TSTP Solution File: BOO039-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : BOO039-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 18:05:58 EDT 2023
% Result : Unsatisfiable 25.43s 25.47s
% Output : CNFRefutation 25.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 6
% Syntax : Number of formulae : 126 ( 120 unt; 4 typ; 0 def)
% Number of atoms : 124 ( 123 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 7 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 316 ( 70 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
nand: ( $i * $i ) > $i ).
tff(decl_23,type,
a: $i ).
tff(decl_24,type,
b: $i ).
tff(decl_25,type,
c: $i ).
cnf(sh_1,axiom,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,nand(X3,X1))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sh_1) ).
cnf(prove_meredith_2_basis,negated_conjecture,
( nand(nand(a,a),nand(b,a)) != a
| nand(a,nand(b,nand(a,c))) != nand(nand(nand(c,b),b),a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_meredith_2_basis) ).
cnf(c_0_2,axiom,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,nand(X3,X1))) = X2,
sh_1 ).
cnf(c_0_3,plain,
nand(nand(nand(X1,nand(X2,X3)),nand(nand(X4,nand(X1,nand(X2,X3))),nand(X1,nand(X2,X3)))),nand(X4,X1)) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
nand(nand(nand(X1,X2),nand(nand(X3,nand(X1,X2)),nand(X1,X2))),nand(X3,X1)) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,nand(X3,nand(nand(X1,X3),X3)))) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_2]) ).
cnf(c_0_6,plain,
nand(nand(X1,nand(nand(nand(X2,nand(nand(X2,X2),X2)),X1),X1)),X2) = nand(X2,nand(nand(X2,X2),X2)),
inference(spm,[status(thm)],[c_0_5,c_0_2]) ).
cnf(c_0_7,plain,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,nand(nand(X2,X2),X2))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_2]),c_0_5]),c_0_5]) ).
cnf(c_0_8,plain,
nand(X1,nand(nand(X1,X1),X1)) = nand(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_5]) ).
cnf(c_0_9,plain,
nand(nand(X1,X1),nand(X1,nand(X2,X1))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_8]) ).
cnf(c_0_10,plain,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,X2)) = X2,
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
nand(nand(X1,X1),nand(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_8]),c_0_8]) ).
cnf(c_0_12,plain,
nand(nand(nand(X1,nand(X2,X1)),nand(X1,nand(X1,nand(X2,X1)))),nand(nand(X1,X1),X1)) = nand(X1,X1),
inference(spm,[status(thm)],[c_0_4,c_0_9]) ).
cnf(c_0_13,plain,
nand(nand(nand(X1,nand(X2,X1)),nand(X1,nand(X1,nand(X2,X1)))),X1) = nand(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_9]),c_0_11]) ).
cnf(c_0_14,plain,
nand(nand(X1,nand(X2,X1)),nand(X1,nand(X1,nand(X2,X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_12]),c_0_13]),c_0_8]),c_0_11]) ).
cnf(c_0_15,plain,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,nand(X1,nand(X3,X1)))) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_14]) ).
cnf(c_0_16,plain,
nand(nand(nand(X1,nand(X2,X1)),nand(X1,nand(X2,X1))),X1) = nand(X1,nand(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_14]),c_0_8]) ).
cnf(c_0_17,plain,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,nand(X1,nand(X1,nand(X3,X1))))) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,plain,
nand(X1,nand(nand(X1,nand(X2,X1)),X1)) = nand(X1,nand(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_14]) ).
cnf(c_0_19,plain,
nand(nand(X1,nand(nand(nand(X1,nand(X2,X1)),X1),X1)),X1) = nand(X1,nand(X2,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_20,plain,
nand(X1,nand(nand(nand(X1,nand(X2,X1)),X1),X1)) = nand(X1,nand(X1,nand(X2,X1))),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
nand(nand(X1,nand(X1,nand(X2,X1))),X1) = nand(X1,nand(X2,X1)),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
nand(X1,nand(X1,nand(X1,nand(X2,X1)))) = nand(X1,nand(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_21]),c_0_18]) ).
cnf(c_0_23,plain,
nand(nand(X1,nand(X2,X1)),nand(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_22]),c_0_14]),c_0_21]) ).
cnf(c_0_24,plain,
nand(nand(X1,nand(X1,nand(X2,X1))),nand(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_25,plain,
nand(X1,nand(nand(X2,nand(nand(X1,X2),X2)),nand(X3,nand(X1,X1)))) = nand(X2,nand(nand(X1,X2),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_10]),c_0_9]) ).
cnf(c_0_26,plain,
nand(nand(X1,nand(X2,X1)),X1) = nand(X1,nand(X1,nand(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_24]),c_0_21]),c_0_18]) ).
cnf(c_0_27,plain,
nand(X1,nand(nand(X1,nand(X2,X1)),nand(X3,nand(X1,X1)))) = nand(X1,nand(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_14]),c_0_21]),c_0_14]),c_0_21]) ).
cnf(c_0_28,plain,
nand(X1,nand(nand(X2,nand(nand(X1,X2),X2)),X1)) = nand(X2,nand(nand(X1,X2),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_10]),c_0_9]) ).
cnf(c_0_29,plain,
nand(nand(X1,nand(nand(X2,X1),X1)),X2) = nand(X2,nand(X1,nand(nand(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_30,plain,
nand(X1,nand(nand(X2,X1),X1)) = nand(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_2]) ).
cnf(c_0_31,plain,
nand(X1,nand(X1,nand(X2,nand(nand(X1,X2),X2)))) = nand(X2,nand(nand(X1,X2),X2)),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
nand(nand(X1,X2),X2) = nand(X2,nand(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_30]) ).
cnf(c_0_33,plain,
nand(X1,nand(X1,nand(X2,X1))) = nand(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_30]),c_0_30]) ).
cnf(c_0_34,plain,
nand(X1,X2) = nand(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_32]),c_0_33]) ).
cnf(c_0_35,plain,
nand(nand(X1,X2),nand(nand(X2,X3),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_4,c_0_30]),c_0_34]) ).
cnf(c_0_36,plain,
nand(nand(X1,X2),nand(X2,nand(X3,X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_5,c_0_30]),c_0_30]) ).
cnf(c_0_37,plain,
nand(X1,nand(X2,nand(X1,nand(X3,X2)))) = nand(X1,nand(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_34]),c_0_34]) ).
cnf(c_0_38,plain,
nand(nand(X1,X2),nand(X2,nand(X1,X3))) = X2,
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_39,plain,
nand(X1,nand(X2,nand(X2,X1))) = nand(X1,X1),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,plain,
nand(X1,nand(X2,X2)) = nand(X1,nand(X1,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_39]) ).
cnf(c_0_41,plain,
nand(nand(X1,X1),X2) = nand(X2,nand(X2,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_42,plain,
nand(nand(X1,X1),X2) = nand(X2,nand(X1,X2)),
inference(spm,[status(thm)],[c_0_41,c_0_34]) ).
cnf(c_0_43,plain,
nand(nand(X1,X1),nand(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_30]) ).
cnf(c_0_44,plain,
nand(nand(X1,X1),nand(X2,nand(nand(X1,X2),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_28]),c_0_8]) ).
cnf(c_0_45,plain,
nand(nand(X1,X2),nand(X2,X2)) = X2,
inference(rw,[status(thm)],[c_0_10,c_0_30]) ).
cnf(c_0_46,plain,
nand(nand(X1,nand(nand(nand(X2,X2),X1),X1)),X2) = nand(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_8]),c_0_8]) ).
cnf(c_0_47,plain,
nand(nand(nand(X1,X2),X3),nand(X3,nand(nand(X1,X1),X2))) = X3,
inference(spm,[status(thm)],[c_0_36,c_0_42]) ).
cnf(c_0_48,plain,
nand(X1,nand(nand(X1,X2),nand(X3,nand(X1,X1)))) = nand(X1,X2),
inference(spm,[status(thm)],[c_0_36,c_0_43]) ).
cnf(c_0_49,plain,
nand(nand(X1,X1),nand(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_30]) ).
cnf(c_0_50,plain,
nand(X1,nand(nand(nand(X1,X1),X2),nand(X3,X1))) = nand(X3,X1),
inference(spm,[status(thm)],[c_0_35,c_0_45]) ).
cnf(c_0_51,plain,
nand(X1,nand(nand(X2,X3),nand(X3,X1))) = nand(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_36]),c_0_34]) ).
cnf(c_0_52,plain,
nand(nand(X1,X2),nand(nand(X3,X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_53,plain,
nand(X1,nand(nand(nand(X1,X1),X1),X1)) = nand(X1,nand(X1,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_46]) ).
cnf(c_0_54,plain,
nand(nand(nand(X1,X2),X3),nand(X3,nand(nand(X2,X2),X4))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_50]) ).
cnf(c_0_55,plain,
nand(nand(X1,X2),nand(nand(X3,X2),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_49]),c_0_34]) ).
cnf(c_0_56,plain,
nand(nand(nand(X1,X2),X3),nand(X3,nand(X4,nand(X2,X3)))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_34]) ).
cnf(c_0_57,plain,
nand(nand(X1,nand(X1,X1)),X1) = nand(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_53]),c_0_44]) ).
cnf(c_0_58,plain,
nand(X1,nand(nand(X2,X2),nand(nand(X3,X2),X1))) = nand(X1,X1),
inference(spm,[status(thm)],[c_0_37,c_0_54]) ).
cnf(c_0_59,plain,
nand(X1,nand(X2,nand(nand(X2,X3),X1))) = nand(nand(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_35]),c_0_34]),c_0_34]) ).
cnf(c_0_60,plain,
nand(nand(X1,nand(X2,nand(X3,X1))),nand(nand(X4,X3),X1)) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_56]) ).
cnf(c_0_61,plain,
nand(nand(X1,nand(nand(X2,X1),X1)),nand(X2,nand(X1,nand(nand(X2,X1),X1)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_10]),c_0_9]),c_0_9]) ).
cnf(c_0_62,plain,
nand(nand(nand(X1,X1),X1),nand(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_2]),c_0_8]),c_0_8]) ).
cnf(c_0_63,plain,
nand(X1,nand(nand(X2,nand(X1,X1)),nand(X3,X1))) = nand(X3,X1),
inference(spm,[status(thm)],[c_0_55,c_0_45]) ).
cnf(c_0_64,plain,
nand(X1,nand(X2,nand(nand(X3,nand(X3,X2)),X1))) = nand(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_40]),c_0_11]) ).
cnf(c_0_65,plain,
nand(X1,nand(X2,nand(X1,nand(X2,X3)))) = nand(X1,nand(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_38]),c_0_34]),c_0_34]) ).
cnf(c_0_66,plain,
nand(X1,nand(X2,nand(X1,nand(X3,nand(X2,X1))))) = nand(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_34]),c_0_34]) ).
cnf(c_0_67,plain,
nand(nand(nand(X1,X2),X3),nand(X3,nand(X1,nand(X2,X2)))) = X3,
inference(spm,[status(thm)],[c_0_36,c_0_40]) ).
cnf(c_0_68,plain,
nand(nand(X1,X1),X1) = nand(X1,nand(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_9]),c_0_9]),c_0_53]) ).
cnf(c_0_69,plain,
nand(X1,nand(X2,nand(X2,nand(X3,nand(X1,X1))))) = nand(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_34]) ).
cnf(c_0_70,plain,
nand(nand(X1,nand(X2,X3)),nand(X1,nand(X4,nand(X2,X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_38]),c_0_34]) ).
cnf(c_0_71,plain,
nand(X1,nand(X2,nand(X3,nand(X1,X2)))) = nand(X1,nand(X2,X2)),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,plain,
nand(X1,X1) = nand(nand(X2,nand(X2,X2)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_67]),c_0_68]),c_0_55]),c_0_68]) ).
cnf(c_0_73,plain,
nand(X1,nand(X1,nand(X1,X2))) = nand(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_74,plain,
nand(nand(X1,X2),nand(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_75,plain,
nand(nand(X1,X2),nand(X1,nand(X3,X2))) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_76,plain,
nand(nand(X1,X1),nand(X2,nand(X2,nand(X3,X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_39]) ).
cnf(c_0_77,plain,
nand(X1,nand(X2,nand(X3,nand(X2,X1)))) = nand(X1,nand(X2,X2)),
inference(spm,[status(thm)],[c_0_71,c_0_34]) ).
cnf(c_0_78,plain,
nand(X1,nand(X2,nand(X2,X2))) = nand(X1,X1),
inference(spm,[status(thm)],[c_0_34,c_0_72]) ).
cnf(c_0_79,plain,
nand(nand(nand(X1,nand(X1,X2)),X3),nand(X3,nand(X2,X4))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_40]),c_0_11]) ).
cnf(c_0_80,plain,
nand(X1,nand(X2,X2)) = nand(X1,nand(X2,X1)),
inference(spm,[status(thm)],[c_0_40,c_0_34]) ).
cnf(c_0_81,plain,
nand(X1,nand(X1,nand(X2,X2))) = nand(X1,X2),
inference(spm,[status(thm)],[c_0_73,c_0_40]) ).
cnf(c_0_82,plain,
nand(X1,nand(X2,X2)) = nand(X1,nand(nand(X3,nand(X3,X1)),X2)),
inference(spm,[status(thm)],[c_0_37,c_0_64]) ).
cnf(c_0_83,plain,
nand(X1,nand(nand(X2,X1),nand(nand(X1,X1),X3))) = nand(X2,X1),
inference(spm,[status(thm)],[c_0_38,c_0_49]) ).
cnf(c_0_84,plain,
nand(X1,nand(nand(X2,nand(X1,X1)),nand(X1,X3))) = nand(X1,X3),
inference(spm,[status(thm)],[c_0_55,c_0_74]) ).
cnf(c_0_85,plain,
nand(nand(X1,X2),nand(X1,nand(X3,nand(X3,nand(X4,X2))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_34]) ).
cnf(c_0_86,plain,
nand(X1,nand(X2,nand(nand(X2,X1),X3))) = nand(X1,nand(X2,X2)),
inference(spm,[status(thm)],[c_0_77,c_0_34]) ).
cnf(c_0_87,plain,
nand(X1,nand(X2,nand(X3,nand(X3,X3)))) = nand(X1,nand(X1,X2)),
inference(spm,[status(thm)],[c_0_40,c_0_78]) ).
cnf(c_0_88,plain,
nand(nand(nand(X1,X2),X3),nand(X3,nand(nand(X2,X1),X4))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_89,plain,
nand(nand(X1,nand(X2,X3)),nand(X1,nand(nand(X2,X2),X3))) = X1,
inference(spm,[status(thm)],[c_0_75,c_0_42]) ).
cnf(c_0_90,plain,
nand(X1,nand(nand(X2,X1),nand(X3,nand(X1,X1)))) = nand(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_30]),c_0_30]) ).
cnf(c_0_91,plain,
nand(X1,nand(nand(X2,nand(X2,X1)),X3)) = nand(X1,nand(X1,X3)),
inference(spm,[status(thm)],[c_0_40,c_0_82]) ).
cnf(c_0_92,plain,
nand(X1,nand(nand(X2,X2),nand(X1,nand(X3,X2)))) = nand(X1,X1),
inference(spm,[status(thm)],[c_0_58,c_0_34]) ).
cnf(c_0_93,plain,
nand(nand(nand(X1,X2),X3),nand(X3,nand(X4,nand(X1,X1)))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_83]),c_0_49]),c_0_84]) ).
cnf(c_0_94,plain,
nand(nand(X1,nand(X2,nand(X2,X2))),X3) = nand(X3,nand(X3,X1)),
inference(spm,[status(thm)],[c_0_41,c_0_78]) ).
cnf(c_0_95,plain,
nand(nand(X1,nand(X2,X3)),nand(X1,nand(nand(X3,X2),X4))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_81]),c_0_34]) ).
cnf(c_0_96,plain,
nand(X1,nand(X1,nand(nand(X2,X3),nand(X3,X2)))) = nand(X1,nand(X3,X2)),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_97,plain,
nand(nand(X1,nand(X2,X3)),nand(X1,nand(X4,nand(X3,X3)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_11]),c_0_63]) ).
cnf(c_0_98,plain,
nand(X1,nand(nand(nand(X1,X1),X2),X3)) = nand(X1,nand(X1,X3)),
inference(spm,[status(thm)],[c_0_91,c_0_41]) ).
cnf(c_0_99,plain,
nand(X1,nand(X1,nand(X2,nand(X2,nand(X3,X1))))) = nand(X2,nand(X2,nand(X3,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_76]),c_0_34]) ).
cnf(c_0_100,plain,
nand(nand(X1,nand(X2,X3)),nand(X1,nand(X4,nand(X3,X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_36]),c_0_34]) ).
cnf(c_0_101,plain,
nand(X1,nand(nand(X1,nand(X2,X3)),nand(X3,X3))) = nand(X1,X1),
inference(spm,[status(thm)],[c_0_92,c_0_34]) ).
cnf(c_0_102,plain,
nand(nand(X1,nand(X2,nand(X3,X3))),nand(nand(X3,X4),X1)) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_93]) ).
cnf(c_0_103,plain,
nand(X1,nand(nand(X2,X3),nand(X1,X2))) = nand(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_35]),c_0_34]) ).
cnf(c_0_104,plain,
nand(X1,nand(X2,X3)) = nand(nand(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]) ).
cnf(c_0_105,plain,
nand(nand(X1,nand(X2,nand(X3,X3))),nand(X1,nand(X4,X3))) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_97]) ).
cnf(c_0_106,negated_conjecture,
( nand(nand(a,a),nand(b,a)) != a
| nand(a,nand(b,nand(a,c))) != nand(nand(nand(c,b),b),a) ),
prove_meredith_2_basis ).
cnf(c_0_107,plain,
nand(X1,nand(nand(X2,nand(X2,nand(X3,nand(X1,X1)))),X4)) = nand(X1,nand(X1,X4)),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_108,plain,
nand(nand(X1,nand(X2,nand(X3,X1))),nand(X1,nand(X4,X3))) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_100]) ).
cnf(c_0_109,plain,
nand(nand(X1,X1),nand(X2,X2)) = nand(nand(X2,nand(X3,X1)),nand(X1,X1)),
inference(spm,[status(thm)],[c_0_59,c_0_101]) ).
cnf(c_0_110,plain,
nand(nand(X1,X1),nand(nand(X1,X1),nand(nand(X1,X2),X3))) = nand(nand(X1,X1),X3),
inference(spm,[status(thm)],[c_0_91,c_0_102]) ).
cnf(c_0_111,plain,
nand(nand(X1,X2),nand(nand(X3,X4),nand(X3,nand(X2,X1)))) = nand(X3,nand(X2,X1)),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_112,plain,
nand(nand(X1,X1),nand(nand(X1,X1),nand(X2,nand(X3,X1)))) = nand(nand(X1,X1),X2),
inference(spm,[status(thm)],[c_0_91,c_0_105]) ).
cnf(c_0_113,negated_conjecture,
nand(nand(nand(c,b),b),a) != nand(a,nand(b,nand(a,c))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_49])]) ).
cnf(c_0_114,plain,
nand(X1,nand(nand(X2,nand(X2,nand(X3,nand(X1,X2)))),X4)) = nand(X1,nand(X1,X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_34]) ).
cnf(c_0_115,plain,
nand(nand(X1,X1),nand(X2,X2)) = nand(nand(X1,nand(X3,X2)),nand(X2,X2)),
inference(spm,[status(thm)],[c_0_34,c_0_109]) ).
cnf(c_0_116,plain,
nand(nand(X1,X1),nand(nand(X2,X3),nand(X2,nand(X4,X1)))) = nand(nand(X1,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112]) ).
cnf(c_0_117,negated_conjecture,
nand(nand(b,nand(c,b)),a) != nand(a,nand(b,nand(a,c))),
inference(rw,[status(thm)],[c_0_113,c_0_32]) ).
cnf(c_0_118,plain,
nand(X1,nand(nand(X2,X2),X3)) = nand(X1,nand(X3,nand(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]),c_0_81]) ).
cnf(c_0_119,negated_conjecture,
nand(a,nand(b,nand(b,c))) != nand(a,nand(b,nand(a,c))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_34]),c_0_34]) ).
cnf(c_0_120,plain,
nand(X1,nand(X2,nand(X2,X3))) = nand(X1,nand(X2,nand(X1,X3))),
inference(spm,[status(thm)],[c_0_118,c_0_41]) ).
cnf(c_0_121,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_120])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO039-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sun Aug 27 08:11:10 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.52 start to proof: theBenchmark
% 25.43/25.47 % Version : CSE_E---1.5
% 25.43/25.47 % Problem : theBenchmark.p
% 25.43/25.47 % Proof found
% 25.43/25.47 % SZS status Theorem for theBenchmark.p
% 25.43/25.47 % SZS output start Proof
% See solution above
% 25.43/25.48 % Total time : 24.945000 s
% 25.43/25.48 % SZS output end Proof
% 25.43/25.48 % Total time : 24.949000 s
%------------------------------------------------------------------------------