TSTP Solution File: GRP705-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP705-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/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 00:23:16 EDT 2023
% Result : Unsatisfiable 0.93s 1.03s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 17
% Syntax : Number of formulae : 81 ( 74 unt; 7 typ; 0 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 9 ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ld: ( $i * $i ) > $i ).
tff(decl_23,type,
mult: ( $i * $i ) > $i ).
tff(decl_24,type,
rd: ( $i * $i ) > $i ).
tff(decl_25,type,
unit: $i ).
tff(decl_26,type,
op_a: $i ).
tff(decl_27,type,
op_b: $i ).
tff(decl_28,type,
a: $i ).
cnf(c05,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
cnf(c07,axiom,
mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
cnf(c06,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
cnf(c02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
cnf(c09,axiom,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
cnf(c01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
cnf(c04,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
cnf(c08,axiom,
mult(op_a,mult(op_a,mult(op_a,op_a))) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
cnf(c03,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
cnf(goals,negated_conjecture,
mult(op_a,mult(op_b,a)) != mult(mult(op_a,op_b),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_10,axiom,
mult(X1,unit) = X1,
c05 ).
cnf(c_0_11,axiom,
mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
c07 ).
cnf(c_0_12,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_10]) ).
cnf(c_0_13,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
mult(unit,X1) = X1,
c06 ).
cnf(c_0_15,axiom,
ld(X1,mult(X1,X2)) = X2,
c02 ).
cnf(c_0_16,axiom,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = unit,
c09 ).
cnf(c_0_17,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_18,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))) = ld(op_b,unit),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
mult(mult(X1,mult(X1,X2)),X2) = mult(X1,mult(X1,mult(X2,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_17]),c_0_17]) ).
cnf(c_0_20,axiom,
mult(X1,ld(X1,X2)) = X2,
c01 ).
cnf(c_0_21,plain,
mult(op_b,mult(mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(ld(op_b,unit),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))),
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_22,axiom,
rd(mult(X1,X2),X2) = X1,
c04 ).
cnf(c_0_23,plain,
mult(op_b,mult(ld(op_b,unit),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_20]),c_0_14]),c_0_21]) ).
cnf(c_0_24,plain,
rd(mult(X1,mult(X2,mult(X2,X3))),X3) = mult(X1,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_25,plain,
mult(ld(op_b,unit),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_23]),c_0_15]) ).
cnf(c_0_26,plain,
ld(mult(X1,X2),mult(X1,mult(X2,X2))) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_27,plain,
rd(mult(X1,mult(X2,X2)),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_12]) ).
cnf(c_0_28,plain,
mult(ld(op_b,unit),mult(op_b,op_b)) = op_b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_22]) ).
cnf(c_0_29,plain,
rd(X1,X1) = unit,
inference(spm,[status(thm)],[c_0_22,c_0_14]) ).
cnf(c_0_30,plain,
ld(mult(X1,mult(X2,mult(X2,X3))),mult(X1,mult(X2,mult(X2,mult(X3,X3))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_13]),c_0_13]) ).
cnf(c_0_31,plain,
mult(ld(op_b,unit),op_b) = unit,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_32,plain,
mult(mult(X1,mult(X1,mult(X2,X2))),X3) = mult(X1,mult(X1,mult(X2,mult(X2,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_17]),c_0_17]) ).
cnf(c_0_33,axiom,
mult(op_a,mult(op_a,mult(op_a,op_a))) = unit,
c08 ).
cnf(c_0_34,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_35,plain,
ld(mult(X1,ld(op_b,unit)),X1) = op_b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_31]),c_0_10]),c_0_31]),c_0_10]) ).
cnf(c_0_36,plain,
mult(mult(X1,mult(X2,mult(X2,X3))),X3) = mult(X1,mult(X2,mult(X2,mult(X3,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
cnf(c_0_37,plain,
mult(op_a,mult(op_a,mult(op_a,mult(op_a,X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_14]) ).
cnf(c_0_38,plain,
mult(X1,mult(ld(X1,X2),ld(X1,X2))) = mult(X2,ld(X1,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_39,plain,
mult(X1,ld(op_b,unit)) = rd(X1,op_b),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
rd(unit,op_b) = ld(op_b,unit),
inference(spm,[status(thm)],[c_0_22,c_0_31]) ).
cnf(c_0_41,plain,
mult(op_a,mult(op_a,mult(op_a,mult(mult(op_a,X1),mult(op_a,X1))))) = mult(X1,mult(op_a,X1)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
ld(mult(X1,mult(X2,X2)),mult(X1,mult(X2,mult(X2,X3)))) = X3,
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_43,plain,
ld(mult(X1,X1),mult(X1,mult(X1,X2))) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_44,plain,
mult(op_b,rd(ld(op_b,unit),op_b)) = ld(op_b,unit),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_39]),c_0_40]) ).
cnf(c_0_45,plain,
mult(X1,mult(X2,mult(X2,ld(mult(X1,mult(X2,X2)),X3)))) = X3,
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_46,plain,
mult(mult(op_a,X1),mult(op_a,X1)) = mult(op_a,mult(X1,mult(op_a,X1))),
inference(spm,[status(thm)],[c_0_37,c_0_41]) ).
cnf(c_0_47,plain,
ld(mult(op_a,mult(op_a,op_a)),X1) = mult(op_a,X1),
inference(spm,[status(thm)],[c_0_42,c_0_37]) ).
cnf(c_0_48,plain,
ld(X1,rd(X1,op_b)) = ld(op_b,unit),
inference(spm,[status(thm)],[c_0_15,c_0_39]) ).
cnf(c_0_49,plain,
rd(ld(op_b,unit),op_b) = ld(mult(op_b,op_b),unit),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_20]) ).
cnf(c_0_50,plain,
mult(ld(op_b,unit),mult(op_b,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_28]),c_0_20]) ).
cnf(c_0_51,axiom,
mult(rd(X1,X2),X2) = X1,
c03 ).
cnf(c_0_52,plain,
mult(mult(op_a,mult(X1,mult(op_a,X1))),X2) = mult(mult(op_a,X1),mult(mult(op_a,X1),X2)),
inference(spm,[status(thm)],[c_0_17,c_0_46]) ).
cnf(c_0_53,plain,
mult(op_a,rd(mult(op_a,mult(op_a,op_a)),op_b)) = ld(op_b,unit),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
rd(rd(X1,op_b),op_b) = mult(X1,ld(mult(op_b,op_b),unit)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_48]),c_0_39]),c_0_49]),c_0_39]) ).
cnf(c_0_55,plain,
mult(ld(op_b,unit),X1) = ld(op_b,X1),
inference(spm,[status(thm)],[c_0_50,c_0_20]) ).
cnf(c_0_56,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_51]) ).
cnf(c_0_57,plain,
ld(op_b,ld(op_b,unit)) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_58,plain,
ld(op_b,ld(op_b,X1)) = mult(ld(mult(op_b,op_b),unit),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_39]),c_0_54]),c_0_13]),c_0_37]),c_0_55]),c_0_55]) ).
cnf(c_0_59,plain,
mult(mult(X1,mult(X2,mult(X2,mult(X3,X3)))),X4) = mult(X1,mult(X2,mult(X2,mult(X3,mult(X3,X4))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_13]),c_0_13]) ).
cnf(c_0_60,plain,
mult(rd(X1,X2),mult(X2,mult(X2,X3))) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_13,c_0_56]) ).
cnf(c_0_61,plain,
rd(mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))) = ld(op_b,unit),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_62,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) = ld(mult(op_b,op_b),unit),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58]),c_0_10]) ).
cnf(c_0_63,plain,
mult(X1,mult(X1,ld(mult(X1,X1),X2))) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_64,plain,
mult(mult(X1,X2),mult(X2,X2)) = mult(X1,mult(X2,mult(X2,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_12]),c_0_13]) ).
cnf(c_0_65,plain,
mult(mult(X1,mult(rd(X2,X3),mult(X2,X3))),X4) = mult(X1,mult(rd(X2,X3),mult(mult(X2,X3),X4))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_56]),c_0_60]) ).
cnf(c_0_66,plain,
rd(mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))),ld(mult(op_b,op_b),unit)) = ld(op_b,unit),
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_67,plain,
mult(mult(X1,mult(X1,mult(X2,mult(X2,mult(X2,X2))))),X3) = mult(X1,mult(X1,mult(X2,mult(X2,mult(X2,mult(X2,X3)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_19]),c_0_17]),c_0_32]) ).
cnf(c_0_68,plain,
mult(X1,ld(mult(X1,X1),X2)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_63]) ).
cnf(c_0_69,plain,
mult(mult(X1,mult(X2,mult(X2,X2))),X3) = mult(mult(X1,X2),mult(X2,mult(X2,X3))),
inference(spm,[status(thm)],[c_0_13,c_0_64]) ).
cnf(c_0_70,plain,
mult(mult(X1,op_b),mult(op_b,mult(op_b,X2))) = mult(X1,mult(op_b,mult(op_b,mult(op_b,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_68]),c_0_20]),c_0_10]),c_0_50]),c_0_69]),c_0_67]),c_0_68]),c_0_20]),c_0_10]),c_0_32]),c_0_55]),c_0_15]) ).
cnf(c_0_71,negated_conjecture,
mult(op_a,mult(op_b,a)) != mult(mult(op_a,op_b),a),
goals ).
cnf(c_0_72,plain,
mult(mult(X1,op_b),X2) = mult(X1,mult(op_b,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_68]),c_0_20]),c_0_20]) ).
cnf(c_0_73,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP705-1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : java -jar /export/starexec/sandbox2/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 : Tue Aug 29 01:58:59 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.93/1.03 % Version : CSE_E---1.5
% 0.93/1.03 % Problem : theBenchmark.p
% 0.93/1.03 % Proof found
% 0.93/1.03 % SZS status Theorem for theBenchmark.p
% 0.93/1.03 % SZS output start Proof
% See solution above
% 0.93/1.04 % Total time : 0.449000 s
% 0.93/1.04 % SZS output end Proof
% 0.93/1.04 % Total time : 0.452000 s
%------------------------------------------------------------------------------