TSTP Solution File: COL106-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL106-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n028.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 : Wed Aug 30 18:22:41 EDT 2023
% Result : Unsatisfiable 2.03s 2.16s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 28
% Syntax : Number of formulae : 84 ( 18 unt; 16 typ; 0 def)
% Number of atoms : 165 ( 113 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 143 ( 46 ~; 97 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 9 >; 16 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 105 ( 28 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
c_Comb_Ocomb_OK: $i ).
tff(decl_23,type,
v_x: $i ).
tff(decl_24,type,
c_Comb_Ocomb_Oop_A_D_D: ( $i * $i ) > $i ).
tff(decl_25,type,
v_ya: $i ).
tff(decl_26,type,
v_xb: $i ).
tff(decl_27,type,
tc_Comb_Ocomb: $i ).
tff(decl_28,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_29,type,
c_Comb_Oparcontract: $i ).
tff(decl_30,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_31,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
c_Comb_Ocomb_OS: $i ).
tff(decl_33,type,
v_sko__uTF: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
v_sko__uTG: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
v_sko__uTI: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
v_sko__uTH: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
v_sko__uTE: ( $i * $i ) > $i ).
cnf(cls_Comb_OK1__parcontractD__dest_0,axiom,
( X2 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X1,X2))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_OK1__parcontractD__dest_0) ).
cnf(cls_Comb_Oparcontract_Ointros__1_0,axiom,
c_in(c_Pair(X1,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__1_0) ).
cnf(cls_Comb_OAp__parcontractE_2,axiom,
( c_in(c_Pair(X1,v_sko__uTI(X1,X2,X3),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| X3 = c_Comb_Ocomb_Oop_A_D_D(X1,X2)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X3)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X1,X2,X3)),v_sko__uTG(X1,X2,X3))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X1,X2),X3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_OAp__parcontractE_2) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),v_xb,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Comb_Ocomb_Oinject__iff1_1,axiom,
( X2 = X4
| c_Comb_Ocomb_Oop_A_D_D(X1,X2) != c_Comb_Ocomb_Oop_A_D_D(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocomb_Oinject__iff1_1) ).
cnf(cls_Comb_Ocomb_Odistinct__3__iff1_0,axiom,
c_Comb_Ocomb_OK != c_Comb_Ocomb_Oop_A_D_D(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocomb_Odistinct__3__iff1_0) ).
cnf(cls_Comb_Ocomb_Oinject__iff1_0,axiom,
( X1 = X3
| c_Comb_Ocomb_Oop_A_D_D(X1,X2) != c_Comb_Ocomb_Oop_A_D_D(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Ocomb_Oinject__iff1_0) ).
cnf(cls_Comb_OAp__parcontractE_0,axiom,
( X3 = c_Comb_Ocomb_Oop_A_D_D(X1,X2)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X3)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X1,X2,X3)),v_sko__uTG(X1,X2,X3))
| X3 = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(X1,X2,X3),v_sko__uTH(X1,X2,X3))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X1,X2),X3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_OAp__parcontractE_0) ).
cnf(cls_Comb_Oparcontract_Ointros__4_0,axiom,
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X3,X1),c_Comb_Ocomb_Oop_A_D_D(X4,X2),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X3,X4,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__4_0) ).
cnf(cls_Comb_Oparcontract_Ointros__2_0,axiom,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__2_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ c_in(c_Pair(v_xb,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(v_x,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Comb_OK1__parcontractD__dest_1,axiom,
( c_in(c_Pair(X1,v_sko__uTE(X1,X2),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Comb_OK1__parcontractD__dest_1) ).
cnf(c_0_12,axiom,
( X2 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X1,X2))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
cls_Comb_OK1__parcontractD__dest_0 ).
cnf(c_0_13,axiom,
c_in(c_Pair(X1,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
cls_Comb_Oparcontract_Ointros__1_0 ).
cnf(c_0_14,axiom,
( c_in(c_Pair(X1,v_sko__uTI(X1,X2,X3),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| X3 = c_Comb_Ocomb_Oop_A_D_D(X1,X2)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X3)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X1,X2,X3)),v_sko__uTG(X1,X2,X3))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X1,X2),X3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
cls_Comb_OAp__parcontractE_2 ).
cnf(c_0_15,negated_conjecture,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),v_xb,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
cls_conjecture_0 ).
cnf(c_0_16,axiom,
( X2 = X4
| c_Comb_Ocomb_Oop_A_D_D(X1,X2) != c_Comb_Ocomb_Oop_A_D_D(X3,X4) ),
cls_Comb_Ocomb_Oinject__iff1_1 ).
cnf(c_0_17,plain,
c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X1,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,axiom,
c_Comb_Ocomb_OK != c_Comb_Ocomb_Oop_A_D_D(X1,X2),
cls_Comb_Ocomb_Odistinct__3__iff1_0 ).
cnf(c_0_20,plain,
( v_sko__uTE(X1,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)) = X2
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1) != c_Comb_Ocomb_Oop_A_D_D(X3,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,axiom,
( X1 = X3
| c_Comb_Ocomb_Oop_A_D_D(X1,X2) != c_Comb_Ocomb_Oop_A_D_D(X3,X4) ),
cls_Comb_Ocomb_Oinject__iff1_0 ).
cnf(c_0_22,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(v_x,v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb))) = v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb ),
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_23,axiom,
( X3 = c_Comb_Ocomb_Oop_A_D_D(X1,X2)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X3)
| X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(X1,X2,X3)),v_sko__uTG(X1,X2,X3))
| X3 = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(X1,X2,X3),v_sko__uTH(X1,X2,X3))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X1,X2),X3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
cls_Comb_OAp__parcontractE_0 ).
cnf(c_0_24,plain,
( X1 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2)
| c_in(c_Pair(c_Comb_Ocomb_OK,v_sko__uTI(c_Comb_Ocomb_OK,v_sko__uTE(X2,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2)),X1),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_17]),c_0_19]),c_0_19]) ).
cnf(c_0_25,axiom,
( c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(X3,X1),c_Comb_Ocomb_Oop_A_D_D(X4,X2),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X3,X4,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
cls_Comb_Oparcontract_Ointros__4_0 ).
cnf(c_0_26,plain,
v_sko__uTE(X1,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)) = X1,
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(v_x,v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb))) = v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)) = X1
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) != c_Comb_Ocomb_Oop_A_D_D(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb),v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) ),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_29,plain,
( c_Comb_Ocomb_Oop_A_D_D(X1,X2) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X3)
| c_in(c_Pair(c_Comb_Ocomb_OK,v_sko__uTI(c_Comb_Ocomb_OK,X3,c_Comb_Ocomb_Oop_A_D_D(X1,X2)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_OK,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X3,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,axiom,
c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2),X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
cls_Comb_Oparcontract_Ointros__2_0 ).
cnf(c_0_31,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(v_x,v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb))) = v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_27]),c_0_19]) ).
cnf(c_0_32,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb),v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)) = X1
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) != c_Comb_Ocomb_Oop_A_D_D(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_33,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2)
| c_in(c_Pair(c_Comb_Ocomb_OK,v_sko__uTI(c_Comb_Ocomb_OK,X2,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X2,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_29,c_0_13]) ).
cnf(c_0_34,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb),X1),v_sko__uTE(v_x,v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb),v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) ),
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_32]),c_0_19]) ).
cnf(c_0_36,plain,
( c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_OK,v_sko__uTE(X1,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)),X2),v_sko__uTH(c_Comb_Ocomb_OK,v_sko__uTE(X1,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)),X2)) = X2
| X2 = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_17]),c_0_19]),c_0_19]) ).
cnf(c_0_37,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X1,c_Comb_Ocomb_Oop_A_D_D(X2,X3))) = c_Comb_Ocomb_Oop_A_D_D(X2,X3)
| ~ c_in(c_Pair(c_Comb_Ocomb_OK,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X1,X3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_12,c_0_25]) ).
cnf(c_0_38,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya)) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)
| c_in(c_Pair(c_Comb_Ocomb_OK,v_sko__uTI(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_33,c_0_15]) ).
cnf(c_0_39,negated_conjecture,
( ~ c_in(c_Pair(v_xb,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(v_x,X1,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
cls_conjecture_1 ).
cnf(c_0_40,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| c_in(c_Pair(v_xb,v_sko__uTE(v_x,v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
( c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_OK,X1,c_Comb_Ocomb_Oop_A_D_D(X2,X3)),v_sko__uTH(c_Comb_Ocomb_OK,X1,c_Comb_Ocomb_Oop_A_D_D(X2,X3))) = c_Comb_Ocomb_Oop_A_D_D(X2,X3)
| c_Comb_Ocomb_Oop_A_D_D(X2,X3) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)
| ~ c_in(c_Pair(c_Comb_Ocomb_OK,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(X1,X3,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_25]),c_0_26]),c_0_26]) ).
cnf(c_0_42,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X1,c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)),X2))) = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)),X2)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya)) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)
| ~ c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| ~ c_in(c_Pair(v_x,v_sko__uTE(v_x,v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,axiom,
( c_in(c_Pair(X1,v_sko__uTE(X1,X2),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb))
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
cls_Comb_OK1__parcontractD__dest_1 ).
cnf(c_0_45,plain,
( c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_OK,X1,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2)),v_sko__uTH(c_Comb_Ocomb_OK,X1,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)
| ~ c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_41,c_0_13]) ).
cnf(c_0_46,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X1,c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)),X1))) = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)),X1)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya)) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) ),
inference(spm,[status(thm)],[c_0_42,c_0_13]) ).
cnf(c_0_47,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| ~ c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb),tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)),v_sko__uTH(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya)) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) ),
inference(spm,[status(thm)],[c_0_45,c_0_15]) ).
cnf(c_0_49,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya)) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)
| c_Comb_Ocomb_OK = X1
| c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)),X2) != c_Comb_Ocomb_Oop_A_D_D(X1,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS,v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)),v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya,v_xb)) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) ),
inference(spm,[status(thm)],[c_0_47,c_0_18]) ).
cnf(c_0_51,negated_conjecture,
( v_sko__uTI(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)) = X1
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya)) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) != c_Comb_Ocomb_Oop_A_D_D(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)),X1) != c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_19]),c_0_16]) ).
cnf(c_0_53,negated_conjecture,
( v_sko__uTI(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)) = c_Comb_Ocomb_OK
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya)) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) ),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_54,plain,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(X1,c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X2)
| ~ c_in(c_Pair(X1,X2,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_37,c_0_13]) ).
cnf(c_0_55,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1) != c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_16]) ).
cnf(c_0_56,negated_conjecture,
c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb),
inference(spm,[status(thm)],[c_0_54,c_0_15]) ).
cnf(c_0_57,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya) = v_xb ),
inference(er,[status(thm)],[c_0_55]) ).
cnf(c_0_58,plain,
c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),
inference(spm,[status(thm)],[c_0_54,c_0_30]) ).
cnf(c_0_59,negated_conjecture,
( v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)) = X1
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) != c_Comb_Ocomb_Oop_A_D_D(X2,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
( c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x)
| c_in(c_Pair(v_xb,v_x,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) ),
inference(spm,[status(thm)],[c_0_30,c_0_57]) ).
cnf(c_0_61,plain,
( v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)) = X3
| c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1) != c_Comb_Ocomb_Oop_A_D_D(X4,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_58]) ).
cnf(c_0_62,negated_conjecture,
v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),v_ya),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb)) = v_xb,
inference(er,[status(thm)],[c_0_59]) ).
cnf(c_0_63,negated_conjecture,
c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,v_x),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_60]),c_0_13])]) ).
cnf(c_0_64,plain,
v_sko__uTE(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1),X2),c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK,X1)) = X1,
inference(er,[status(thm)],[c_0_61]) ).
cnf(c_0_65,negated_conjecture,
~ c_in(c_Pair(v_x,v_xb,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)),
inference(spm,[status(thm)],[c_0_39,c_0_13]) ).
cnf(c_0_66,negated_conjecture,
v_xb = v_x,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_67,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL106-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 04:24:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 2.03/2.16 % Version : CSE_E---1.5
% 2.03/2.16 % Problem : theBenchmark.p
% 2.03/2.16 % Proof found
% 2.03/2.16 % SZS status Theorem for theBenchmark.p
% 2.03/2.16 % SZS output start Proof
% See solution above
% 2.03/2.17 % Total time : 1.574000 s
% 2.03/2.17 % SZS output end Proof
% 2.03/2.17 % Total time : 1.577000 s
%------------------------------------------------------------------------------