TSTP Solution File: GRP683+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP683+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n021.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 00:23:03 EDT 2023
% Result : Theorem 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 14
% Syntax : Number of formulae : 80 ( 68 unt; 6 typ; 0 def)
% Number of atoms : 80 ( 79 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 9 ~; 4 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 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 : 157 ( 0 sgn; 38 !; 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,
esk1_0: $i ).
tff(decl_26,type,
esk2_0: $i ).
tff(decl_27,type,
esk3_0: $i ).
fof(f01,axiom,
! [X1] : ld(X1,mult(X1,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f03,axiom,
! [X2,X1] : mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f02,axiom,
! [X1] : rd(mult(X1,X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f04,axiom,
! [X2,X1] : mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f07,axiom,
! [X2,X1] : ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
fof(f06,axiom,
! [X3,X4,X2,X1] : rd(mult(mult(X1,X2),rd(X4,X3)),rd(X4,X3)) = mult(X1,rd(mult(X2,X3),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f05,axiom,
! [X3,X4,X2,X1] : ld(ld(X1,X2),mult(ld(X1,X2),mult(X4,X3))) = mult(ld(X1,mult(X1,X4)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(goals,conjecture,
! [X5,X6,X7] :
( mult(X5,ld(X6,mult(X6,X7))) = mult(X5,X7)
& mult(rd(mult(X5,X6),X6),X7) = mult(X5,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_8,plain,
! [X8] : ld(X8,mult(X8,X8)) = X8,
inference(variable_rename,[status(thm)],[f01]) ).
fof(c_0_9,plain,
! [X10,X11] : mult(X11,ld(X11,X10)) = ld(X11,mult(X11,X10)),
inference(variable_rename,[status(thm)],[f03]) ).
fof(c_0_10,plain,
! [X9] : rd(mult(X9,X9),X9) = X9,
inference(variable_rename,[status(thm)],[f02]) ).
fof(c_0_11,plain,
! [X12,X13] : mult(rd(X13,X12),X12) = rd(mult(X13,X12),X12),
inference(variable_rename,[status(thm)],[f04]) ).
fof(c_0_12,plain,
! [X22,X23] : ld(X23,mult(X23,ld(X22,X22))) = rd(mult(rd(X23,X23),X22),X22),
inference(variable_rename,[status(thm)],[f07]) ).
cnf(c_0_13,plain,
ld(X1,mult(X1,X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,plain,
! [X18,X19,X20,X21] : rd(mult(mult(X21,X20),rd(X19,X18)),rd(X19,X18)) = mult(X21,rd(mult(X20,X18),X18)),
inference(variable_rename,[status(thm)],[f06]) ).
cnf(c_0_16,plain,
rd(mult(X1,X1),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
mult(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
mult(rd(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,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_18,c_0_17]),c_0_14]) ).
cnf(c_0_23,plain,
mult(X1,ld(X1,ld(X1,X1))) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_24,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_20,c_0_17]),c_0_17]) ).
cnf(c_0_25,plain,
rd(X1,X1) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_21]),c_0_22]),c_0_23]) ).
cnf(c_0_26,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_24,c_0_25]) ).
cnf(c_0_27,plain,
mult(rd(ld(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_28,plain,
mult(mult(rd(X1,ld(X2,X2)),ld(X2,X2)),ld(X2,X2)) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_17]),c_0_27]),c_0_23]) ).
cnf(c_0_29,plain,
mult(rd(X1,ld(X1,X1)),ld(X1,X1)) = rd(X1,ld(X1,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_30,plain,
rd(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_29]),c_0_19]) ).
fof(c_0_31,plain,
! [X14,X15,X16,X17] : ld(ld(X17,X16),mult(ld(X17,X16),mult(X15,X14))) = mult(ld(X17,mult(X17,X15)),X14),
inference(variable_rename,[status(thm)],[f05]) ).
cnf(c_0_32,plain,
mult(X1,mult(rd(X2,ld(X3,X3)),ld(X3,X3))) = mult(rd(mult(X1,X2),X3),X3),
inference(spm,[status(thm)],[c_0_24,c_0_30]) ).
cnf(c_0_33,plain,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_34,plain,
mult(ld(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_21,c_0_25]) ).
cnf(c_0_35,plain,
mult(mult(rd(X1,X2),X2),X2) = mult(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_30]),c_0_19]),c_0_17]) ).
cnf(c_0_36,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_33,c_0_14]),c_0_14]) ).
cnf(c_0_37,plain,
mult(rd(mult(X1,ld(X2,X2)),X2),X2) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_34]) ).
cnf(c_0_38,plain,
mult(mult(X1,ld(X1,ld(X2,X2))),X2) = mult(ld(X1,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_22]),c_0_25]) ).
cnf(c_0_39,plain,
mult(ld(X1,X1),ld(ld(X1,X1),X1)) = ld(ld(X1,X1),X1),
inference(spm,[status(thm)],[c_0_14,c_0_34]) ).
cnf(c_0_40,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_36,c_0_19]) ).
cnf(c_0_41,plain,
mult(X1,ld(ld(X2,X2),ld(X2,X2))) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_37]),c_0_27]),c_0_19]) ).
cnf(c_0_42,plain,
mult(ld(ld(X1,X1),ld(X1,X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_19]),c_0_34]) ).
cnf(c_0_43,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(ld(X1,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_34]),c_0_38]) ).
cnf(c_0_44,plain,
ld(ld(X1,X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_19]),c_0_19]) ).
cnf(c_0_45,plain,
ld(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_41]),c_0_42]) ).
cnf(c_0_46,plain,
mult(ld(X1,X1),X2) = mult(X1,ld(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_47,plain,
mult(rd(mult(X1,X2),X3),X3) = mult(X1,mult(rd(X2,X3),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_45]),c_0_26]),c_0_32]) ).
cnf(c_0_48,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_43]),c_0_46]) ).
cnf(c_0_49,plain,
mult(X1,mult(X1,ld(X1,ld(X2,X2)))) = mult(rd(X1,X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_19]),c_0_27]) ).
cnf(c_0_50,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_19]),c_0_14]) ).
cnf(c_0_51,plain,
mult(rd(X1,X2),X2) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_52,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[c_0_43,c_0_46]) ).
cnf(c_0_53,plain,
mult(mult(X1,X2),ld(X3,X3)) = mult(X1,mult(X2,ld(X3,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_51]),c_0_51]) ).
cnf(c_0_54,plain,
mult(X1,ld(X1,ld(X1,X2))) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_52]) ).
cnf(c_0_55,plain,
mult(X1,ld(X1,mult(X2,ld(X3,X3)))) = mult(X1,mult(ld(X1,X2),ld(X3,X3))),
inference(spm,[status(thm)],[c_0_48,c_0_53]) ).
cnf(c_0_56,plain,
mult(X1,ld(X1,mult(ld(X1,X2),X3))) = mult(ld(X1,X2),X3),
inference(spm,[status(thm)],[c_0_48,c_0_54]) ).
cnf(c_0_57,plain,
ld(X1,mult(X2,ld(X3,X3))) = mult(ld(X1,X2),ld(X3,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_55]),c_0_14]),c_0_56]),c_0_54]) ).
cnf(c_0_58,plain,
mult(ld(X1,X2),ld(X2,X2)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_57,c_0_19]) ).
cnf(c_0_59,plain,
ld(ld(X1,X2),ld(X1,X2)) = mult(X1,ld(X1,ld(X2,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_58]),c_0_52]) ).
fof(c_0_60,negated_conjecture,
~ ! [X5,X6,X7] :
( mult(X5,ld(X6,mult(X6,X7))) = mult(X5,X7)
& mult(rd(mult(X5,X6),X6),X7) = mult(X5,X7) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_61,plain,
mult(X1,ld(X1,mult(X2,ld(X2,X3)))) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_59]),c_0_48]),c_0_46]),c_0_43]),c_0_46]) ).
fof(c_0_62,negated_conjecture,
( mult(esk1_0,ld(esk2_0,mult(esk2_0,esk3_0))) != mult(esk1_0,esk3_0)
| mult(rd(mult(esk1_0,esk2_0),esk2_0),esk3_0) != mult(esk1_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])]) ).
cnf(c_0_63,plain,
ld(X1,mult(X2,ld(X2,X3))) = ld(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_61]),c_0_14]),c_0_54]),c_0_54]) ).
cnf(c_0_64,negated_conjecture,
( mult(esk1_0,ld(esk2_0,mult(esk2_0,esk3_0))) != mult(esk1_0,esk3_0)
| mult(rd(mult(esk1_0,esk2_0),esk2_0),esk3_0) != mult(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_65,plain,
mult(mult(X1,mult(rd(X2,X3),X3)),X3) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_35,c_0_47]) ).
cnf(c_0_66,plain,
mult(X1,mult(X2,ld(X2,X3))) = mult(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_63]),c_0_50]) ).
cnf(c_0_67,negated_conjecture,
( mult(esk1_0,mult(esk2_0,ld(esk2_0,esk3_0))) != mult(esk1_0,esk3_0)
| mult(mult(rd(esk1_0,esk2_0),esk2_0),esk3_0) != mult(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_14]),c_0_17]) ).
cnf(c_0_68,plain,
mult(mult(X1,mult(X2,ld(X3,X3))),X3) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_65,c_0_51]) ).
cnf(c_0_69,plain,
mult(rd(X1,X2),mult(X2,ld(X3,X3))) = mult(X1,ld(X3,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_51]),c_0_53]),c_0_46]),c_0_66]) ).
cnf(c_0_70,plain,
mult(mult(X1,ld(X2,X2)),X2) = mult(X1,X2),
inference(rw,[status(thm)],[c_0_35,c_0_51]) ).
cnf(c_0_71,negated_conjecture,
( mult(esk1_0,mult(esk2_0,ld(esk2_0,esk3_0))) != mult(esk1_0,esk3_0)
| mult(mult(esk1_0,ld(esk2_0,esk2_0)),esk3_0) != mult(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[c_0_67,c_0_51]) ).
cnf(c_0_72,plain,
mult(mult(X1,ld(X2,X2)),X3) = mult(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_51]) ).
cnf(c_0_73,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_66])]),c_0_72])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP683+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 20:20:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.61 % Version : CSE_E---1.5
% 0.20/0.61 % Problem : theBenchmark.p
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark.p
% 0.20/0.61 % SZS output start Proof
% See solution above
% 0.20/0.61 % Total time : 0.021000 s
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61 % Total time : 0.023000 s
%------------------------------------------------------------------------------