TSTP Solution File: RNG006-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG006-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 13:48:23 EDT 2023
% Result : Unsatisfiable 0.79s 0.89s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 28
% Syntax : Number of formulae : 69 ( 32 unt; 13 typ; 0 def)
% Number of atoms : 101 ( 12 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 92 ( 47 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 5 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
additive_identity: $i ).
tff(decl_23,type,
sum: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
multiply: ( $i * $i ) > $i ).
tff(decl_25,type,
product: ( $i * $i * $i ) > $o ).
tff(decl_26,type,
add: ( $i * $i ) > $i ).
tff(decl_27,type,
additive_inverse: $i > $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
c: $i ).
tff(decl_30,type,
bS_Ic: $i ).
tff(decl_31,type,
a: $i ).
tff(decl_32,type,
aPb: $i ).
tff(decl_33,type,
aPc: $i ).
tff(decl_34,type,
aPb_S_IaPc: $i ).
cnf(associativity_of_addition1,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition1) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(associativity_of_addition2,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
cnf(aPb_plus_IaPc,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aPb_plus_IaPc) ).
cnf(b_plus_inverse_c,hypothesis,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_inverse_c) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
cnf(distributivity1,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity1) ).
cnf(a_times_b,hypothesis,
product(a,b,aPb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
cnf(a_times_c,hypothesis,
product(a,c,aPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(prove_a_times_bS_Ic_is_aPb_S__IaPc,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
cnf(c_0_15,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1 ).
cnf(c_0_16,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_17,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_19,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_20,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_21,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_22,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2 ).
cnf(c_0_23,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
aPb_plus_IaPc ).
cnf(c_0_24,plain,
( sum(X1,X2,X3)
| ~ sum(additive_inverse(X1),X3,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_26,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,hypothesis,
sum(b,additive_inverse(c),bS_Ic),
b_plus_inverse_c ).
cnf(c_0_28,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_29,hypothesis,
( sum(X1,additive_inverse(aPc),X2)
| ~ sum(X3,aPb_S_IaPc,X2)
| ~ sum(X3,aPb,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_31,plain,
sum(X1,additive_identity,additive_inverse(additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
cnf(c_0_32,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
distributivity1 ).
cnf(c_0_34,hypothesis,
product(a,b,aPb),
a_times_b ).
cnf(c_0_35,hypothesis,
sum(additive_inverse(c),b,bS_Ic),
inference(spm,[status(thm)],[c_0_20,c_0_27]) ).
cnf(c_0_36,plain,
sum(X1,add(additive_inverse(X1),X2),X2),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_37,plain,
( X1 = additive_identity
| ~ sum(additive_inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_38,hypothesis,
( sum(X1,additive_inverse(aPc),add(X2,aPb_S_IaPc))
| ~ sum(X2,aPb,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_39,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_40,hypothesis,
( sum(X1,X2,aPb)
| ~ product(a,X3,X2)
| ~ product(a,X4,X1)
| ~ sum(X4,X3,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,hypothesis,
product(a,c,aPc),
a_times_c ).
cnf(c_0_42,hypothesis,
sum(c,bS_Ic,b),
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_43,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_30,c_0_36]) ).
cnf(c_0_44,hypothesis,
( add(X1,aPb_S_IaPc) = additive_identity
| ~ sum(X1,aPb,aPc) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_45,hypothesis,
( sum(X1,aPc,aPb)
| ~ product(a,X2,X1)
| ~ sum(X2,c,b) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,hypothesis,
sum(bS_Ic,c,b),
inference(spm,[status(thm)],[c_0_20,c_0_42]) ).
cnf(c_0_47,hypothesis,
( X1 = aPb_S_IaPc
| ~ sum(additive_inverse(X1),aPb,aPc) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_32]) ).
cnf(c_0_48,plain,
( sum(additive_inverse(X1),X2,X3)
| ~ sum(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_28]) ).
cnf(c_0_49,hypothesis,
( sum(X1,aPc,aPb)
| ~ product(a,bS_Ic,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_51,hypothesis,
( X1 = aPb_S_IaPc
| ~ sum(X1,aPc,aPb) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,hypothesis,
sum(multiply(a,bS_Ic),aPc,aPb),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,hypothesis,
multiply(a,bS_Ic) = aPb_S_IaPc,
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_54,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
prove_a_times_bS_Ic_is_aPb_S__IaPc ).
cnf(c_0_55,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_53]),c_0_54]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG006-3 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n011.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 02:52:54 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.79/0.89 % Version : CSE_E---1.5
% 0.79/0.89 % Problem : theBenchmark.p
% 0.79/0.89 % Proof found
% 0.79/0.89 % SZS status Theorem for theBenchmark.p
% 0.79/0.89 % SZS output start Proof
% See solution above
% 0.79/0.90 % Total time : 0.293000 s
% 0.79/0.90 % SZS output end Proof
% 0.79/0.90 % Total time : 0.296000 s
%------------------------------------------------------------------------------