thm)],[1])).
% cnf(36,plain,(surjection(h)),inference(split_conjunct,[status(thm)],[4])).
% fof(37, plain,![X1]:![X2]:![X3]:((~(surjection(X1))|~(morphism(X1,X2,X3)))|![X4]:(~(element(X4,X3))|?[X5]:(element(X5,X2)&apply(X1,X5)=X4))),inference(fof_nnf,[status(thm)],[5])).
% fof(38, plain,![X6]:![X7]:![X8]:((~(surjection(X6))|~(morphism(X6,X7,X8)))|![X9]:(~(element(X9,X8))|?[X10]:(element(X10,X7)&apply(X6,X10)=X9))),inference(variable_rename,[status(thm)],[37])).
% fof(39, plain,![X6]:![X7]:![X8]:((~(surjection(X6))|~(morphism(X6,X7,X8)))|![X9]:(~(element(X9,X8))|(element(esk1_4(X6,X7,X8,X9),X7)&apply(X6,esk1_4(X6,X7,X8,X9))=X9))),inference(skolemize,[status(esa)],[38])).
% fof(40, plain,![X6]:![X7]:![X8]:![X9]:((~(element(X9,X8))|(element(esk1_4(X6,X7,X8,X9),X7)&apply(X6,esk1_4(X6,X7,X8,X9))=X9))|(~(surjection(X6))|~(morphism(X6,X7,X8)))),inference(shift_quantors,[status(thm)],[39])).
% fof(41, plain,![X6]:![X7]:![X8]:![X9]:(((element(esk1_4(X6,X7,X8,X9),X7)|~(element(X9,X8)))|(~(surjection(X6))|~(morphism(X6,X7,X8))))&((apply(X6,esk1_4(X6,X7,X8,X9))=X9|~(element(X9,X8)))|(~(surjection(X6))|~(morphism(X6,X7,X8))))),inference(distribute,[status(thm)],[40])).
% cnf(42,plain,(apply(X1,esk1_4(X1,X2,X3,X4))=X4|~morphism(X1,X2,X3)|~surjection(X1)|~element(X4,X3)),inference(split_conjunct,[status(thm)],[41])).
% cnf(43,plain,(element(esk1_4(X1,X2,X3,X4),X2)|~morphism(X1,X2,X3)|~surjection(X1)|~element(X4,X3)),inference(split_conjunct,[status(thm)],[41])).
% cnf(51,plain,(morphism(delta,e,r)),inference(split_conjunct,[status(thm)],[7])).
% cnf(52,plain,(morphism(g,b,e)),inference(split_conjunct,[status(thm)],[8])).
% cnf(53,plain,(commute(beta,h,g,delta)),inference(split_conjunct,[status(thm)],[9])).
% fof(54, plain,![X1]:![X2]:![X3]:(~(morphism(X1,X2,X3))|(![X6]:(~(element(X6,X2))|element(apply(X1,X6),X3))&apply(X1,zero(X2))=zero(X3))),inference(fof_nnf,[status(thm)],[10])).
% fof(55, plain,![X7]:![X8]:![X9]:(~(morphism(X7,X8,X9))|(![X10]:(~(element(X10,X8))|element(apply(X7,X10),X9))&apply(X7,zero(X8))=zero(X9))),inference(variable_rename,[status(thm)],[54])).
% fof(56, plain,![X7]:![X8]:![X9]:![X10]:(((~(element(X10,X8))|element(apply(X7,X10),X9))&apply(X7,zero(X8))=zero(X9))|~(morphism(X7,X8,X9))),inference(shift_quantors,[status(thm)],[55])).
% fof(57, plain,![X7]:![X8]:![X9]:![X10]:(((~(element(X10,X8))|element(apply(X7,X10),X9))|~(morphism(X7,X8,X9)))&(apply(X7,zero(X8))=zero(X9)|~(morphism(X7,X8,X9)))),inference(distribute,[status(thm)],[56])).
% cnf(58,plain,(apply(X1,zero(X2))=zero(X3)|~morphism(X1,X2,X3)),inference(split_conjunct,[status(thm)],[57])).
% cnf(59,plain,(element(apply(X1,X4),X3)|~morphism(X1,X2,X3)|~element(X4,X2)),inference(split_conjunct,[status(thm)],[57])).
% fof(72, plain,![X9]:![X10]:![X11]:![X12]:![X2]:![X13]:![X14]:![X3]:(((((~(commute(X9,X10,X11,X12))|~(morphism(X9,X2,X13)))|~(morphism(X10,X13,X3)))|~(morphism(X11,X2,X14)))|~(morphism(X12,X14,X3)))|![X5]:(~(element(X5,X2))|apply(X10,apply(X9,X5))=apply(X12,apply(X11,X5)))),inference(fof_nnf,[status(thm)],[13])).
% fof(73, plain,![X15]:![X16]:![X17]:![X18]:![X19]:![X20]:![X21]:![X22]:(((((~(commute(X15,X16,X17,X18))|~(morphism(X15,X19,X20)))|~(morphism(X16,X20,X22)))|~(morphism(X17,X19,X21)))|~(morphism(X18,X21,X22)))|![X23]:(~(element(X23,X19))|apply(X16,apply(X15,X23))=apply(X18,apply(X17,X23)))),inference(variable_rename,[status(thm)],[72])).
% fof(74, plain,![X15]:![X16]:![X17]:![X18]:![X19]:![X20]:![X21]:![X22]:![X23]:((~(element(X23,X19))|apply(X16,apply(X15,X23))=apply(X18,apply(X17,X23)))|((((~(commute(X15,X16,X17,X18))|~(morphism(X15,X19,X20)))|~(morphism(X16,X20,X22)))|~(morphism(X17,X19,X21)))|~(morphism(X18,X21,X22)))),inference(shift_quantors,[status(thm)],[73])).
% cnf(75,plain,(apply(X6,apply(X8,X9))=apply(X1,apply(X4,X9))|~morphism(X1,X2,X3)|~morphism(X4,X5,X2)|~morphism(X6,X7,X3)|~morphism(X8,X5,X7)|~commute(X8,X6,X4,X1)|~element(X9,X5)),inference(split_conjunct,[status(thm)],[74])).
% fof(82, plain,![X1]:![X2]:![X3]:(~(morphism(X1,X2,X3))|![X7]:![X8]:((~(element(X7,X2))|~(element(X8,X2)))|apply(X1,subtract(X2,X7,X8))=subtract(X3,apply(X1,X7),apply(X1,X8)))),inference(fof_nnf,[status(thm)],[15])).
% fof(83, plain,![X9]:![X10]:![X11]:(~(morphism(X9,X10,X11))|![X12]:![X13]:((~(element(X12,X10))|~(element(X13,X10)))|apply(X9,subtract(X10,X12,X13))=subtract(X11,apply(X9,X12),apply(X9,X13)))),inference(variable_rename,[status(thm)],[82])).
% fof(84, plain,![X9]:![X10]:![X11]:![X12]:![X13]:(((~(element(X12,X10))|~(element(X13,X10)))|apply(X9,subtract(X10,X12,X13))=subtract(X11,apply(X9,X12),apply(X9,X13)))|~(morphism(X9,X10,X11))),inference(shift_quantors,[status(thm)],[83])).
% cnf(85,plain,(apply(X1,subtract(X2,X4,X5))=subtract(X3,apply(X1,X4),apply(X1,X5))|~morphism(X1,X2,X3)|~element(X5,X2)|~element(X4,X2)),inference(split_conjunct,[status(thm)],[84])).
% cnf(86,plain,(morphism(h,c,r)),inference(split_conjunct,[status(thm)],[16])).
% cnf(87,plain,(morphism(beta,b,c)),inference(split_conjunct,[status(thm)],[17])).
% fof(88, plain,![X2]:![X7]:![X8]:((~(element(X7,X2))|~(element(X8,X2)))|subtract(X2,X7,subtract(X2,X7,X8))=X8),inference(fof_nnf,[status(thm)],[18])).
% fof(89, plain,![X9]:![X10]:![X11]:((~(element(X10,X9))|~(element(X11,X9)))|subtract(X9,X10,subtract(X9,X10,X11))=X11),inference(variable_rename,[status(thm)],[88])).
% cnf(90,plain,(subtract(X1,X2,subtract(X1,X2,X3))=X3|~element(X3,X1)|~element(X2,X1)),inference(split_conjunct,[status(thm)],[89])).
% fof(91, plain,![X2]:![X7]:![X8]:((~(element(X7,X2))|~(element(X8,X2)))|element(subtract(X2,X7,X8),X2)),inference(fof_nnf,[status(thm)],[19])).
% fof(92, plain,![X9]:![X10]:![X11]:((~(element(X10,X9))|~(element(X11,X9)))|element(subtract(X9,X10,X11),X9)),inference(variable_rename,[status(thm)],[91])).
% cnf(93,plain,(element(subtract(X1,X2,X3),X1)|~element(X3,X1)|~element(X2,X1)),inference(split_conjunct,[status(thm)],[92])).
% fof(94, plain,![X15]:![X16]:![X2]:![X17]:![X3]:(((~(exact(X15,X16))|~(morphism(X15,X2,X17)))|~(morphism(X16,X17,X3)))|![X18]:(((~(element(X18,X17))|~(apply(X16,X18)=zero(X3)))|?[X5]:(element(X5,X2)&apply(X15,X5)=X18))&(![X5]:(~(element(X5,X2))|~(apply(X15,X5)=X18))|(element(X18,X17)&apply(X16,X18)=zero(X3))))),inference(fof_nnf,[status(thm)],[20])).
% fof(95, plain,![X19]:![X20]:![X21]:![X22]:![X23]:(((~(exact(X19,X20))|~(morphism(X19,X21,X22)))|~(morphism(X20,X22,X23)))|![X24]:(((~(element(X24,X22))|~(apply(X20,X24)=zero(X23)))|?[X25]:(element(X25,X21)&apply(X19,X25)=X24))&(![X26]:(~(element(X26,X21))|~(apply(X19,X26)=X24))|(element(X24,X22)&apply(X20,X24)=zero(X23))))),inference(variable_rename,[status(thm)],[94])).
% fof(96, plain,![X19]:![X20]:![X21]:![X22]:![X23]:(((~(exact(X19,X20))|~(morphism(X19,X21,X22)))|~(morphism(X20,X22,X23)))|![X24]:(((~(element(X24,X22))|~(apply(X20,X24)=zero(X23)))|(element(esk6_6(X19,X20,X21,X22,X23,X24),X21)&apply(X19,esk6_6(X19,X20,X21,X22,X23,X24))=X24))&(![X26]:(~(element(X26,X21))|~(apply(X19,X26)=X24))|(element(X24,X22)&apply(X20,X24)=zero(X23))))),inference(skolemize,[status(esa)],[95])).
% fof(97, plain,![X19]:![X20]:![X21]:![X22]:![X23]:![X24]:![X26]:((((~(element(X26,X21))|~(apply(X19,X26)=X24))|(element(X24,X22)&apply(X20,X24)=zero(X23)))&((~(element(X24,X22))|~(apply(X20,X24)=zero(X23)))|(element(esk6_6(X19,X20,X21,X22,X23,X24),X21)&apply(X19,esk6_6(X19,X20,X21,X22,X23,X24))=X24)))|((~(exact(X19,X20))|~(morphism(X19,X21,X22)))|~(morphism(X20,X22,X23)))),inference(shift_quantors,[status(thm)],[96])).
% fof(98, plain,![X19]:![X20]:![X21]:![X22]:![X23]:![X24]:![X26]:((((element(X24,X22)|(~(element(X26,X21))|~(apply(X19,X26)=X24)))|((~(exact(X19,X20))|~(morphism(X19,X21,X22)))|~(morphism(X20,X22,X23))))&((apply(X20,X24)=zero(X23)|(~(element(X26,X21))|~(apply(X19,X26)=X24)))|((~(exact(X19,X20))|~(morphism(X19,X21,X22)))|~(morphism(X20,X22,X23)))))&(((element(esk6_6(X19,X20,X21,X22,X23,X24),X21)|(~(element(X24,X22))|~(apply(X20,X24)=zero(X23))))|((~(exact(X19,X20))|~(morphism(X19,X21,X22)))|~(morphism(X20,X22,X23))))&((apply(X19,esk6_6(X19,X20,X21,X22,X23,X24))=X24|(~(element(X24,X22))|~(apply(X20,X24)=zero(X23))))|((~(exact(X19,X20))|~(morphism(X19,X21,X22)))|~(morphism(X20,X22,X23)))))),inference(distribute,[status(thm)],[97])).
% cnf(100,plain,(element(esk6_6(X4,X1,X5,X2,X3,X6),X5)|~morphism(X1,X2,X3)|~morphism(X4,X5,X2)|~exact(X4,X1)|apply(X1,X6)!=zero(X3)|~element(X6,X2)),inference(split_conjunct,[status(thm)],[98])).
% cnf(101,plain,(apply(X1,X7)=zero(X3)|~morphism(X1,X2,X3)|~morphism(X4,X5,X2)|~exact(X4,X1)|apply(X4,X6)!=X7|~element(X6,X5)),inference(split_conjunct,[status(thm)],[98])).
% fof(114, plain,![X2]:![X6]:(~(element(X6,X2))|subtract(X2,X6,X6)=zero(X2)),inference(fof_nnf,[status(thm)],[23])).
% fof(115, plain,![X7]:![X8]:(~(element(X8,X7))|subtract(X7,X8,X8)=zero(X7)),inference(variable_rename,[status(thm)],[114])).
% cnf(116,plain,(subtract(X1,X2,X2)=zero(X1)|~element(X2,X1)),inference(split_conjunct,[status(thm)],[115])).
% cnf(117,plain,(exact(alpha,beta)),inference(split_conjunct,[status(thm)],[24])).
% cnf(119,plain,(morphism(alpha,a,b)),inference(split_conjunct,[status(thm)],[26])).
% fof(124, negated_conjecture,?[X19]:(element(X19,e)&![X20]:![X21]:((((~(element(X20,r))|~(apply(delta,X19)=X20))|~(element(X21,b)))|~(apply(h,apply(beta,X21))=X20))|~(apply(delta,apply(g,X21))=X20))),inference(fof_nnf,[status(thm)],[32])).
% fof(125, negated_conjecture,?[X22]:(element(X22,e)&![X23]:![X24]:((((~(element(X23,r))|~(apply(delta,X22)=X23))|~(element(X24,b)))|~(apply(h,apply(beta,X24))=X23))|~(apply(delta,apply(g,X24))=X23))),inference(variable_rename,[status(thm)],[124])).
% fof(126, negated_conjecture,(element(esk9_0,e)&![X23]:![X24]:((((~(element(X23,r))|~(apply(delta,esk9_0)=X23))|~(element(X24,b)))|~(apply(h,apply(beta,X24))=X23))|~(apply(delta,apply(g,X24))=X23))),inference(skolemize,[status(esa)],[125])).
% fof(127, negated_conjecture,![X23]:![X24]:(((((~(element(X23,r))|~(apply(delta,esk9_0)=X23))|~(element(X24,b)))|~(apply(h,apply(beta,X24))=X23))|~(apply(delta,apply(g,X24))=X23))&element(esk9_0,e)),inference(shift_quantors,[status(thm)],[126])).
% cnf(128,negated_conjecture,(element(esk9_0,e)),inference(split_conjunct,[status(thm)],[127])).
% cnf(129,negated_conjecture,(apply(delta,apply(g,X1))!=X2|apply(h,apply(beta,X1))!=X2|~element(X1,b)|apply(delta,esk9_0)!=X2|~element(X2,r)),inference(split_conjunct,[status(thm)],[127])).
% cnf(130,plain,(element(zero(X1),X1)|~element(X2,X1)),inference(spm,[status(thm)],[93,116,theory(equality)])).
% cnf(133,plain,(apply(g,zero(b))=zero(e)),inference(spm,[status(thm)],[58,52,theory(equality)])).
% cnf(134,plain,(apply(h,zero(c))=zero(r)),inference(spm,[status(thm)],[58,86,theory(equality)])).
% cnf(136,plain,(apply(delta,zero(e))=zero(r)),inference(spm,[status(thm)],[58,51,theory(equality)])).
% cnf(137,plain,(apply(beta,zero(b))=zero(c)),inference(spm,[status(thm)],[58,87,theory(equality)])).
% cnf(139,plain,(element(apply(alpha,X1),b)|~element(X1,a)),inference(spm,[status(thm)],[59,119,theory(equality)])).
% cnf(140,plain,(element(apply(g,X1),e)|~element(X1,b)),inference(spm,[status(thm)],[59,52,theory(equality)])).
% cnf(141,plain,(element(apply(h,X1),r)|~element(X1,c)),inference(spm,[status(thm)],[59,86,theory(equality)])).
% cnf(143,plain,(element(apply(delta,X1),r)|~element(X1,e)),inference(spm,[status(thm)],[59,51,theory(equality)])).
% cnf(144,plain,(element(apply(beta,X1),c)|~element(X1,b)),inference(spm,[status(thm)],[59,87,theory(equality)])).
% cnf(146,plain,(subtract(X1,X2,zero(X1))=X2|~element(X2,X1)),inference(spm,[status(thm)],[90,116,theory(equality)])).
% cnf(147,negated_conjecture,(apply(delta,apply(g,X1))!=apply(h,apply(beta,X1))|apply(delta,esk9_0)!=apply(h,apply(beta,X1))|~element(apply(h,apply(beta,X1)),r)|~element(X1,b)),inference(er,[status(thm)],[129,theory(equality)])).
% cnf(177,plain,(apply(X1,X2)=zero(X3)|apply(alpha,X4)!=X2|~exact(alpha,X1)|~element(X4,a)|~morphism(X1,b,X3)),inference(spm,[status(thm)],[101,119,theory(equality)])).
% cnf(185,plain,(subtract(e,apply(g,X1),apply(g,X2))=apply(g,subtract(b,X1,X2))|~element(X2,b)|~element(X1,b)),inference(spm,[status(thm)],[85,52,theory(equality)])).
% cnf(186,plain,(subtract(r,apply(h,X1),apply(h,X2))=apply(h,subtract(c,X1,X2))|~element(X2,c)|~element(X1,c)),inference(spm,[status(thm)],[85,86,theory(equality)])).
% cnf(188,plain,(subtract(r,apply(delta,X1),apply(delta,X2))=apply(delta,subtract(e,X1,X2))|~element(X2,e)|~element(X1,e)),inference(spm,[status(thm)],[85,51,theory(equality)])).
% cnf(189,plain,(subtract(c,apply(beta,X1),apply(beta,X2))=apply(beta,subtract(b,X1,X2))|~element(X2,b)|~element(X1,b)),inference(spm,[status(thm)],[85,87,theory(equality)])).
% cnf(215,plain,(apply(delta,apply(g,X1))=apply(h,apply(beta,X1))|~element(X1,X2)|~morphism(beta,X2,X3)|~morphism(h,X3,X4)|~morphism(g,X2,X5)|~morphism(delta,X5,X4)),inference(spm,[status(thm)],[75,53,theory(equality)])).
% cnf(234,negated_conjecture,(element(zero(e),e)),inference(spm,[status(thm)],[130,128,theory(equality)])).
% cnf(235,plain,(element(zero(X1),X1)|apply(X3,X6)!=zero(X5)|~exact(X2,X3)|~element(X6,X4)|~morphism(X2,X1,X4)|~morphism(X3,X4,X5)),inference(spm,[status(thm)],[130,100,theory(equality)])).
% cnf(240,plain,(element(zero(X1),X1)|~element(X4,X3)|~morphism(X2,X1,X3)|~surjection(X2)),inference(spm,[status(thm)],[130,43,theory(equality)])).
% cnf(253,plain,(element(zero(r),r)|~element(zero(e),e)),inference(spm,[status(thm)],[143,136,theory(equality)])).
% cnf(256,plain,(element(zero(r),r)|$false),inference(rw,[status(thm)],[253,234,theory(equality)])).
% cnf(257,plain,(element(zero(r),r)),inference(cn,[status(thm)],[256,theory(equality)])).
% cnf(276,negated_conjecture,(apply(h,apply(beta,X1))!=apply(delta,apply(g,X1))|apply(h,apply(beta,X1))!=apply(delta,esk9_0)|~element(X1,b)|~element(apply(beta,X1),c)),inference(spm,[status(thm)],[147,141,theory(equality)])).
% cnf(303,negated_conjecture,(apply(h,apply(beta,X1))!=apply(delta,apply(g,X1))|apply(h,apply(beta,X1))!=apply(delta,esk9_0)|~element(X1,b)),inference(csr,[status(thm)],[276,144])).
% cnf(526,plain,(element(zero(c),c)|~element(X1,r)|~surjection(h)),inference(spm,[status(thm)],[240,86,theory(equality)])).
% cnf(529,plain,(element(zero(b),b)|~element(X1,c)|~surjection(beta)),inference(spm,[status(thm)],[240,87,theory(equality)])).
% cnf(530,plain,(element(zero(c),c)|~element(X1,r)|$false),inference(rw,[status(thm)],[526,36,theory(equality)])).
% cnf(531,plain,(element(zero(c),c)|~element(X1,r)),inference(cn,[status(thm)],[530,theory(equality)])).
% cnf(537,plain,(element(zero(b),b)|~element(X1,c)|$false),inference(rw,[status(thm)],[529,33,theory(equality)])).
% cnf(538,plain,(element(zero(b),b)|~element(X1,c)),inference(cn,[status(thm)],[537,theory(equality)])).
% cnf(556,plain,(element(zero(c),c)),inference(spm,[status(thm)],[531,257,theory(equality)])).
% cnf(561,plain,(element(zero(b),b)),inference(spm,[status(thm)],[538,556,theory(equality)])).
% cnf(687,plain,(apply(beta,X1)=zero(c)|apply(alpha,X2)!=X1|~exact(alpha,beta)|~element(X2,a)),inference(spm,[status(thm)],[177,87,theory(equality)])).
% cnf(688,plain,(apply(beta,X1)=zero(c)|apply(alpha,X2)!=X1|$false|~element(X2,a)),inference(rw,[status(thm)],[687,117,theory(equality)])).
% cnf(689,plain,(apply(beta,X1)=zero(c)|apply(alpha,X2)!=X1|~element(X2,a)),inference(cn,[status(thm)],[688,theory(equality)])).
% cnf(693,plain,(apply(beta,apply(alpha,X1))=zero(c)|~element(X1,a)),inference(er,[status(thm)],[689,theory(equality)])).
% cnf(749,plain,(subtract(e,apply(g,X1),zero(e))=apply(g,subtract(b,X1,zero(b)))|~element(zero(b),b)|~element(X1,b)),inference(spm,[status(thm)],[185,133,theory(equality)])).
% cnf(754,plain,(subtract(e,apply(g,X1),zero(e))=apply(g,subtract(b,X1,zero(b)))|$false|~element(X1,b)),inference(rw,[status(thm)],[749,561,theory(equality)])).
% cnf(755,plain,(subtract(e,apply(g,X1),zero(e))=apply(g,subtract(b,X1,zero(b)))|~element(X1,b)),inference(cn,[status(thm)],[754,theory(equality)])).
% cnf(770,plain,(element(apply(g,subtract(b,X1,zero(b))),e)|~element(zero(e),e)|~element(apply(g,X1),e)|~element(X1,b)),inference(spm,[status(thm)],[93,755,theory(equality)])).
% cnf(779,plain,(element(apply(g,subtract(b,X1,zero(b))),e)|$false|~element(apply(g,X1),e)|~element(X1,b)),inference(rw,[status(thm)],[770,234,theory(equality)])).
% cnf(780,plain,(element(apply(g,subtract(b,X1,zero(b))),e)|~element(apply(g,X1),e)|~element(X1,b)),inference(cn,[status(thm)],[779,theory(equality)])).
% cnf(787,plain,(element(apply(g,subtract(b,X1,zero(b))),e)|~element(X1,b)),inference(csr,[status(thm)],[780,140])).
% cnf(948,plain,(subtract(r,apply(delta,X1),zero(r))=apply(delta,subtract(e,X1,zero(e)))|~element(zero(e),e)|~element(X1,e)),inference(spm,[status(thm)],[188,136,theory(equality)])).
% cnf(955,plain,(subtract(r,apply(delta,X1),zero(r))=apply(delta,subtract(e,X1,zero(e)))|$false|~element(X1,e)),inference(rw,[status(thm)],[948,234,theory(equality)])).
% cnf(956,plain,(subtract(r,apply(delta,X1),zero(r))=apply(delta,subtract(e,X1,zero(e)))|~element(X1,e)),inference(cn,[status(thm)],[955,theory(equality)])).
% cnf(1162,plain,(subtract(r,apply(h,X1),zero(r))=apply(h,subtract(c,X1,zero(c)))|~element(zero(c),c)|~element(X1,c)),inference(spm,[status(thm)],[186,134,theory(equality)])).
% cnf(1169,plain,(subtract(r,apply(h,X1),zero(r))=apply(h,subtract(c,X1,zero(c)))|$false|~element(X1,c)),inference(rw,[status(thm)],[1162,556,theory(equality)])).
% cnf(1170,plain,(subtract(r,apply(h,X1),zero(r))=apply(h,subtract(c,X1,zero(c)))|~element(X1,c)),inference(cn,[status(thm)],[1169,theory(equality)])).
% cnf(1288,plain,(subtract(c,apply(beta,X1),zero(c))=apply(beta,subtract(b,X1,zero(b)))|~element(zero(b),b)|~element(X1,b)),inference(spm,[status(thm)],[189,137,theory(equality)])).
% cnf(1289,plain,(subtract(c,apply(beta,X1),zero(c))=apply(beta,subtract(b,X1,apply(alpha,X2)))|~element(apply(alpha,X2),b)|~element(X1,b)|~element(X2,a)),inference(spm,[status(thm)],[189,693,theory(equality)])).
% cnf(1297,plain,(subtract(c,apply(beta,X1),zero(c))=apply(beta,subtract(b,X1,zero(b)))|$false|~element(X1,b)),inference(rw,[status(thm)],[1288,561,theory(equality)])).
% cnf(1298,plain,(subtract(c,apply(beta,X1),zero(c))=apply(beta,subtract(b,X1,zero(b)))|~element(X1,b)),inference(cn,[status(thm)],[1297,theory(equality)])).
% cnf(1596,plain,(apply(delta,subtract(e,X1,zero(e)))=apply(delta,X1)|~element(apply(delta,X1),r)|~element(X1,e)),inference(spm,[status(thm)],[146,956,theory(equality)])).
% cnf(1670,plain,(apply(delta,subtract(e,X1,zero(e)))=apply(delta,X1)|~element(X1,e)),inference(csr,[status(thm)],[1596,143])).
% cnf(1682,plain,(apply(delta,apply(g,subtract(b,X1,zero(b))))=apply(delta,apply(g,X1))|~element(apply(g,X1),e)|~element(X1,b)),inference(spm,[status(thm)],[1670,755,theory(equality)])).
% cnf(1804,plain,(apply(delta,apply(g,subtract(b,X1,zero(b))))=apply(delta,apply(g,X1))|~element(X1,b)),inference(csr,[status(thm)],[1682,140])).
% cnf(1808,plain,(subtract(r,apply(delta,apply(g,X1)),zero(r))=apply(delta,subtract(e,apply(g,subtract(b,X1,zero(b))),zero(e)))|~element(apply(g,subtract(b,X1,zero(b))),e)|~element(X1,b)),inference(spm,[status(thm)],[956,1804,theory(equality)])).
% cnf(2114,plain,(apply(h,subtract(c,X1,zero(c)))=apply(h,X1)|~element(apply(h,X1),r)|~element(X1,c)),inference(spm,[status(thm)],[146,1170,theory(equality)])).
% cnf(2236,plain,(apply(h,subtract(c,X1,zero(c)))=apply(h,X1)|~element(X1,c)),inference(csr,[status(thm)],[2114,141])).
% cnf(2425,plain,(element(apply(beta,subtract(b,X1,zero(b))),c)|~element(zero(c),c)|~element(apply(beta,X1),c)|~element(X1,b)),inference(spm,[status(thm)],[93,1298,theory(equality)])).
% cnf(2432,plain,(apply(h,apply(beta,subtract(b,X1,zero(b))))=apply(h,apply(beta,X1))|~element(apply(beta,X1),c)|~element(X1,b)),inference(spm,[status(thm)],[2236,1298,theory(equality)])).
% cnf(2446,plain,(element(apply(beta,subtract(b,X1,zero(b))),c)|$false|~element(apply(beta,X1),c)|~element(X1,b)),inference(rw,[status(thm)],[2425,556,theory(equality)])).
% cnf(2447,plain,(element(apply(beta,subtract(b,X1,zero(b))),c)|~element(apply(beta,X1),c)|~element(X1,b)),inference(cn,[status(thm)],[2446,theory(equality)])).
% cnf(2460,plain,(element(apply(beta,subtract(b,X1,zero(b))),c)|~element(X1,b)),inference(csr,[status(thm)],[2447,144])).
% cnf(2786,plain,(apply(h,apply(beta,X1))=apply(delta,apply(g,X1))|~element(X1,b)|~morphism(h,c,X2)|~morphism(g,b,X3)|~morphism(delta,X3,X2)),inference(spm,[status(thm)],[215,87,theory(equality)])).
% cnf(2876,plain,(apply(h,apply(beta,subtract(b,X1,zero(b))))=apply(h,apply(beta,X1))|~element(X1,b)),inference(csr,[status(thm)],[2432,144])).
% cnf(2878,plain,(subtract(r,apply(h,apply(beta,X1)),apply(h,X2))=apply(h,subtract(c,apply(beta,subtract(b,X1,zero(b))),X2))|~element(X2,c)|~element(apply(beta,subtract(b,X1,zero(b))),c)|~element(X1,b)),inference(spm,[status(thm)],[186,2876,theory(equality)])).
% cnf(3605,plain,(element(zero(a),a)|apply(X1,X2)!=zero(X3)|~exact(alpha,X1)|~element(X2,b)|~morphism(X1,b,X3)),inference(spm,[status(thm)],[235,119,theory(equality)])).
% cnf(13718,plain,(subtract(c,apply(beta,X1),zero(c))=apply(beta,subtract(b,X1,apply(alpha,X2)))|~element(X1,b)|~element(X2,a)),inference(csr,[status(thm)],[1289,139])).
% cnf(13758,plain,(apply(h,apply(beta,subtract(b,X1,apply(alpha,X2))))=apply(h,apply(beta,X1))|~element(apply(beta,X1),c)|~element(X1,b)|~element(X2,a)),inference(spm,[status(thm)],[2236,13718,theory(equality)])).
% cnf(21452,plain,(apply(h,apply(beta,subtract(b,X1,apply(alpha,X2))))=apply(h,apply(beta,X1))|~element(X1,b)|~element(X2,a)),inference(csr,[status(thm)],[13758,144])).
% cnf(21520,plain,(apply(h,subtract(c,apply(beta,X1),zero(c)))=apply(h,apply(beta,X1))|~element(X1,b)|~element(X2,a)),inference(spm,[status(thm)],[21452,13718,theory(equality)])).
% cnf(22173,plain,(apply(delta,subtract(e,apply(g,subtract(b,X1,zero(b))),zero(e)))=subtract(r,apply(delta,apply(g,X1)),zero(r))|~element(X1,b)),inference(csr,[status(thm)],[1808,787])).
% cnf(22216,plain,(apply(delta,subtract(e,apply(g,X1),zero(e)))=subtract(r,apply(delta,apply(g,X1)),zero(r))|~element(X1,b)),inference(spm,[status(thm)],[22173,146,theory(equality)])).
% cnf(34386,plain,(element(zero(a),a)|apply(beta,X1)!=zero(c)|~exact(alpha,beta)|~element(X1,b)),inference(spm,[status(thm)],[3605,87,theory(equality)])).
% cnf(34387,plain,(element(zero(a),a)|apply(beta,X1)!=zero(c)|$false|~element(X1,b)),inference(rw,[status(thm)],[34386,117,theory(equality)])).
% cnf(34388,plain,(element(zero(a),a)|apply(beta,X1)!=zero(c)|~element(X1,b)),inference(cn,[status(thm)],[34387,theory(equality)])).
% cnf(34472,plain,(element(zero(a),a)|~element(zero(b),b)),inference(spm,[status(thm)],[34388,137,theory(equality)])).
% cnf(34482,plain,(element(zero(a),a)|$false),inference(rw,[status(thm)],[34472,561,theory(equality)])).
% cnf(34483,plain,(element(zero(a),a)),inference(cn,[status(thm)],[34482,theory(equality)])).
% cnf(34496,plain,(apply(h,subtract(c,apply(beta,X1),zero(c)))=apply(h,apply(beta,X1))|~element(X1,b)),inference(spm,[status(thm)],[21520,34483,theory(equality)])).
% cnf(58174,plain,(apply(h,apply(beta,X1))=apply(delta,apply(g,X1))|~element(X1,b)|~morphism(g,b,X2)|~morphism(delta,X2,r)),inference(spm,[status(thm)],[2786,86,theory(equality)])).
% cnf(58404,plain,(apply(h,apply(beta,X1))=apply(delta,apply(g,X1))|~element(X1,b)|~morphism(delta,e,r)),inference(spm,[status(thm)],[58174,52,theory(equality)])).
% cnf(58405,plain,(apply(h,apply(beta,X1))=apply(delta,apply(g,X1))|~element(X1,b)|$false),inference(rw,[status(thm)],[58404,51,theory(equality)])).
% cnf(58406,plain,(apply(h,apply(beta,X1))=apply(delta,apply(g,X1))|~element(X1,b)),inference(cn,[status(thm)],[58405,theory(equality)])).
% cnf(58489,negated_conjecture,(apply(delta,apply(g,X1))!=apply(delta,esk9_0)|~element(X1,b)),inference(spm,[status(thm)],[303,58406,theory(equality)])).
% cnf(63847,plain,(apply(h,subtract(c,apply(beta,subtract(b,X1,zero(b))),X2))=subtract(r,apply(h,apply(beta,X1)),apply(h,X2))|~element(X1,b)|~element(X2,c)),inference(csr,[status(thm)],[2878,2460])).
% cnf(63913,plain,(apply(h,subtract(c,apply(beta,X1),X2))=subtract(r,apply(h,apply(beta,X1)),apply(h,X2))|~element(X2,c)|~element(X1,b)),inference(spm,[status(thm)],[63847,146,theory(equality)])).
% cnf(64646,plain,(subtract(r,apply(delta,apply(g,X1)),apply(h,X2))=apply(h,subtract(c,apply(beta,X1),X2))|~element(X2,c)|~element(X1,b)),inference(spm,[status(thm)],[63913,58406,theory(equality)])).
% cnf(66182,plain,(subtract(r,apply(delta,apply(g,X1)),zero(r))=apply(h,subtract(c,apply(beta,X1),zero(c)))|~element(zero(c),c)|~element(X1,b)),inference(spm,[status(thm)],[64646,134,theory(equality)])).
% cnf(66283,plain,(subtract(r,apply(delta,apply(g,X1)),zero(r))=apply(h,subtract(c,apply(beta,X1),zero(c)))|$false|~element(X1,b)),inference(rw,[status(thm)],[66182,556,theory(equality)])).
% cnf(66284,plain,(subtract(r,apply(delta,apply(g,X1)),zero(r))=apply(h,subtract(c,apply(beta,X1),zero(c)))|~element(X1,b)),inference(cn,[status(thm)],[66283,theory(equality)])).
% cnf(70327,plain,(apply(h,subtract(c,apply(beta,X1),zero(c)))=apply(delta,subtract(e,apply(g,X1),zero(e)))|~element(X1,b)),inference(spm,[status(thm)],[22216,66284,theory(equality)])).
% cnf(74239,plain,(apply(delta,subtract(e,apply(g,X1),zero(e)))=apply(h,apply(beta,X1))|~element(X1,b)),inference(spm,[status(thm)],[34496,70327,theory(equality)])).
% cnf(74639,plain,(apply(delta,apply(g,subtract(b,X1,zero(b))))=apply(h,apply(beta,X1))|~element(X1,b)),inference(spm,[status(thm)],[74239,755,theory(equality)])).
% cnf(74996,negated_conjecture,(apply(h,apply(beta,X1))!=apply(delta,esk9_0)|~element(subtract(b,X1,zero(b)),b)|~element(X1,b)),inference(spm,[status(thm)],[58489,74639,theory(equality)])).
% cnf(75341,negated_conjecture,(apply(h,apply(beta,X1))!=apply(delta,esk9_0)|~element(X1,b)),inference(spm,[status(thm)],[74996,146,theory(equality)])).
% cnf(75477,negated_conjecture,(apply(h,X3)!=apply(delta,esk9_0)|~element(esk1_4(beta,X1,X2,X3),b)|~element(X3,X2)|~morphism(beta,X1,X2)|~surjection(beta)),inference(spm,[status(thm)],[75341,42,theory(equality)])).
% cnf(75559,negated_conjecture,(apply(h,X3)!=apply(delta,esk9_0)|~element(esk1_4(beta,X1,X2,X3),b)|~element(X3,X2)|~morphism(beta,X1,X2)|$false),inference(rw,[status(thm)],[75477,33,theory(equality)])).
% cnf(75560,negated_conjecture,(apply(h,X3)!=apply(delta,esk9_0)|~element(esk1_4(beta,X1,X2,X3),b)|~element(X3,X2)|~morphism(beta,X1,X2)),inference(cn,[status(thm)],[75559,theory(equality)])).
% cnf(75722,negated_conjecture,(apply(h,X1)!=apply(delta,esk9_0)|~element(X1,X2)|~morphism(beta,b,X2)|~surjection(beta)),inference(spm,[status(thm)],[75560,43,theory(equality)])).
% cnf(75723,negated_conjecture,(apply(h,X1)!=apply(delta,esk9_0)|~element(X1,X2)|~morphism(beta,b,X2)|$false),inference(rw,[status(thm)],[75722,33,theory(equality)])).
% cnf(75724,negated_conjecture,(apply(h,X1)!=apply(delta,esk9_0)|~element(X1,X2)|~morphism(beta,b,X2)),inference(cn,[status(thm)],[75723,theory(equality)])).
% cnf(75725,negated_conjecture,(apply(h,X1)!=apply(delta,esk9_0)|~element(X1,c)),inference(spm,[status(thm)],[75724,87,theory(equality)])).
% cnf(75742,negated_conjecture,(X3!=apply(delta,esk9_0)|~element(esk1_4(h,X1,X2,X3),c)|~element(X3,X2)|~morphism(h,X1,X2)|~surjection(h)),inference(spm,[status(thm)],[75725,42,theory(equality)])).
% cnf(75837,negated_conjecture,(X3!=apply(delta,esk9_0)|~element(esk1_4(h,X1,X2,X3),c)|~element(X3,X2)|~morphism(h,X1,X2)|$false),inference(rw,[status(thm)],[75742,36,theory(equality)])).
% cnf(75838,negated_conjecture,(X3!=apply(delta,esk9_0)|~element(esk1_4(h,X1,X2,X3),c)|~element(X3,X2)|~morphism(h,X1,X2)),inference(cn,[status(thm)],[75837,theory(equality)])).
% cnf(76157,negated_conjecture,(X1!=apply(delta,esk9_0)|~element(X1,X2)|~morphism(h,c,X2)|~surjection(h)),inference(spm,[status(thm)],[75838,43,theory(equality)])).
% cnf(76158,negated_conjecture,(X1!=apply(delta,esk9_0)|~element(X1,X2)|~morphism(h,c,X2)|$false),inference(rw,[status(thm)],[76157,36,theory(equality)])).
% cnf(76159,negated_conjecture,(X1!=apply(delta,esk9_0)|~element(X1,X2)|~morphism(h,c,X2)),inference(cn,[status(thm)],[76158,theory(equality)])).
% cnf(76160,negated_conjecture,(X1!=apply(delta,esk9_0)|~element(X1,r)),inference(spm,[status(thm)],[76159,86,theory(equality)])).
% cnf(76161,negated_conjecture,(~element(apply(delta,esk9_0),r)),inference(er,[status(thm)],[76160,theory(equality)])).
% cnf(76162,negated_conjecture,(~element(esk9_0,e)),inference(spm,[status(thm)],[76161,143,theory(equality)])).
% cnf(76163,negated_conjecture,($false),inference(rw,[status(thm)],[76162,128,theory(equality)])).
% cnf(76164,negated_conjecture,($false),inference(cn,[status(thm)],[76163,theory(equality)])).
% cnf(76165,negated_conjecture,($false),76164,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses : 6961
% # ...of these trivial : 11
% # ...subsumed : 5092
% # ...remaining for further processing: 1858
% # Other redundant clauses eliminated : 4
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed : 234
% # Backward-rewritten : 192
% # Generated clauses : 48871
% # ...of the previous two non-trivial : 44508
% # Contextual simplify-reflections : 4196
% # Paramodulations : 48797
% # Factorizations : 0
% # Equation resolutions : 42
% # Current number of processed clauses: 1375
% # Positive orientable unit clauses: 53
% # Positive unorientable unit clauses: 0
% # Negative unit clauses : 13
% # Non-unit-clauses : 1309
% # Current number of unprocessed clauses: 32199
% # ...number of literals in the above : 205990
% # Clause-clause subsumption calls (NU) : 103850
% # Rec. Clause-clause subsumption calls : 49511
% # Unit Clause-clause subsumption calls : 14237
% # Rewrite failures with RHS unbound : 0
% # Indexed BW rewrite attempts : 46
% # Indexed BW rewrite successes : 19
% # Backwards rewriting index: 914 leaves, 2.84+/-4.318 terms/leaf
% # Paramod-from index: 206 leaves, 3.01+/-3.751 terms/leaf
% # Paramod-into index: 585 leaves, 2.61+/-3.831 terms/leaf
% # -------------------------------------------------
% # User time : 3.377 s
% # System time : 0.115 s
% # Total time : 3.492 s
% # Maximum resident set size: 0 pages
% PrfWatch: 4.71 CPU 4.82 WC
% FINAL PrfWatch: 4.71 CPU 4.82 WC
% SZS output end Solution for /tmp/SystemOnTPTP24173/HAL004+1.tptp
%
%------------------------------------------------------------------------------