%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM135+1 : TPTP v9.2.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n016.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 : Tue May 5 04:13:19 PM UTC 2026
% Result : Theorem 29.34s 17.85s
% Output : CNFRefutation 29.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 98 ( 23 unt; 0 def)
% Number of atoms : 364 ( 279 equ)
% Maximal formula atoms : 72 ( 3 avg)
% Number of connectives : 413 ( 147 ~; 195 |; 45 &)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 6 con; 0-3 aty)
% Number of variables : 387 ( 41 sgn 145 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subst2,axiom,
! [X1,X4,X6,X19,X12,X9,X11,X13] :
( ( X1 = X9
& X4 = X11
& X6 = vapp(X12,X13) )
=> ( X19 = vsubst(X1,X4,X6)
=> X19 = vapp(vsubst(X9,X11,X12),vsubst(X9,X11,X13)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',subst2) ).
fof(subst0,axiom,
! [X9,X21,X1,X4,X6,X19,X11] :
( ( X1 = X9
& X4 = X11
& X6 = vvar(X21) )
=> ( X9 = X21
=> ( X19 = vsubst(X1,X4,X6)
=> X19 = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',subst0) ).
fof(subst1,axiom,
! [X11,X9,X1,X4,X6,X19,X21] :
( ( X1 = X9
& X4 = X11
& X6 = vvar(X21) )
=> ( X9 != X21
=> ( X19 = vsubst(X1,X4,X6)
=> X19 = vvar(X21) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',subst1) ).
fof('EQ-app',axiom,
! [X4,X6,X7,X8] :
( ( vapp(X4,X6) = vapp(X7,X8)
=> ( X4 = X7
& X6 = X8 ) )
& ( ( X4 = X7
& X6 = X8 )
=> vapp(X4,X6) = vapp(X7,X8) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','EQ-app') ).
fof('T-subst-var',conjecture,
! [X15,X20,X9,X11,X21,X34] :
( ( vtcheck(X20,X11,X15)
& vtcheck(vbind(X9,X15,X20),vvar(X21),X34) )
=> vtcheck(X20,vsubst(X9,X11,vvar(X21)),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-var') ).
fof('T-Strong',axiom,
! [X9,X10,X20,X11,X15] :
( ( ~ visFreeVar(X9,X11)
& vtcheck(vbind(X9,X10,X20),X11,X15) )
=> vtcheck(X20,X11,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Strong') ).
fof(isFreeVar0,axiom,
! [X1,X4,X9,X14] :
( ( X1 = X14
& X4 = vvar(X9) )
=> ( ( X9 = X14
=> visFreeVar(X1,X4) )
& ( visFreeVar(X1,X4)
=> X9 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',isFreeVar0) ).
fof('DIFF-var-app',axiom,
! [X1,X4,X6] : vvar(X1) != vapp(X4,X6),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','DIFF-var-app') ).
fof('DIFF-var-abs',axiom,
! [X1,X2,X3,X4] : vvar(X1) != vabs(X2,X3,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','DIFF-var-abs') ).
fof('T-inv',axiom,
! [X11,X15,X20] :
( vtcheck(X20,X11,X15)
=> ( ? [X9] :
( X11 = vvar(X9)
& vlookup(X9,X20) = vsomeType(X15) )
| ? [X9,X13,X33,X34] :
( X11 = vabs(X9,X33,X13)
& X15 = varrow(X33,X34)
& vtcheck(vbind(X9,X33,X20),X13,X34) )
| ? [X12,X13,X10] :
( X11 = vapp(X12,X13)
& vtcheck(X20,X12,varrow(X10,X15))
& vtcheck(X20,X13,X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax','T-inv') ).
fof(subst3,axiom,
! [X11,X9,X1,X4,X6,X19,X21,X15,X12] :
( ( X1 = X9
& X4 = X11
& X6 = vabs(X21,X15,X12) )
=> ( X9 = X21
=> ( X19 = vsubst(X1,X4,X6)
=> X19 = vabs(X21,X15,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',subst3) ).
fof(lookup1,axiom,
! [X20,X9,X21,X1,X16,X19,X22] :
( ( X1 = X9
& X16 = vbind(X21,X22,X20) )
=> ( X9 = X21
=> ( X19 = vlookup(X1,X16)
=> X19 = vsomeType(X22) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',lookup1) ).
fof(getSomeType0,axiom,
! [X18,X19,X11] :
( X18 = vsomeType(X11)
=> ( X19 = vgetSomeType(X18)
=> X19 = X11 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',getSomeType0) ).
fof(c_0_13,plain,
! [X489,X490,X491,X492,X493,X494,X495,X496] :
( X489 != X494
| X490 != X495
| X491 != vapp(X493,X496)
| X492 != vsubst(X489,X490,X491)
| X492 = vapp(vsubst(X494,X495,X493),vsubst(X494,X495,X496)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subst2])]) ).
cnf(c_0_14,plain,
( X8 = vapp(vsubst(X2,X4,X6),vsubst(X2,X4,X7))
| X1 != X2
| X3 != X4
| X5 != vapp(X6,X7)
| X8 != vsubst(X1,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_15,plain,
! [X475,X476,X477,X478,X479,X480,X481] :
( X477 != X475
| X478 != X481
| X479 != vvar(X476)
| X475 != X476
| X480 != vsubst(X477,X478,X479)
| X480 = X481 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subst0])]) ).
cnf(c_0_16,plain,
( X1 = vapp(vsubst(X2,X3,X4),vsubst(X2,X3,X5))
| X1 != vsubst(X2,X3,X6)
| X6 != vapp(X4,X5) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])]) ).
cnf(c_0_17,plain,
( X7 = X4
| X1 != X2
| X3 != X4
| X5 != vvar(X6)
| X2 != X6
| X7 != vsubst(X1,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
( vsubst(X1,X2,X3) = vapp(vsubst(X1,X2,X4),vsubst(X1,X2,X5))
| X3 != vapp(X4,X5) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
( X1 = X2
| X2 != vsubst(X3,X1,X4)
| X4 != vvar(X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_17])])]) ).
cnf(c_0_20,plain,
vapp(vsubst(X1,X2,X3),vsubst(X1,X2,X4)) = vsubst(X1,X2,vapp(X3,X4)),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
( vsubst(X1,X2,X3) = X2
| X3 != vvar(X1) ),
inference(er,[status(thm)],[c_0_19]) ).
fof(c_0_22,plain,
! [X482,X483,X484,X485,X486,X487,X488] :
( X484 != X483
| X485 != X482
| X486 != vvar(X488)
| X483 = X488
| X487 != vsubst(X484,X485,X486)
| X487 = vvar(X488) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subst1])]) ).
cnf(c_0_23,plain,
( vapp(vsubst(X1,X2,X3),X2) = vsubst(X1,X2,vapp(X3,X4))
| X4 != vvar(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
( X2 = X6
| X7 = vvar(X6)
| X1 != X2
| X3 != X4
| X5 != vvar(X6)
| X7 != vsubst(X1,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_25,plain,
( vapp(X1,X1) = vsubst(X2,X1,vapp(X3,X4))
| X4 != vvar(X2)
| X3 != vvar(X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_26,plain,
( X1 = vvar(X2)
| X3 = X2
| X1 != vsubst(X3,X4,X5)
| X5 != vvar(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_24])]) ).
fof(c_0_27,plain,
! [X371,X372,X373,X374] :
( ( X371 = X373
| vapp(X371,X372) != vapp(X373,X374) )
& ( X372 = X374
| vapp(X371,X372) != vapp(X373,X374) )
& ( X371 != X373
| X372 != X374
| vapp(X371,X372) = vapp(X373,X374) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['EQ-app'])])]) ).
cnf(c_0_28,plain,
( vapp(vsubst(X1,X2,X3),X2) = vapp(X2,X2)
| X4 != vvar(X1)
| X3 != vvar(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).
cnf(c_0_29,plain,
( vsubst(X1,X2,X3) = vvar(X4)
| X1 = X4
| X3 != vvar(X4) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
( X1 = X2
| vapp(X1,X3) != vapp(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,plain,
( vapp(vsubst(X1,X2,X3),X2) = vapp(X2,X2)
| X3 != vvar(X1) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_32,plain,
( vsubst(X1,X2,vvar(X3)) = vvar(X3)
| X1 = X3 ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_33,plain,
( vsubst(X1,X2,X3) = X4
| vapp(X2,X2) != vapp(X4,X5)
| X3 != vvar(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_34,negated_conjecture,
~ ! [X15,X20,X9,X11,X21,X34] :
( ( vtcheck(X20,X11,X15)
& vtcheck(vbind(X9,X15,X20),vvar(X21),X34) )
=> vtcheck(X20,vsubst(X9,X11,vvar(X21)),X34) ),
inference(assume_negation,[status(cth)],['T-subst-var']) ).
fof(c_0_35,plain,
! [X9,X10,X20,X11,X15] :
( ( ~ visFreeVar(X9,X11)
& vtcheck(vbind(X9,X10,X20),X11,X15) )
=> vtcheck(X20,X11,X15) ),
inference(fof_simplification,[status(thm)],['T-Strong']) ).
cnf(c_0_36,plain,
( vsubst(X1,X2,vapp(vvar(X3),X4)) = vapp(vvar(X3),vsubst(X1,X2,X4))
| X1 = X3 ),
inference(spm,[status(thm)],[c_0_20,c_0_32]) ).
cnf(c_0_37,plain,
( vsubst(X1,X2,vapp(vvar(X3),X4)) = vapp(vvar(X3),X2)
| X1 = X3
| X4 != vvar(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_32]) ).
cnf(c_0_38,plain,
( vsubst(X1,X2,X3) = vsubst(X4,X5,X6)
| vapp(X2,X2) != vapp(X5,X5)
| X3 != vvar(X1)
| X6 != vvar(X4) ),
inference(spm,[status(thm)],[c_0_33,c_0_31]) ).
fof(c_0_39,negated_conjecture,
( vtcheck(esk33_0,esk35_0,esk32_0)
& vtcheck(vbind(esk34_0,esk32_0,esk33_0),vvar(esk36_0),esk37_0)
& ~ vtcheck(esk33_0,vsubst(esk34_0,esk35_0,vvar(esk36_0)),esk37_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])]) ).
fof(c_0_40,plain,
! [X629,X630,X631,X632,X633] :
( visFreeVar(X629,X632)
| ~ vtcheck(vbind(X629,X630,X631),X632,X633)
| vtcheck(X631,X632,X633) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])]) ).
cnf(c_0_41,plain,
( vapp(vvar(X1),vsubst(X2,X3,X4)) = vapp(vvar(X1),X3)
| X2 = X1
| X4 != vvar(X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
( vsubst(X1,X2,X3) = vsubst(X4,X2,X5)
| X3 != vvar(X1)
| X5 != vvar(X4) ),
inference(er,[status(thm)],[c_0_38]) ).
fof(c_0_43,plain,
! [X396,X397,X398,X399] :
( ( X398 != X399
| visFreeVar(X396,X397)
| X396 != X399
| X397 != vvar(X398) )
& ( ~ visFreeVar(X396,X397)
| X398 = X399
| X396 != X399
| X397 != vvar(X398) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isFreeVar0])])]) ).
cnf(c_0_44,negated_conjecture,
~ vtcheck(esk33_0,vsubst(esk34_0,esk35_0,vvar(esk36_0)),esk37_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
( visFreeVar(X1,X2)
| vtcheck(X4,X2,X5)
| ~ vtcheck(vbind(X1,X3,X4),X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_46,negated_conjecture,
vtcheck(vbind(esk34_0,esk32_0,esk33_0),vvar(esk36_0),esk37_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_47,plain,
! [X379,X380,X381] : vvar(X379) != vapp(X380,X381),
inference(variable_rename,[status(thm)],['DIFF-var-app']) ).
cnf(c_0_48,plain,
( vapp(vvar(X1),vsubst(X2,X3,X4)) = vapp(vvar(X1),X3)
| X5 = X1
| X6 != vvar(X5)
| X4 != vvar(X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
fof(c_0_49,plain,
! [X375,X376,X377,X378] : vvar(X375) != vabs(X376,X377,X378),
inference(variable_rename,[status(thm)],['DIFF-var-abs']) ).
fof(c_0_50,plain,
! [X613,X614,X615] :
( ( X613 = vapp(esk29_3(X613,X614,X615),esk30_3(X613,X614,X615))
| X613 = vabs(esk25_3(X613,X614,X615),esk27_3(X613,X614,X615),esk26_3(X613,X614,X615))
| X613 = vvar(esk24_3(X613,X614,X615))
| ~ vtcheck(X615,X613,X614) )
& ( vtcheck(X615,esk29_3(X613,X614,X615),varrow(esk31_3(X613,X614,X615),X614))
| X613 = vabs(esk25_3(X613,X614,X615),esk27_3(X613,X614,X615),esk26_3(X613,X614,X615))
| X613 = vvar(esk24_3(X613,X614,X615))
| ~ vtcheck(X615,X613,X614) )
& ( vtcheck(X615,esk30_3(X613,X614,X615),esk31_3(X613,X614,X615))
| X613 = vabs(esk25_3(X613,X614,X615),esk27_3(X613,X614,X615),esk26_3(X613,X614,X615))
| X613 = vvar(esk24_3(X613,X614,X615))
| ~ vtcheck(X615,X613,X614) )
& ( X613 = vapp(esk29_3(X613,X614,X615),esk30_3(X613,X614,X615))
| X614 = varrow(esk27_3(X613,X614,X615),esk28_3(X613,X614,X615))
| X613 = vvar(esk24_3(X613,X614,X615))
| ~ vtcheck(X615,X613,X614) )
& ( vtcheck(X615,esk29_3(X613,X614,X615),varrow(esk31_3(X613,X614,X615),X614))
| X614 = varrow(esk27_3(X613,X614,X615),esk28_3(X613,X614,X615))
| X613 = vvar(esk24_3(X613,X614,X615))
| ~ vtcheck(X615,X613,X614) )
& ( vtcheck(X615,esk30_3(X613,X614,X615),esk31_3(X613,X614,X615))
| X614 = varrow(esk27_3(X613,X614,X615),esk28_3(X613,X614,X615))
| X613 = vvar(esk24_3(X613,X614,X615))
| ~ vtcheck(X615,X613,X614) )
& ( X613 = vapp(esk29_3(X613,X614,X615),esk30_3(X613,X614,X615))
| vtcheck(vbind(esk25_3(X613,X614,X615),esk27_3(X613,X614,X615),X615),esk26_3(X613,X614,X615),esk28_3(X613,X614,X615))
| X613 = vvar(esk24_3(X613,X614,X615))
| ~ vtcheck(X615,X613,X614) )
& ( vtcheck(X615,esk29_3(X613,X614,X615),varrow(esk31_3(X613,X614,X615),X614))
| vtcheck(vbind(esk25_3(X613,X614,X615),esk27_3(X613,X614,X615),X615),esk26_3(X613,X614,X615),esk28_3(X613,X614,X615))
| X613 = vvar(esk24_3(X613,X614,X615))
| ~ vtcheck(X615,X613,X614) )
& ( vtcheck(X615,esk30_3(X613,X614,X615),esk31_3(X613,X614,X615))
| vtcheck(vbind(esk25_3(X613,X614,X615),esk27_3(X613,X614,X615),X615),esk26_3(X613,X614,X615),esk28_3(X613,X614,X615))
| X613 = vvar(esk24_3(X613,X614,X615))
| ~ vtcheck(X615,X613,X614) )
& ( X613 = vapp(esk29_3(X613,X614,X615),esk30_3(X613,X614,X615))
| X613 = vabs(esk25_3(X613,X614,X615),esk27_3(X613,X614,X615),esk26_3(X613,X614,X615))
| vlookup(esk24_3(X613,X614,X615),X615) = vsomeType(X614)
| ~ vtcheck(X615,X613,X614) )
& ( vtcheck(X615,esk29_3(X613,X614,X615),varrow(esk31_3(X613,X614,X615),X614))
| X613 = vabs(esk25_3(X613,X614,X615),esk27_3(X613,X614,X615),esk26_3(X613,X614,X615))
| vlookup(esk24_3(X613,X614,X615),X615) = vsomeType(X614)
| ~ vtcheck(X615,X613,X614) )
& ( vtcheck(X615,esk30_3(X613,X614,X615),esk31_3(X613,X614,X615))
| X613 = vabs(esk25_3(X613,X614,X615),esk27_3(X613,X614,X615),esk26_3(X613,X614,X615))
| vlookup(esk24_3(X613,X614,X615),X615) = vsomeType(X614)
| ~ vtcheck(X615,X613,X614) )
& ( X613 = vapp(esk29_3(X613,X614,X615),esk30_3(X613,X614,X615))
| X614 = varrow(esk27_3(X613,X614,X615),esk28_3(X613,X614,X615))
| vlookup(esk24_3(X613,X614,X615),X615) = vsomeType(X614)
| ~ vtcheck(X615,X613,X614) )
& ( vtcheck(X615,esk29_3(X613,X614,X615),varrow(esk31_3(X613,X614,X615),X614))
| X614 = varrow(esk27_3(X613,X614,X615),esk28_3(X613,X614,X615))
| vlookup(esk24_3(X613,X614,X615),X615) = vsomeType(X614)
| ~ vtcheck(X615,X613,X614) )
& ( vtcheck(X615,esk30_3(X613,X614,X615),esk31_3(X613,X614,X615))
| X614 = varrow(esk27_3(X613,X614,X615),esk28_3(X613,X614,X615))
| vlookup(esk24_3(X613,X614,X615),X615) = vsomeType(X614)
| ~ vtcheck(X615,X613,X614) )
& ( X613 = vapp(esk29_3(X613,X614,X615),esk30_3(X613,X614,X615))
| vtcheck(vbind(esk25_3(X613,X614,X615),esk27_3(X613,X614,X615),X615),esk26_3(X613,X614,X615),esk28_3(X613,X614,X615))
| vlookup(esk24_3(X613,X614,X615),X615) = vsomeType(X614)
| ~ vtcheck(X615,X613,X614) )
& ( vtcheck(X615,esk29_3(X613,X614,X615),varrow(esk31_3(X613,X614,X615),X614))
| vtcheck(vbind(esk25_3(X613,X614,X615),esk27_3(X613,X614,X615),X615),esk26_3(X613,X614,X615),esk28_3(X613,X614,X615))
| vlookup(esk24_3(X613,X614,X615),X615) = vsomeType(X614)
| ~ vtcheck(X615,X613,X614) )
& ( vtcheck(X615,esk30_3(X613,X614,X615),esk31_3(X613,X614,X615))
| vtcheck(vbind(esk25_3(X613,X614,X615),esk27_3(X613,X614,X615),X615),esk26_3(X613,X614,X615),esk28_3(X613,X614,X615))
| vlookup(esk24_3(X613,X614,X615),X615) = vsomeType(X614)
| ~ vtcheck(X615,X613,X614) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['T-inv'])])])]) ).
cnf(c_0_51,plain,
( X3 = X4
| ~ visFreeVar(X1,X2)
| X1 != X4
| X2 != vvar(X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_52,negated_conjecture,
( esk36_0 = esk34_0
| ~ vtcheck(esk33_0,vvar(esk36_0),esk37_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_32]) ).
cnf(c_0_53,negated_conjecture,
( vtcheck(esk33_0,vvar(esk36_0),esk37_0)
| visFreeVar(esk34_0,vvar(esk36_0)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_54,plain,
vvar(X1) != vapp(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_55,plain,
( vapp(vvar(X1),vsubst(X2,X3,X4)) = vapp(vvar(X1),X3)
| X5 = X1
| X4 != vvar(X2) ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_56,plain,
vvar(X1) != vabs(X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_57,plain,
( X1 = vapp(esk29_3(X1,X2,X3),esk30_3(X1,X2,X3))
| X1 = vabs(esk25_3(X1,X2,X3),esk27_3(X1,X2,X3),esk26_3(X1,X2,X3))
| X1 = vvar(esk24_3(X1,X2,X3))
| ~ vtcheck(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_58,plain,
( X1 = X2
| X3 != vvar(X1)
| ~ visFreeVar(X2,X3) ),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_59,negated_conjecture,
( esk36_0 = esk34_0
| visFreeVar(esk34_0,vvar(esk36_0)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_60,plain,
! [X497,X498,X499,X500,X501,X502,X503,X504,X505] :
( X499 != X498
| X500 != X497
| X501 != vabs(X503,X504,X505)
| X498 != X503
| X502 != vsubst(X499,X500,X501)
| X502 = vabs(X503,X504,X505) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subst3])]) ).
cnf(c_0_61,plain,
vvar(X1) != vsubst(X2,X3,vapp(X4,X5)),
inference(spm,[status(thm)],[c_0_54,c_0_20]) ).
cnf(c_0_62,plain,
( vapp(vvar(X1),vsubst(X2,X3,vvar(X2))) = vapp(vvar(X1),X3)
| X4 = X1 ),
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_63,plain,
( vapp(esk29_3(X1,X2,X3),esk30_3(X1,X2,X3)) = X1
| vvar(esk24_3(X1,X2,X3)) = X1
| vvar(X4) != X1
| ~ vtcheck(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,negated_conjecture,
( esk36_0 = esk34_0
| X1 = esk34_0
| vvar(esk36_0) != vvar(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
( X9 = vabs(X6,X7,X8)
| X1 != X2
| X3 != X4
| X5 != vabs(X6,X7,X8)
| X2 != X6
| X9 != vsubst(X1,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,plain,
( X1 = X2
| vapp(X3,X1) != vapp(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_67,plain,
vapp(vvar(X1),vsubst(X2,X3,vvar(X2))) = vapp(vvar(X1),X3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_62]) ).
cnf(c_0_68,plain,
( vvar(esk24_3(vvar(X1),X2,X3)) = vvar(X1)
| ~ vtcheck(X3,vvar(X1),X2) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_63]),c_0_54]) ).
cnf(c_0_69,negated_conjecture,
esk36_0 = esk34_0,
inference(er,[status(thm)],[c_0_64]) ).
fof(c_0_70,plain,
! [X433,X434,X435,X436,X437,X438,X439] :
( X436 != X434
| X437 != vbind(X435,X439,X433)
| X434 != X435
| X438 != vlookup(X436,X437)
| X438 = vsomeType(X439) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lookup1])]) ).
cnf(c_0_71,plain,
( X1 = vabs(X2,X3,X4)
| X1 != vsubst(X2,X5,X6)
| X6 != vabs(X2,X3,X4) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_65])])]) ).
cnf(c_0_72,plain,
( vsubst(X1,X2,vvar(X1)) = X3
| vapp(vvar(X4),X2) != vapp(X5,X3) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,plain,
( vsubst(X1,X2,vvar(X3)) = vvar(X3)
| X1 = esk24_3(vvar(X3),X4,X5)
| ~ vtcheck(X5,vvar(X3),X4) ),
inference(spm,[status(thm)],[c_0_32,c_0_68]) ).
cnf(c_0_74,negated_conjecture,
vtcheck(vbind(esk34_0,esk32_0,esk33_0),vvar(esk34_0),esk37_0),
inference(rw,[status(thm)],[c_0_46,c_0_69]) ).
cnf(c_0_75,plain,
( X7 = vsomeType(X5)
| X1 != X2
| X3 != vbind(X4,X5,X6)
| X2 != X4
| X7 != vlookup(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
fof(c_0_76,plain,
! [X426,X427,X428] :
( X426 != vsomeType(X428)
| X427 != vgetSomeType(X426)
| X427 = X428 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[getSomeType0])]) ).
cnf(c_0_77,plain,
( X1 = vapp(esk29_3(X1,X2,X3),esk30_3(X1,X2,X3))
| X1 = vabs(esk25_3(X1,X2,X3),esk27_3(X1,X2,X3),esk26_3(X1,X2,X3))
| vlookup(esk24_3(X1,X2,X3),X3) = vsomeType(X2)
| ~ vtcheck(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_78,plain,
( vsubst(X1,X2,X3) = vabs(X1,X4,X5)
| X3 != vabs(X1,X4,X5) ),
inference(er,[status(thm)],[c_0_71]) ).
cnf(c_0_79,plain,
vsubst(X1,X2,vvar(X1)) = X2,
inference(er,[status(thm)],[c_0_72]) ).
cnf(c_0_80,negated_conjecture,
( X1 = esk24_3(vvar(esk34_0),esk37_0,vbind(esk34_0,esk32_0,esk33_0))
| vsubst(X1,X2,vvar(esk34_0)) = vvar(esk34_0) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,plain,
( X1 = vsomeType(X2)
| X3 != vbind(X4,X2,X5)
| X1 != vlookup(X4,X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_75])]) ).
cnf(c_0_82,plain,
( X3 = X2
| X1 != vsomeType(X2)
| X3 != vgetSomeType(X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_83,plain,
( vapp(esk29_3(X1,X2,X3),esk30_3(X1,X2,X3)) = X1
| vlookup(esk24_3(X1,X2,X3),X3) = vsomeType(X2)
| vvar(X4) != X1
| ~ vtcheck(X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_77]) ).
cnf(c_0_84,plain,
vsubst(X1,X2,vabs(X1,X3,X4)) = vabs(X1,X3,X4),
inference(er,[status(thm)],[c_0_78]) ).
cnf(c_0_85,negated_conjecture,
( esk24_3(vvar(esk34_0),esk37_0,vbind(esk34_0,esk32_0,esk33_0)) = esk34_0
| vvar(esk34_0) = X1 ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_86,plain,
( X1 = vsomeType(X2)
| X1 != vlookup(X3,vbind(X3,X2,X4)) ),
inference(er,[status(thm)],[c_0_81]) ).
cnf(c_0_87,plain,
( X1 = vgetSomeType(X2)
| X2 != vsomeType(X1) ),
inference(er,[status(thm)],[c_0_82]) ).
cnf(c_0_88,plain,
( vlookup(esk24_3(vvar(X1),X2,X3),X3) = vsomeType(X2)
| ~ vtcheck(X3,vvar(X1),X2) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_83]),c_0_54]) ).
cnf(c_0_89,negated_conjecture,
esk24_3(vvar(esk34_0),esk37_0,vbind(esk34_0,esk32_0,esk33_0)) = esk34_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_56]) ).
cnf(c_0_90,plain,
vlookup(X1,vbind(X1,X2,X3)) = vsomeType(X2),
inference(er,[status(thm)],[c_0_86]) ).
cnf(c_0_91,negated_conjecture,
( vvar(esk36_0) != vvar(esk34_0)
| ~ vtcheck(esk33_0,esk35_0,esk37_0) ),
inference(spm,[status(thm)],[c_0_44,c_0_21]) ).
cnf(c_0_92,plain,
vgetSomeType(vsomeType(X1)) = X1,
inference(er,[status(thm)],[c_0_87]) ).
cnf(c_0_93,negated_conjecture,
vsomeType(esk37_0) = vsomeType(esk32_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90]),c_0_74])]) ).
cnf(c_0_94,negated_conjecture,
~ vtcheck(esk33_0,esk35_0,esk37_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_69])]) ).
cnf(c_0_95,negated_conjecture,
esk37_0 = esk32_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_92]) ).
cnf(c_0_96,negated_conjecture,
vtcheck(esk33_0,esk35_0,esk32_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_96])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM135+1 : TPTP v9.2.1. Released v6.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 16:22:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 29.34/17.85 % Version : CSE_E---1.7
% 29.34/17.85 % Problem : theBenchmark.p
% 29.34/17.85 % SZS status Theorem for theBenchmark.p
% 29.34/17.85 % SZS output start CNFRefutation
% See solution above
% 29.44/17.96 % Total time : 13.450s
%------------------------------------------------------------------------------