%------------------------------------------------------------------------------
% File     : SRASS---0.1
% Problem  : SEU214+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : SRASS -q2 -a 0 10 10 10 -i3 -n60 %s

% Computer : art05.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 : Thu Dec 30 01:54:27 EST 2010

% Result   : Theorem 95.41s
% Output   : Solution 97.31s
% 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/SystemOnTPTP6470/SEU214+2.tptp
% Adding relevance values
% Extracting the conjecture
% Sorting axioms by relevance
% Looking for THM       ... 
% not found
% Adding ~C to TBU       ... ~t22_funct_1:
% ---- Iteration 1 (0 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... antisymmetry_r2_hidden:
%  CSA axiom antisymmetry_r2_hidden found
% Looking for CSA axiom ... dt_k5_relat_1: CSA axiom dt_k5_relat_1 found
% Looking for CSA axiom ... fc1_funct_1:
%  CSA axiom fc1_funct_1 found
% ---- Iteration 2 (3 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... rc1_funct_1:
% t21_funct_1:
%  CSA axiom t21_funct_1 found
% Looking for CSA axiom ... t2_tarski:
%  CSA axiom t2_tarski found
% Looking for CSA axiom ... t8_funct_1:
%  CSA axiom t8_funct_1 found
% ---- Iteration 3 (6 axioms selected)
% Looking for TBU SAT   ... 
% yes
% Looking for TBU model ...
%  not found
% Looking for CSA axiom ... rc1_funct_1:
% d8_relat_1:
%  CSA axiom d8_relat_1 found
% Looking for CSA axiom ... t44_relat_1: CSA axiom t44_relat_1 found
% Looking for CSA axiom ... d4_relat_1:
%  CSA axiom d4_relat_1 found
% ---- Iteration 4 (9 axioms selected)
% Looking for TBU SAT   ... 
% no
% Looking for TBU UNS   ... 
% yes - theorem proved
% ---- Selection completed
% Selected axioms are   ... :d4_relat_1:t44_relat_1:d8_relat_1:t8_funct_1:t2_tarski:t21_funct_1:fc1_funct_1:dt_k5_relat_1:antisymmetry_r2_hidden (9)
% Unselected axioms are ... :rc1_funct_1:d4_funct_1:t86_relat_1:d1_relat_1:d2_relat_1:fc10_relat_1:fc9_relat_1:t46_relat_1:t47_relat_1:fc5_relat_1:fc7_relat_1:d1_xboole_0:d1_tarski:d2_xboole_0:d3_xboole_0:d4_xboole_0:d2_tarski:d4_tarski:involutiveness_k4_relat_1:t20_relat_1:t74_relat_1:t143_relat_1:t64_relat_1:t65_relat_1:t160_relat_1:cc1_funct_1:t145_relat_1:t146_relat_1:t37_relat_1:t56_relat_1:t90_relat_1:t94_relat_1:d5_relat_1:d10_relat_1:d11_relat_1:d12_relat_1:d13_relat_1:d14_relat_1:d7_relat_1:commutativity_k2_tarski:commutativity_k2_xboole_0:commutativity_k3_xboole_0:d10_xboole_0:dt_k7_relat_1:existence_m1_subset_1:idempotence_k2_xboole_0:idempotence_k3_xboole_0:rc1_xboole_0:rc2_xboole_0:reflexivity_r1_tarski:t10_zfmisc_1:t1_xboole_1:t33_zfmisc_1:t45_relat_1:t25_relat_1:d3_tarski:t167_relat_1:t1_subset:t7_boole:cc1_relat_1:d1_zfmisc_1:rc1_relat_1:rc2_relat_1:t71_relat_1:d6_relat_1:t115_relat_1:fc1_relat_1:fc2_relat_1:t3_xboole_0:dt_k4_relat_1:dt_k6_relat_1:dt_k8_relat_1:l23_zfmisc_1:t46_zfmisc_1:t65_zfmisc_1:rc3_relat_1:t140_relat_1:t166_relat_1:t21_relat_1:d3_relat_1:d4_subset_1:t60_relat_1:d2_zfmisc_1:t116_relat_1:t118_relat_1:t136_zfmisc_1:t144_relat_1:t30_relat_1:t99_relat_1:d1_setfam_1:l2_zfmisc_1:l50_zfmisc_1:t37_zfmisc_1:t38_zfmisc_1:t88_relat_1:t92_zfmisc_1:antisymmetry_r2_xboole_0:irreflexivity_r2_xboole_0:symmetry_r1_xboole_0:t118_zfmisc_1:t119_zfmisc_1:t3_subset:t3_xboole_1:d2_subset_1:fc4_relat_1:fc6_relat_1:fc8_relat_1:l3_subset_1:l71_subset_1:t2_subset:t4_subset:t4_xboole_0:t99_zfmisc_1:l1_zfmisc_1:l25_zfmisc_1:l28_zfmisc_1:l55_zfmisc_1:t106_zfmisc_1:t174_relat_1:t39_xboole_1:t40_xboole_1:t48_xboole_1:t6_boole:t117_relat_1:t178_relat_1:t1_boole:t2_boole:t3_boole:t4_boole:t69_enumset1:t6_zfmisc_1:t83_xboole_1:t8_boole:t8_zfmisc_1:t9_tarski:t9_zfmisc_1:d8_xboole_0:t12_xboole_1:t28_xboole_1:t17_xboole_1:t19_xboole_1:t26_xboole_1:t33_xboole_1:t36_xboole_1:t7_xboole_1:t8_xboole_1:t119_relat_1:t2_xboole_1:fc2_subset_1:fc2_xboole_0:fc3_subset_1:fc3_xboole_0:dt_k5_setfam_1:fc1_subset_1:fc1_xboole_0:fc1_zfmisc_1:l3_zfmisc_1:d7_xboole_0:fc12_relat_1:fc4_subset_1:l4_zfmisc_1:t39_zfmisc_1:t45_xboole_1:t5_subset:d5_tarski:l32_xboole_1:t1_zfmisc_1:t37_xboole_1:t54_subset_1:d8_setfam_1:involutiveness_k3_subset_1:involutiveness_k7_setfam_1:rc1_subset_1:rc2_subset_1:t50_subset_1:t60_xboole_1:t63_xboole_1:redefinition_k5_setfam_1:d5_subset_1:dt_k2_subset_1:redefinition_k6_subset_1:t43_subset_1:redefinition_k6_setfam_1:t46_setfam_1:dt_k3_subset_1:dt_k6_setfam_1:dt_k6_subset_1:dt_k7_setfam_1:t47_setfam_1:t48_setfam_1:dt_k10_relat_1:dt_k1_funct_1:dt_k1_relat_1:dt_k1_setfam_1:dt_k1_tarski:dt_k1_xboole_0:dt_k1_zfmisc_1:dt_k2_relat_1:dt_k2_tarski:dt_k2_xboole_0:dt_k2_zfmisc_1:dt_k3_relat_1:dt_k3_tarski:dt_k3_xboole_0:dt_k4_tarski:dt_k4_xboole_0:dt_k9_relat_1:dt_m1_subset_1 (208)
% SZS status THM for /tmp/SystemOnTPTP6470/SEU214+2.tptp
% Looking for THM       ... 
% found
% SZS output start Solution for /tmp/SystemOnTPTP6470/SEU214+2.tptp
% TreeLimitedRun: ----------------------------------------------------------
% TreeLimitedRun: /home/graph/tptp/Systems/EP---1.2/eproof --print-statistics -xAuto -tAuto --cpu-limit=600 --proof-time-unlimited --memory-limit=Auto --tstp-in --tstp-out /tmp/SRASS.s.p 
% TreeLimitedRun: CPU time limit is 600s
% TreeLimitedRun: WC  time limit is 1200s
% TreeLimitedRun: PID is 8642
% TreeLimitedRun: ----------------------------------------------------------
% PrfWatch: 0.00 CPU 0.02 WC
% # Preprocessing time     : 0.016 s
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% fof(1, axiom,![X1]:(relation(X1)=>![X2]:(X2=relation_dom(X1)<=>![X3]:(in(X3,X2)<=>?[X4]:in(ordered_pair(X3,X4),X1)))),file('/tmp/SRASS.s.p', d4_relat_1)).
% fof(3, axiom,![X1]:(relation(X1)=>![X2]:(relation(X2)=>![X3]:(relation(X3)=>(X3=relation_composition(X1,X2)<=>![X4]:![X5]:(in(ordered_pair(X4,X5),X3)<=>?[X6]:(in(ordered_pair(X4,X6),X1)&in(ordered_pair(X6,X5),X2))))))),file('/tmp/SRASS.s.p', d8_relat_1)).
% fof(4, axiom,![X1]:![X2]:![X3]:((relation(X3)&function(X3))=>(in(ordered_pair(X1,X2),X3)<=>(in(X1,relation_dom(X3))&X2=apply(X3,X1)))),file('/tmp/SRASS.s.p', t8_funct_1)).
% fof(6, axiom,![X1]:![X2]:((relation(X2)&function(X2))=>![X3]:((relation(X3)&function(X3))=>(in(X1,relation_dom(relation_composition(X3,X2)))<=>(in(X1,relation_dom(X3))&in(apply(X3,X1),relation_dom(X2)))))),file('/tmp/SRASS.s.p', t21_funct_1)).
% fof(7, axiom,![X1]:![X2]:((((relation(X1)&function(X1))&relation(X2))&function(X2))=>(relation(relation_composition(X1,X2))&function(relation_composition(X1,X2)))),file('/tmp/SRASS.s.p', fc1_funct_1)).
% fof(8, axiom,![X1]:![X2]:((relation(X1)&relation(X2))=>relation(relation_composition(X1,X2))),file('/tmp/SRASS.s.p', dt_k5_relat_1)).
% fof(10, conjecture,![X1]:![X2]:((relation(X2)&function(X2))=>![X3]:((relation(X3)&function(X3))=>(in(X1,relation_dom(relation_composition(X3,X2)))=>apply(relation_composition(X3,X2),X1)=apply(X2,apply(X3,X1))))),file('/tmp/SRASS.s.p', t22_funct_1)).
% fof(11, negated_conjecture,~(![X1]:![X2]:((relation(X2)&function(X2))=>![X3]:((relation(X3)&function(X3))=>(in(X1,relation_dom(relation_composition(X3,X2)))=>apply(relation_composition(X3,X2),X1)=apply(X2,apply(X3,X1)))))),inference(assume_negation,[status(cth)],[10])).
% fof(13, plain,![X1]:(~(relation(X1))|![X2]:((~(X2=relation_dom(X1))|![X3]:((~(in(X3,X2))|?[X4]:in(ordered_pair(X3,X4),X1))&(![X4]:~(in(ordered_pair(X3,X4),X1))|in(X3,X2))))&(?[X3]:((~(in(X3,X2))|![X4]:~(in(ordered_pair(X3,X4),X1)))&(in(X3,X2)|?[X4]:in(ordered_pair(X3,X4),X1)))|X2=relation_dom(X1)))),inference(fof_nnf,[status(thm)],[1])).
% fof(14, plain,![X5]:(~(relation(X5))|![X6]:((~(X6=relation_dom(X5))|![X7]:((~(in(X7,X6))|?[X8]:in(ordered_pair(X7,X8),X5))&(![X9]:~(in(ordered_pair(X7,X9),X5))|in(X7,X6))))&(?[X10]:((~(in(X10,X6))|![X11]:~(in(ordered_pair(X10,X11),X5)))&(in(X10,X6)|?[X12]:in(ordered_pair(X10,X12),X5)))|X6=relation_dom(X5)))),inference(variable_rename,[status(thm)],[13])).
% fof(15, plain,![X5]:(~(relation(X5))|![X6]:((~(X6=relation_dom(X5))|![X7]:((~(in(X7,X6))|in(ordered_pair(X7,esk1_3(X5,X6,X7)),X5))&(![X9]:~(in(ordered_pair(X7,X9),X5))|in(X7,X6))))&(((~(in(esk2_2(X5,X6),X6))|![X11]:~(in(ordered_pair(esk2_2(X5,X6),X11),X5)))&(in(esk2_2(X5,X6),X6)|in(ordered_pair(esk2_2(X5,X6),esk3_2(X5,X6)),X5)))|X6=relation_dom(X5)))),inference(skolemize,[status(esa)],[14])).
% fof(16, plain,![X5]:![X6]:![X7]:![X9]:![X11]:(((((~(in(ordered_pair(esk2_2(X5,X6),X11),X5))|~(in(esk2_2(X5,X6),X6)))&(in(esk2_2(X5,X6),X6)|in(ordered_pair(esk2_2(X5,X6),esk3_2(X5,X6)),X5)))|X6=relation_dom(X5))&(((~(in(ordered_pair(X7,X9),X5))|in(X7,X6))&(~(in(X7,X6))|in(ordered_pair(X7,esk1_3(X5,X6,X7)),X5)))|~(X6=relation_dom(X5))))|~(relation(X5))),inference(shift_quantors,[status(thm)],[15])).
% fof(17, plain,![X5]:![X6]:![X7]:![X9]:![X11]:(((((~(in(ordered_pair(esk2_2(X5,X6),X11),X5))|~(in(esk2_2(X5,X6),X6)))|X6=relation_dom(X5))|~(relation(X5)))&(((in(esk2_2(X5,X6),X6)|in(ordered_pair(esk2_2(X5,X6),esk3_2(X5,X6)),X5))|X6=relation_dom(X5))|~(relation(X5))))&((((~(in(ordered_pair(X7,X9),X5))|in(X7,X6))|~(X6=relation_dom(X5)))|~(relation(X5)))&(((~(in(X7,X6))|in(ordered_pair(X7,esk1_3(X5,X6,X7)),X5))|~(X6=relation_dom(X5)))|~(relation(X5))))),inference(distribute,[status(thm)],[16])).
% cnf(18,plain,(in(ordered_pair(X3,esk1_3(X1,X2,X3)),X1)|~relation(X1)|X2!=relation_dom(X1)|~in(X3,X2)),inference(split_conjunct,[status(thm)],[17])).
% fof(26, plain,![X1]:(~(relation(X1))|![X2]:(~(relation(X2))|![X3]:(~(relation(X3))|((~(X3=relation_composition(X1,X2))|![X4]:![X5]:((~(in(ordered_pair(X4,X5),X3))|?[X6]:(in(ordered_pair(X4,X6),X1)&in(ordered_pair(X6,X5),X2)))&(![X6]:(~(in(ordered_pair(X4,X6),X1))|~(in(ordered_pair(X6,X5),X2)))|in(ordered_pair(X4,X5),X3))))&(?[X4]:?[X5]:((~(in(ordered_pair(X4,X5),X3))|![X6]:(~(in(ordered_pair(X4,X6),X1))|~(in(ordered_pair(X6,X5),X2))))&(in(ordered_pair(X4,X5),X3)|?[X6]:(in(ordered_pair(X4,X6),X1)&in(ordered_pair(X6,X5),X2))))|X3=relation_composition(X1,X2)))))),inference(fof_nnf,[status(thm)],[3])).
% fof(27, plain,![X7]:(~(relation(X7))|![X8]:(~(relation(X8))|![X9]:(~(relation(X9))|((~(X9=relation_composition(X7,X8))|![X10]:![X11]:((~(in(ordered_pair(X10,X11),X9))|?[X12]:(in(ordered_pair(X10,X12),X7)&in(ordered_pair(X12,X11),X8)))&(![X13]:(~(in(ordered_pair(X10,X13),X7))|~(in(ordered_pair(X13,X11),X8)))|in(ordered_pair(X10,X11),X9))))&(?[X14]:?[X15]:((~(in(ordered_pair(X14,X15),X9))|![X16]:(~(in(ordered_pair(X14,X16),X7))|~(in(ordered_pair(X16,X15),X8))))&(in(ordered_pair(X14,X15),X9)|?[X17]:(in(ordered_pair(X14,X17),X7)&in(ordered_pair(X17,X15),X8))))|X9=relation_composition(X7,X8)))))),inference(variable_rename,[status(thm)],[26])).
% fof(28, plain,![X7]:(~(relation(X7))|![X8]:(~(relation(X8))|![X9]:(~(relation(X9))|((~(X9=relation_composition(X7,X8))|![X10]:![X11]:((~(in(ordered_pair(X10,X11),X9))|(in(ordered_pair(X10,esk4_5(X7,X8,X9,X10,X11)),X7)&in(ordered_pair(esk4_5(X7,X8,X9,X10,X11),X11),X8)))&(![X13]:(~(in(ordered_pair(X10,X13),X7))|~(in(ordered_pair(X13,X11),X8)))|in(ordered_pair(X10,X11),X9))))&(((~(in(ordered_pair(esk5_3(X7,X8,X9),esk6_3(X7,X8,X9)),X9))|![X16]:(~(in(ordered_pair(esk5_3(X7,X8,X9),X16),X7))|~(in(ordered_pair(X16,esk6_3(X7,X8,X9)),X8))))&(in(ordered_pair(esk5_3(X7,X8,X9),esk6_3(X7,X8,X9)),X9)|(in(ordered_pair(esk5_3(X7,X8,X9),esk7_3(X7,X8,X9)),X7)&in(ordered_pair(esk7_3(X7,X8,X9),esk6_3(X7,X8,X9)),X8))))|X9=relation_composition(X7,X8)))))),inference(skolemize,[status(esa)],[27])).
% fof(29, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X13]:![X16]:((((((((~(in(ordered_pair(esk5_3(X7,X8,X9),X16),X7))|~(in(ordered_pair(X16,esk6_3(X7,X8,X9)),X8)))|~(in(ordered_pair(esk5_3(X7,X8,X9),esk6_3(X7,X8,X9)),X9)))&(in(ordered_pair(esk5_3(X7,X8,X9),esk6_3(X7,X8,X9)),X9)|(in(ordered_pair(esk5_3(X7,X8,X9),esk7_3(X7,X8,X9)),X7)&in(ordered_pair(esk7_3(X7,X8,X9),esk6_3(X7,X8,X9)),X8))))|X9=relation_composition(X7,X8))&((((~(in(ordered_pair(X10,X13),X7))|~(in(ordered_pair(X13,X11),X8)))|in(ordered_pair(X10,X11),X9))&(~(in(ordered_pair(X10,X11),X9))|(in(ordered_pair(X10,esk4_5(X7,X8,X9,X10,X11)),X7)&in(ordered_pair(esk4_5(X7,X8,X9,X10,X11),X11),X8))))|~(X9=relation_composition(X7,X8))))|~(relation(X9)))|~(relation(X8)))|~(relation(X7))),inference(shift_quantors,[status(thm)],[28])).
% fof(30, plain,![X7]:![X8]:![X9]:![X10]:![X11]:![X13]:![X16]:((((((((~(in(ordered_pair(esk5_3(X7,X8,X9),X16),X7))|~(in(ordered_pair(X16,esk6_3(X7,X8,X9)),X8)))|~(in(ordered_pair(esk5_3(X7,X8,X9),esk6_3(X7,X8,X9)),X9)))|X9=relation_composition(X7,X8))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))&((((((in(ordered_pair(esk5_3(X7,X8,X9),esk7_3(X7,X8,X9)),X7)|in(ordered_pair(esk5_3(X7,X8,X9),esk6_3(X7,X8,X9)),X9))|X9=relation_composition(X7,X8))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))&(((((in(ordered_pair(esk7_3(X7,X8,X9),esk6_3(X7,X8,X9)),X8)|in(ordered_pair(esk5_3(X7,X8,X9),esk6_3(X7,X8,X9)),X9))|X9=relation_composition(X7,X8))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))))&(((((((~(in(ordered_pair(X10,X13),X7))|~(in(ordered_pair(X13,X11),X8)))|in(ordered_pair(X10,X11),X9))|~(X9=relation_composition(X7,X8)))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))&((((((in(ordered_pair(X10,esk4_5(X7,X8,X9,X10,X11)),X7)|~(in(ordered_pair(X10,X11),X9)))|~(X9=relation_composition(X7,X8)))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))&(((((in(ordered_pair(esk4_5(X7,X8,X9,X10,X11),X11),X8)|~(in(ordered_pair(X10,X11),X9)))|~(X9=relation_composition(X7,X8)))|~(relation(X9)))|~(relation(X8)))|~(relation(X7)))))),inference(distribute,[status(thm)],[29])).
% cnf(32,plain,(in(ordered_pair(X4,esk4_5(X1,X2,X3,X4,X5)),X1)|~relation(X1)|~relation(X2)|~relation(X3)|X3!=relation_composition(X1,X2)|~in(ordered_pair(X4,X5),X3)),inference(split_conjunct,[status(thm)],[30])).
% cnf(33,plain,(in(ordered_pair(X4,X5),X3)|~relation(X1)|~relation(X2)|~relation(X3)|X3!=relation_composition(X1,X2)|~in(ordered_pair(X6,X5),X2)|~in(ordered_pair(X4,X6),X1)),inference(split_conjunct,[status(thm)],[30])).
% fof(37, plain,![X1]:![X2]:![X3]:((~(relation(X3))|~(function(X3)))|((~(in(ordered_pair(X1,X2),X3))|(in(X1,relation_dom(X3))&X2=apply(X3,X1)))&((~(in(X1,relation_dom(X3)))|~(X2=apply(X3,X1)))|in(ordered_pair(X1,X2),X3)))),inference(fof_nnf,[status(thm)],[4])).
% fof(38, plain,![X4]:![X5]:![X6]:((~(relation(X6))|~(function(X6)))|((~(in(ordered_pair(X4,X5),X6))|(in(X4,relation_dom(X6))&X5=apply(X6,X4)))&((~(in(X4,relation_dom(X6)))|~(X5=apply(X6,X4)))|in(ordered_pair(X4,X5),X6)))),inference(variable_rename,[status(thm)],[37])).
% fof(39, plain,![X4]:![X5]:![X6]:((((in(X4,relation_dom(X6))|~(in(ordered_pair(X4,X5),X6)))|(~(relation(X6))|~(function(X6))))&((X5=apply(X6,X4)|~(in(ordered_pair(X4,X5),X6)))|(~(relation(X6))|~(function(X6)))))&(((~(in(X4,relation_dom(X6)))|~(X5=apply(X6,X4)))|in(ordered_pair(X4,X5),X6))|(~(relation(X6))|~(function(X6))))),inference(distribute,[status(thm)],[38])).
% cnf(40,plain,(in(ordered_pair(X2,X3),X1)|~function(X1)|~relation(X1)|X3!=apply(X1,X2)|~in(X2,relation_dom(X1))),inference(split_conjunct,[status(thm)],[39])).
% cnf(41,plain,(X3=apply(X1,X2)|~function(X1)|~relation(X1)|~in(ordered_pair(X2,X3),X1)),inference(split_conjunct,[status(thm)],[39])).
% fof(49, plain,![X1]:![X2]:((~(relation(X2))|~(function(X2)))|![X3]:((~(relation(X3))|~(function(X3)))|((~(in(X1,relation_dom(relation_composition(X3,X2))))|(in(X1,relation_dom(X3))&in(apply(X3,X1),relation_dom(X2))))&((~(in(X1,relation_dom(X3)))|~(in(apply(X3,X1),relation_dom(X2))))|in(X1,relation_dom(relation_composition(X3,X2))))))),inference(fof_nnf,[status(thm)],[6])).
% fof(50, plain,![X4]:![X5]:((~(relation(X5))|~(function(X5)))|![X6]:((~(relation(X6))|~(function(X6)))|((~(in(X4,relation_dom(relation_composition(X6,X5))))|(in(X4,relation_dom(X6))&in(apply(X6,X4),relation_dom(X5))))&((~(in(X4,relation_dom(X6)))|~(in(apply(X6,X4),relation_dom(X5))))|in(X4,relation_dom(relation_composition(X6,X5))))))),inference(variable_rename,[status(thm)],[49])).
% fof(51, plain,![X4]:![X5]:![X6]:(((~(relation(X6))|~(function(X6)))|((~(in(X4,relation_dom(relation_composition(X6,X5))))|(in(X4,relation_dom(X6))&in(apply(X6,X4),relation_dom(X5))))&((~(in(X4,relation_dom(X6)))|~(in(apply(X6,X4),relation_dom(X5))))|in(X4,relation_dom(relation_composition(X6,X5))))))|(~(relation(X5))|~(function(X5)))),inference(shift_quantors,[status(thm)],[50])).
% fof(52, plain,![X4]:![X5]:![X6]:(((((in(X4,relation_dom(X6))|~(in(X4,relation_dom(relation_composition(X6,X5)))))|(~(relation(X6))|~(function(X6))))|(~(relation(X5))|~(function(X5))))&(((in(apply(X6,X4),relation_dom(X5))|~(in(X4,relation_dom(relation_composition(X6,X5)))))|(~(relation(X6))|~(function(X6))))|(~(relation(X5))|~(function(X5)))))&((((~(in(X4,relation_dom(X6)))|~(in(apply(X6,X4),relation_dom(X5))))|in(X4,relation_dom(relation_composition(X6,X5))))|(~(relation(X6))|~(function(X6))))|(~(relation(X5))|~(function(X5))))),inference(distribute,[status(thm)],[51])).
% cnf(54,plain,(in(apply(X2,X3),relation_dom(X1))|~function(X1)|~relation(X1)|~function(X2)|~relation(X2)|~in(X3,relation_dom(relation_composition(X2,X1)))),inference(split_conjunct,[status(thm)],[52])).
% fof(56, plain,![X1]:![X2]:((((~(relation(X1))|~(function(X1)))|~(relation(X2)))|~(function(X2)))|(relation(relation_composition(X1,X2))&function(relation_composition(X1,X2)))),inference(fof_nnf,[status(thm)],[7])).
% fof(57, plain,![X3]:![X4]:((((~(relation(X3))|~(function(X3)))|~(relation(X4)))|~(function(X4)))|(relation(relation_composition(X3,X4))&function(relation_composition(X3,X4)))),inference(variable_rename,[status(thm)],[56])).
% fof(58, plain,![X3]:![X4]:((relation(relation_composition(X3,X4))|(((~(relation(X3))|~(function(X3)))|~(relation(X4)))|~(function(X4))))&(function(relation_composition(X3,X4))|(((~(relation(X3))|~(function(X3)))|~(relation(X4)))|~(function(X4))))),inference(distribute,[status(thm)],[57])).
% cnf(59,plain,(function(relation_composition(X2,X1))|~function(X1)|~relation(X1)|~function(X2)|~relation(X2)),inference(split_conjunct,[status(thm)],[58])).
% fof(61, plain,![X1]:![X2]:((~(relation(X1))|~(relation(X2)))|relation(relation_composition(X1,X2))),inference(fof_nnf,[status(thm)],[8])).
% fof(62, plain,![X3]:![X4]:((~(relation(X3))|~(relation(X4)))|relation(relation_composition(X3,X4))),inference(variable_rename,[status(thm)],[61])).
% cnf(63,plain,(relation(relation_composition(X1,X2))|~relation(X2)|~relation(X1)),inference(split_conjunct,[status(thm)],[62])).
% fof(67, negated_conjecture,?[X1]:?[X2]:((relation(X2)&function(X2))&?[X3]:((relation(X3)&function(X3))&(in(X1,relation_dom(relation_composition(X3,X2)))&~(apply(relation_composition(X3,X2),X1)=apply(X2,apply(X3,X1)))))),inference(fof_nnf,[status(thm)],[11])).
% fof(68, negated_conjecture,?[X4]:?[X5]:((relation(X5)&function(X5))&?[X6]:((relation(X6)&function(X6))&(in(X4,relation_dom(relation_composition(X6,X5)))&~(apply(relation_composition(X6,X5),X4)=apply(X5,apply(X6,X4)))))),inference(variable_rename,[status(thm)],[67])).
% fof(69, negated_conjecture,((relation(esk10_0)&function(esk10_0))&((relation(esk11_0)&function(esk11_0))&(in(esk9_0,relation_dom(relation_composition(esk11_0,esk10_0)))&~(apply(relation_composition(esk11_0,esk10_0),esk9_0)=apply(esk10_0,apply(esk11_0,esk9_0)))))),inference(skolemize,[status(esa)],[68])).
% cnf(70,negated_conjecture,(apply(relation_composition(esk11_0,esk10_0),esk9_0)!=apply(esk10_0,apply(esk11_0,esk9_0))),inference(split_conjunct,[status(thm)],[69])).
% cnf(71,negated_conjecture,(in(esk9_0,relation_dom(relation_composition(esk11_0,esk10_0)))),inference(split_conjunct,[status(thm)],[69])).
% cnf(72,negated_conjecture,(function(esk11_0)),inference(split_conjunct,[status(thm)],[69])).
% cnf(73,negated_conjecture,(relation(esk11_0)),inference(split_conjunct,[status(thm)],[69])).
% cnf(74,negated_conjecture,(function(esk10_0)),inference(split_conjunct,[status(thm)],[69])).
% cnf(75,negated_conjecture,(relation(esk10_0)),inference(split_conjunct,[status(thm)],[69])).
% cnf(94,plain,(in(ordered_pair(X1,apply(X2,X1)),X2)|~function(X2)|~in(X1,relation_dom(X2))|~relation(X2)),inference(er,[status(thm)],[40,theory(equality)])).
% cnf(111,plain,(apply(X1,X2)=esk4_5(X1,X3,X4,X2,X5)|~function(X1)|~relation(X1)|relation_composition(X1,X3)!=X4|~in(ordered_pair(X2,X5),X4)|~relation(X4)|~relation(X3)),inference(spm,[status(thm)],[41,32,theory(equality)])).
% cnf(135,plain,(in(ordered_pair(X1,apply(X2,X3)),X4)|relation_composition(X5,X2)!=X4|~in(ordered_pair(X1,X3),X5)|~relation(X4)|~relation(X2)|~relation(X5)|~function(X2)|~in(X3,relation_dom(X2))),inference(spm,[status(thm)],[33,94,theory(equality)])).
% cnf(426,plain,(in(ordered_pair(X1,apply(X2,X1)),X2)|relation_composition(X2,X3)!=X4|~in(ordered_pair(X1,X5),X4)|~relation(X4)|~relation(X3)|~relation(X2)|~function(X2)),inference(spm,[status(thm)],[32,111,theory(equality)])).
% cnf(1114,plain,(in(ordered_pair(X1,apply(X2,X1)),X2)|relation_composition(X2,X3)!=X4|~function(X2)|~relation(X4)|~relation(X3)|~relation(X2)|relation_dom(X4)!=X5|~in(X1,X5)),inference(spm,[status(thm)],[426,18,theory(equality)])).
% cnf(7837,plain,(in(ordered_pair(X1,apply(X2,X1)),X2)|relation_dom(relation_composition(X2,X3))!=X4|~function(X2)|~in(X1,X4)|~relation(relation_composition(X2,X3))|~relation(X3)|~relation(X2)),inference(er,[status(thm)],[1114,theory(equality)])).
% cnf(7999,plain,(in(ordered_pair(X1,apply(X2,X1)),X2)|relation_dom(relation_composition(X2,X3))!=X4|~function(X2)|~in(X1,X4)|~relation(X3)|~relation(X2)),inference(csr,[status(thm)],[7837,63])).
% cnf(8000,plain,(in(ordered_pair(X1,apply(X2,X1)),X2)|~function(X2)|~in(X1,relation_dom(relation_composition(X2,X3)))|~relation(X3)|~relation(X2)),inference(er,[status(thm)],[7999,theory(equality)])).
% cnf(8005,negated_conjecture,(in(ordered_pair(esk9_0,apply(esk11_0,esk9_0)),esk11_0)|~function(esk11_0)|~relation(esk10_0)|~relation(esk11_0)),inference(spm,[status(thm)],[8000,71,theory(equality)])).
% cnf(8131,negated_conjecture,(in(ordered_pair(esk9_0,apply(esk11_0,esk9_0)),esk11_0)|$false|~relation(esk10_0)|~relation(esk11_0)),inference(rw,[status(thm)],[8005,72,theory(equality)])).
% cnf(8132,negated_conjecture,(in(ordered_pair(esk9_0,apply(esk11_0,esk9_0)),esk11_0)|$false|$false|~relation(esk11_0)),inference(rw,[status(thm)],[8131,75,theory(equality)])).
% cnf(8133,negated_conjecture,(in(ordered_pair(esk9_0,apply(esk11_0,esk9_0)),esk11_0)|$false|$false|$false),inference(rw,[status(thm)],[8132,73,theory(equality)])).
% cnf(8134,negated_conjecture,(in(ordered_pair(esk9_0,apply(esk11_0,esk9_0)),esk11_0)),inference(cn,[status(thm)],[8133,theory(equality)])).
% cnf(8170,negated_conjecture,(in(ordered_pair(esk9_0,apply(X1,apply(esk11_0,esk9_0))),X2)|relation_composition(esk11_0,X1)!=X2|~function(X1)|~in(apply(esk11_0,esk9_0),relation_dom(X1))|~relation(X2)|~relation(X1)|~relation(esk11_0)),inference(spm,[status(thm)],[135,8134,theory(equality)])).
% cnf(8200,negated_conjecture,(in(ordered_pair(esk9_0,apply(X1,apply(esk11_0,esk9_0))),X2)|relation_composition(esk11_0,X1)!=X2|~function(X1)|~in(apply(esk11_0,esk9_0),relation_dom(X1))|~relation(X2)|~relation(X1)|$false),inference(rw,[status(thm)],[8170,73,theory(equality)])).
% cnf(8201,negated_conjecture,(in(ordered_pair(esk9_0,apply(X1,apply(esk11_0,esk9_0))),X2)|relation_composition(esk11_0,X1)!=X2|~function(X1)|~in(apply(esk11_0,esk9_0),relation_dom(X1))|~relation(X2)|~relation(X1)),inference(cn,[status(thm)],[8200,theory(equality)])).
% cnf(9152,negated_conjecture,(apply(X1,esk9_0)=apply(X2,apply(esk11_0,esk9_0))|~function(X1)|~relation(X1)|relation_composition(esk11_0,X2)!=X1|~function(X2)|~in(apply(esk11_0,esk9_0),relation_dom(X2))|~relation(X2)),inference(spm,[status(thm)],[41,8201,theory(equality)])).
% cnf(9662,negated_conjecture,(apply(relation_composition(esk11_0,X1),esk9_0)=apply(X1,apply(esk11_0,esk9_0))|~function(relation_composition(esk11_0,X1))|~function(X1)|~in(apply(esk11_0,esk9_0),relation_dom(X1))|~relation(relation_composition(esk11_0,X1))|~relation(X1)),inference(er,[status(thm)],[9152,theory(equality)])).
% cnf(9663,negated_conjecture,(~function(relation_composition(esk11_0,esk10_0))|~function(esk10_0)|~in(apply(esk11_0,esk9_0),relation_dom(esk10_0))|~relation(relation_composition(esk11_0,esk10_0))|~relation(esk10_0)),inference(spm,[status(thm)],[70,9662,theory(equality)])).
% cnf(9707,negated_conjecture,(~function(relation_composition(esk11_0,esk10_0))|$false|~in(apply(esk11_0,esk9_0),relation_dom(esk10_0))|~relation(relation_composition(esk11_0,esk10_0))|~relation(esk10_0)),inference(rw,[status(thm)],[9663,74,theory(equality)])).
% cnf(9708,negated_conjecture,(~function(relation_composition(esk11_0,esk10_0))|$false|~in(apply(esk11_0,esk9_0),relation_dom(esk10_0))|~relation(relation_composition(esk11_0,esk10_0))|$false),inference(rw,[status(thm)],[9707,75,theory(equality)])).
% cnf(9709,negated_conjecture,(~function(relation_composition(esk11_0,esk10_0))|~in(apply(esk11_0,esk9_0),relation_dom(esk10_0))|~relation(relation_composition(esk11_0,esk10_0))),inference(cn,[status(thm)],[9708,theory(equality)])).
% cnf(9719,negated_conjecture,(~function(relation_composition(esk11_0,esk10_0))|~relation(relation_composition(esk11_0,esk10_0))|~function(esk11_0)|~function(esk10_0)|~in(esk9_0,relation_dom(relation_composition(esk11_0,esk10_0)))|~relation(esk11_0)|~relation(esk10_0)),inference(spm,[status(thm)],[9709,54,theory(equality)])).
% cnf(9724,negated_conjecture,(~function(relation_composition(esk11_0,esk10_0))|~relation(relation_composition(esk11_0,esk10_0))|$false|~function(esk10_0)|~in(esk9_0,relation_dom(relation_composition(esk11_0,esk10_0)))|~relation(esk11_0)|~relation(esk10_0)),inference(rw,[status(thm)],[9719,72,theory(equality)])).
% cnf(9725,negated_conjecture,(~function(relation_composition(esk11_0,esk10_0))|~relation(relation_composition(esk11_0,esk10_0))|$false|$false|~in(esk9_0,relation_dom(relation_composition(esk11_0,esk10_0)))|~relation(esk11_0)|~relation(esk10_0)),inference(rw,[status(thm)],[9724,74,theory(equality)])).
% cnf(9726,negated_conjecture,(~function(relation_composition(esk11_0,esk10_0))|~relation(relation_composition(esk11_0,esk10_0))|$false|$false|$false|~relation(esk11_0)|~relation(esk10_0)),inference(rw,[status(thm)],[9725,71,theory(equality)])).
% cnf(9727,negated_conjecture,(~function(relation_composition(esk11_0,esk10_0))|~relation(relation_composition(esk11_0,esk10_0))|$false|$false|$false|$false|~relation(esk10_0)),inference(rw,[status(thm)],[9726,73,theory(equality)])).
% cnf(9728,negated_conjecture,(~function(relation_composition(esk11_0,esk10_0))|~relation(relation_composition(esk11_0,esk10_0))|$false|$false|$false|$false|$false),inference(rw,[status(thm)],[9727,75,theory(equality)])).
% cnf(9729,negated_conjecture,(~function(relation_composition(esk11_0,esk10_0))|~relation(relation_composition(esk11_0,esk10_0))),inference(cn,[status(thm)],[9728,theory(equality)])).
% cnf(9763,negated_conjecture,(~relation(relation_composition(esk11_0,esk10_0))|~function(esk11_0)|~function(esk10_0)|~relation(esk11_0)|~relation(esk10_0)),inference(spm,[status(thm)],[9729,59,theory(equality)])).
% cnf(9764,negated_conjecture,(~relation(relation_composition(esk11_0,esk10_0))|$false|~function(esk10_0)|~relation(esk11_0)|~relation(esk10_0)),inference(rw,[status(thm)],[9763,72,theory(equality)])).
% cnf(9765,negated_conjecture,(~relation(relation_composition(esk11_0,esk10_0))|$false|$false|~relation(esk11_0)|~relation(esk10_0)),inference(rw,[status(thm)],[9764,74,theory(equality)])).
% cnf(9766,negated_conjecture,(~relation(relation_composition(esk11_0,esk10_0))|$false|$false|$false|~relation(esk10_0)),inference(rw,[status(thm)],[9765,73,theory(equality)])).
% cnf(9767,negated_conjecture,(~relation(relation_composition(esk11_0,esk10_0))|$false|$false|$false|$false),inference(rw,[status(thm)],[9766,75,theory(equality)])).
% cnf(9768,negated_conjecture,(~relation(relation_composition(esk11_0,esk10_0))),inference(cn,[status(thm)],[9767,theory(equality)])).
% cnf(9769,negated_conjecture,(~relation(esk10_0)|~relation(esk11_0)),inference(spm,[status(thm)],[9768,63,theory(equality)])).
% cnf(9770,negated_conjecture,($false|~relation(esk11_0)),inference(rw,[status(thm)],[9769,75,theory(equality)])).
% cnf(9771,negated_conjecture,($false|$false),inference(rw,[status(thm)],[9770,73,theory(equality)])).
% cnf(9772,negated_conjecture,($false),inference(cn,[status(thm)],[9771,theory(equality)])).
% cnf(9773,negated_conjecture,($false),9772,['proof']).
% # SZS output end CNFRefutation
% # Processed clauses                  : 1127
% # ...of these trivial                : 31
% # ...subsumed                        : 242
% # ...remaining for further processing: 854
% # Other redundant clauses eliminated : 1
% # Clauses deleted for lack of memory : 0
% # Backward-subsumed                  : 69
% # Backward-rewritten                 : 0
% # Generated clauses                  : 7472
% # ...of the previous two non-trivial : 7367
% # Contextual simplify-reflections    : 364
% # Paramodulations                    : 7283
% # Factorizations                     : 38
% # Equation resolutions               : 151
% # Current number of processed clauses: 757
% #    Positive orientable unit clauses: 10
% #    Positive unorientable unit clauses: 0
% #    Negative unit clauses           : 11
% #    Non-unit-clauses                : 736
% # Current number of unprocessed clauses: 5405
% # ...number of literals in the above : 59755
% # Clause-clause subsumption calls (NU) : 36329
% # Rec. Clause-clause subsumption calls : 7244
% # Unit Clause-clause subsumption calls : 213
% # Rewrite failures with RHS unbound  : 0
% # Indexed BW rewrite attempts        : 6
% # Indexed BW rewrite successes       : 1
% # Backwards rewriting index:   461 leaves,   2.54+/-2.969 terms/leaf
% # Paramod-from index:           72 leaves,   2.32+/-2.692 terms/leaf
% # Paramod-into index:          348 leaves,   2.26+/-2.316 terms/leaf
% # -------------------------------------------------
% # User time              : 0.815 s
% # System time            : 0.027 s
% # Total time             : 0.842 s
% # Maximum resident set size: 0 pages
% PrfWatch: 1.17 CPU 1.27 WC
% FINAL PrfWatch: 1.17 CPU 1.27 WC
% SZS output end Solution for /tmp/SystemOnTPTP6470/SEU214+2.tptp
% 
%------------------------------------------------------------------------------