TSTP Solution File: GRP682-11 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP682-11 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n019.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 : Thu Aug 31 00:23:02 EDT 2023
% Result : Unsatisfiable 0.19s 0.60s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 67 unt; 6 typ; 0 def)
% Number of atoms : 67 ( 66 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 143 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
mult: ( $i * $i ) > $i ).
tff(decl_23,type,
ld: ( $i * $i ) > $i ).
tff(decl_24,type,
rd: ( $i * $i ) > $i ).
tff(decl_25,type,
x0: $i ).
tff(decl_26,type,
x1: $i ).
tff(decl_27,type,
x2: $i ).
cnf(f01,axiom,
ld(X1,mult(X1,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
cnf(f03,axiom,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
cnf(f02,axiom,
rd(mult(X1,X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
cnf(f04,axiom,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
cnf(f07,axiom,
ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
cnf(f05,axiom,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
cnf(f06,axiom,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
cnf(goal,negated_conjecture,
ld(rd(x0,x1),mult(rd(x0,x1),x2)) != ld(x0,mult(x0,x2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c_0_8,axiom,
ld(X1,mult(X1,X1)) = X1,
f01 ).
cnf(c_0_9,axiom,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
f03 ).
cnf(c_0_10,axiom,
rd(mult(X1,X1),X1) = X1,
f02 ).
cnf(c_0_11,axiom,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
f04 ).
cnf(c_0_12,axiom,
ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
f07 ).
cnf(c_0_13,plain,
mult(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
mult(rd(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
mult(rd(rd(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_11]),c_0_9]) ).
cnf(c_0_16,plain,
mult(X1,ld(X1,ld(X1,X1))) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_17,axiom,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
f05 ).
cnf(c_0_18,plain,
rd(X1,X1) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_14]),c_0_15]),c_0_16]) ).
cnf(c_0_19,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_9]),c_0_9]) ).
cnf(c_0_20,plain,
mult(ld(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_21,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(mult(X1,ld(X1,X3)),ld(X3,X3)),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_22,plain,
mult(ld(X1,X1),ld(ld(X1,X1),X1)) = ld(ld(X1,X1),X1),
inference(spm,[status(thm)],[c_0_9,c_0_20]) ).
cnf(c_0_23,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_13]),c_0_13]) ).
cnf(c_0_24,plain,
mult(rd(ld(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_25,plain,
ld(ld(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
mult(ld(X1,X2),ld(ld(X1,X2),ld(X1,X1))) = ld(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_16]),c_0_13]) ).
cnf(c_0_27,plain,
mult(X1,ld(X1,ld(ld(X1,X1),ld(X1,X1)))) = ld(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_18]),c_0_20]) ).
cnf(c_0_28,plain,
mult(mult(ld(X1,X1),ld(ld(X1,X1),X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_29,plain,
ld(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_25]),c_0_27]) ).
cnf(c_0_30,axiom,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
f06 ).
cnf(c_0_31,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_28]),c_0_19]) ).
cnf(c_0_32,plain,
mult(rd(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,mult(rd(X2,X4),X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_11]),c_0_11]) ).
cnf(c_0_33,plain,
rd(mult(X1,ld(X1,mult(X2,X3))),X3) = mult(rd(mult(X1,ld(X1,X2)),X3),X3),
inference(spm,[status(thm)],[c_0_11,c_0_31]) ).
cnf(c_0_34,plain,
mult(rd(mult(X1,X2),ld(X3,X3)),ld(X3,X3)) = mult(X1,mult(rd(X2,X3),X3)),
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_35,plain,
mult(mult(X1,ld(X1,X2)),ld(mult(X1,ld(X1,X2)),X1)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_9]) ).
cnf(c_0_36,plain,
rd(mult(X1,ld(X1,X2)),ld(X2,X2)) = mult(X1,mult(rd(ld(X1,X2),X2),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_13]),c_0_34]) ).
cnf(c_0_37,plain,
mult(X1,ld(X1,ld(X1,X2))) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_38,plain,
mult(rd(X1,ld(X1,X1)),ld(X1,X1)) = rd(X1,ld(X1,X1)),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_39,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_25]),c_0_20]),c_0_9]) ).
cnf(c_0_40,plain,
mult(X1,mult(rd(X2,ld(X3,X3)),ld(X3,X3))) = mult(X1,mult(rd(X2,X3),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_29]),c_0_34]) ).
cnf(c_0_41,plain,
rd(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_36]),c_0_24]),c_0_37]),c_0_13]),c_0_38]) ).
cnf(c_0_42,plain,
mult(X1,ld(X1,mult(mult(X1,X2),X3))) = mult(mult(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_9]),c_0_39]) ).
cnf(c_0_43,plain,
mult(X1,ld(X1,mult(X2,ld(mult(X1,ld(X1,X2)),X1)))) = X1,
inference(rw,[status(thm)],[c_0_35,c_0_31]) ).
cnf(c_0_44,plain,
mult(X1,mult(rd(mult(X2,X3),X4),X4)) = mult(X1,mult(X2,mult(rd(X3,X4),X4))),
inference(spm,[status(thm)],[c_0_40,c_0_34]) ).
cnf(c_0_45,plain,
mult(X1,mult(rd(X2,mult(X1,X2)),mult(X1,X2))) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_41]),c_0_13]) ).
cnf(c_0_46,plain,
mult(mult(X1,X2),ld(mult(X1,X2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_9]),c_0_39]) ).
cnf(c_0_47,plain,
mult(X1,mult(rd(X2,X3),X3)) = mult(X1,mult(X2,ld(X3,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_13]),c_0_24]),c_0_39]) ).
cnf(c_0_48,plain,
mult(mult(X1,X2),mult(rd(ld(mult(X1,X2),X1),X1),X1)) = X1,
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,plain,
mult(rd(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,mult(X2,ld(X4,X4))),
inference(rw,[status(thm)],[c_0_32,c_0_47]) ).
cnf(c_0_50,plain,
mult(mult(X1,X2),mult(ld(mult(X1,X2),X1),ld(X1,X1))) = X1,
inference(rw,[status(thm)],[c_0_48,c_0_47]) ).
cnf(c_0_51,plain,
mult(X1,ld(X1,mult(ld(X1,X2),X3))) = mult(ld(X1,X2),X3),
inference(spm,[status(thm)],[c_0_31,c_0_37]) ).
cnf(c_0_52,plain,
mult(X1,ld(X1,ld(mult(X1,X2),X3))) = ld(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_42,c_0_37]) ).
cnf(c_0_53,plain,
mult(rd(mult(X1,X2),X3),X3) = mult(X1,mult(X2,ld(X3,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_41]),c_0_29]) ).
cnf(c_0_54,plain,
mult(ld(mult(X1,X2),X1),ld(X1,X1)) = ld(mult(X1,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_50]),c_0_51]) ).
cnf(c_0_55,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_31]),c_0_13]) ).
cnf(c_0_56,plain,
mult(mult(X1,X2),ld(mult(X1,X2),ld(X1,X3))) = ld(X1,X3),
inference(spm,[status(thm)],[c_0_52,c_0_46]) ).
cnf(c_0_57,plain,
mult(mult(rd(X1,X2),X2),X2) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_11]),c_0_13]) ).
cnf(c_0_58,plain,
ld(ld(mult(X1,X2),X1),ld(mult(X1,X2),X1)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_54]),c_0_55]),c_0_56]) ).
cnf(c_0_59,plain,
rd(mult(X1,ld(X1,mult(X2,X3))),X3) = mult(X1,mult(ld(X1,X2),ld(X3,X3))),
inference(rw,[status(thm)],[c_0_33,c_0_53]) ).
cnf(c_0_60,plain,
mult(ld(X1,X1),X2) = mult(X1,ld(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_15]),c_0_31]),c_0_20]),c_0_18]) ).
cnf(c_0_61,negated_conjecture,
ld(rd(x0,x1),mult(rd(x0,x1),x2)) != ld(x0,mult(x0,x2)),
goal ).
cnf(c_0_62,plain,
mult(mult(X1,X2),ld(mult(X1,X2),X3)) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_58]),c_0_55]),c_0_55]) ).
cnf(c_0_63,plain,
mult(rd(X1,X2),X2) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_9]),c_0_39]),c_0_11]),c_0_60]),c_0_39]) ).
cnf(c_0_64,negated_conjecture,
mult(rd(x0,x1),ld(rd(x0,x1),x2)) != mult(x0,ld(x0,x2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_9]),c_0_9]) ).
cnf(c_0_65,plain,
mult(rd(X1,X2),ld(rd(X1,X2),X3)) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_62]) ).
cnf(c_0_66,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP682-11 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n019.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 : Tue Aug 29 01:15:42 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.60 % Version : CSE_E---1.5
% 0.19/0.60 % Problem : theBenchmark.p
% 0.19/0.60 % Proof found
% 0.19/0.60 % SZS status Theorem for theBenchmark.p
% 0.19/0.60 % SZS output start Proof
% See solution above
% 0.19/0.60 % Total time : 0.036000 s
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60 % Total time : 0.038000 s
%------------------------------------------------------------------------------