TSTP Solution File: RNG006-10 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG006-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n013.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 28.73s 28.93s
% Output : CNFRefutation 28.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 33
% Syntax : Number of formulae : 87 ( 71 unt; 16 typ; 0 def)
% Number of atoms : 71 ( 70 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 : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 19 ( 7 >; 12 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 130 ( 4 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(decl_24,type,
additive_identity: $i ).
tff(decl_25,type,
sum: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
true: $i ).
tff(decl_27,type,
multiply: ( $i * $i ) > $i ).
tff(decl_28,type,
product: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
add: ( $i * $i ) > $i ).
tff(decl_30,type,
additive_inverse: $i > $i ).
tff(decl_31,type,
b: $i ).
tff(decl_32,type,
c: $i ).
tff(decl_33,type,
bS_Ic: $i ).
tff(decl_34,type,
a: $i ).
tff(decl_35,type,
aPb: $i ).
tff(decl_36,type,
aPc: $i ).
tff(decl_37,type,
aPb_S_IaPc: $i ).
cnf(associativity_of_addition2,axiom,
ifeq(sum(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X1,X6),true,sum(X6,X2,X5),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
cnf(ifeq_axiom_001,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(b_plus_inverse_c,hypothesis,
sum(b,additive_inverse(c),bS_Ic) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_inverse_c) ).
cnf(addition_is_well_defined,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X1,X2,X4),true,X4,X3),X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
cnf(ifeq_axiom,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(commutativity_of_addition,axiom,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(aPb_plus_IaPc,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aPb_plus_IaPc) ).
cnf(distributivity1,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X4,X5),true,ifeq(product(X1,X6,X7),true,ifeq(sum(X6,X4,X2),true,sum(X7,X5,X3),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
cnf(a_times_c,hypothesis,
product(a,c,aPc) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c) ).
cnf(multiplication_is_well_defined,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
cnf(a_times_b,hypothesis,
product(a,b,aPb) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(prove_a_times_bS_Ic_is_aPb_S__IaPc,negated_conjecture,
product(a,bS_Ic,aPb_S_IaPc) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
cnf(c_0_17,axiom,
ifeq(sum(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X1,X6),true,sum(X6,X2,X5),true),true),true) = true,
associativity_of_addition2 ).
cnf(c_0_18,axiom,
sum(X1,additive_identity,X1) = true,
additive_identity2 ).
cnf(c_0_19,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_20,hypothesis,
sum(b,additive_inverse(c),bS_Ic) = true,
b_plus_inverse_c ).
cnf(c_0_21,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X1,X2,X4),true,X4,X3),X3) = X3,
addition_is_well_defined ).
cnf(c_0_22,axiom,
sum(additive_identity,X1,X1) = true,
additive_identity1 ).
cnf(c_0_23,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_24,axiom,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
commutativity_of_addition ).
cnf(c_0_25,axiom,
sum(X1,X2,add(X1,X2)) = true,
closure_of_addition ).
cnf(c_0_26,plain,
ifeq(sum(X1,X2,additive_identity),true,ifeq(sum(X3,X1,X4),true,sum(X4,X2,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_27,axiom,
sum(additive_inverse(X1),X1,additive_identity) = true,
left_inverse ).
cnf(c_0_28,hypothesis,
ifeq(sum(additive_inverse(c),X1,X2),true,ifeq(sum(b,X2,X3),true,sum(bS_Ic,X1,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_19]) ).
cnf(c_0_29,plain,
ifeq2(sum(additive_identity,X1,X2),true,X1,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_30,plain,
sum(X1,X2,add(X2,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_19]) ).
cnf(c_0_31,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc) = true,
aPb_plus_IaPc ).
cnf(c_0_32,plain,
ifeq(sum(X1,additive_inverse(X2),X3),true,sum(X3,X2,X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19]) ).
cnf(c_0_33,hypothesis,
ifeq(sum(b,additive_identity,X1),true,sum(bS_Ic,c,X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_27]),c_0_19]) ).
cnf(c_0_34,plain,
add(X1,additive_identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_23]) ).
cnf(c_0_35,plain,
ifeq2(sum(X1,X2,X3),true,add(X1,X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_25]),c_0_23]) ).
cnf(c_0_36,hypothesis,
ifeq(sum(additive_inverse(aPc),X1,X2),true,ifeq(sum(aPb,X2,X3),true,sum(aPb_S_IaPc,X1,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_31]),c_0_19]) ).
cnf(c_0_37,plain,
sum(add(additive_inverse(X1),X2),X1,X2) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_30]),c_0_19]) ).
cnf(c_0_38,plain,
sum(additive_identity,X1,additive_inverse(additive_inverse(X1))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_27]),c_0_19]) ).
cnf(c_0_39,plain,
add(additive_identity,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_23]) ).
cnf(c_0_40,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X4,X5),true,ifeq(product(X1,X6,X7),true,ifeq(sum(X6,X4,X2),true,sum(X7,X5,X3),true),true),true),true) = true,
distributivity1 ).
cnf(c_0_41,hypothesis,
product(a,c,aPc) = true,
a_times_c ).
cnf(c_0_42,hypothesis,
sum(bS_Ic,c,b) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_25]),c_0_34]),c_0_19]) ).
cnf(c_0_43,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
multiplication_is_well_defined ).
cnf(c_0_44,hypothesis,
product(a,b,aPb) = true,
a_times_b ).
cnf(c_0_45,plain,
sum(add(X1,additive_inverse(X2)),X2,X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_19]) ).
cnf(c_0_46,plain,
add(X1,X2) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_23]) ).
cnf(c_0_47,hypothesis,
ifeq(sum(additive_inverse(aPc),X1,X2),true,sum(aPb_S_IaPc,X1,add(aPb,X2)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_25]),c_0_19]) ).
cnf(c_0_48,plain,
sum(X1,add(additive_inverse(X1),X2),X2) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_37]),c_0_19]) ).
cnf(c_0_49,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_38]),c_0_39]),c_0_23]) ).
cnf(c_0_50,hypothesis,
ifeq(product(a,X1,X2),true,ifeq(product(a,X3,X4),true,ifeq(sum(c,X3,X1),true,sum(aPc,X4,X2),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_19]) ).
cnf(c_0_51,hypothesis,
sum(c,bS_Ic,b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_42]),c_0_19]) ).
cnf(c_0_52,hypothesis,
ifeq2(product(a,b,X1),true,X1,aPb) = aPb,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_23]) ).
cnf(c_0_53,axiom,
product(X1,X2,multiply(X1,X2)) = true,
closure_of_multiplication ).
cnf(c_0_54,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_45]),c_0_23]),c_0_46]) ).
cnf(c_0_55,hypothesis,
sum(aPb_S_IaPc,add(aPc,X1),add(aPb,X1)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_19]) ).
cnf(c_0_56,hypothesis,
ifeq(product(a,b,X1),true,ifeq(product(a,bS_Ic,X2),true,sum(aPc,X2,X1),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_19]) ).
cnf(c_0_57,hypothesis,
multiply(a,b) = aPb,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_23]) ).
cnf(c_0_58,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_54,c_0_49]) ).
cnf(c_0_59,hypothesis,
add(aPb_S_IaPc,add(aPc,X1)) = add(aPb,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_55]),c_0_23]) ).
cnf(c_0_60,hypothesis,
ifeq(product(a,bS_Ic,X1),true,sum(aPc,X1,aPb),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_53]),c_0_57]),c_0_19]) ).
cnf(c_0_61,hypothesis,
add(add(aPb,X1),additive_inverse(add(aPc,X1))) = aPb_S_IaPc,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_46]) ).
cnf(c_0_62,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_58]),c_0_46]) ).
cnf(c_0_63,hypothesis,
sum(aPc,multiply(a,bS_Ic),aPb) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_53]),c_0_19]) ).
cnf(c_0_64,plain,
ifeq2(sum(additive_inverse(X1),X1,X2),true,additive_identity,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_27]),c_0_23]) ).
cnf(c_0_65,hypothesis,
add(X1,add(aPb,additive_inverse(add(aPc,X1)))) = aPb_S_IaPc,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_49]),c_0_46]) ).
cnf(c_0_66,hypothesis,
add(aPc,multiply(a,bS_Ic)) = aPb,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_63]),c_0_23]) ).
cnf(c_0_67,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_30]),c_0_23]) ).
cnf(c_0_68,hypothesis,
multiply(a,bS_Ic) = aPb_S_IaPc,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_34]) ).
cnf(c_0_69,negated_conjecture,
product(a,bS_Ic,aPb_S_IaPc) != true,
prove_a_times_bS_Ic_is_aPb_S__IaPc ).
cnf(c_0_70,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_68]),c_0_69]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG006-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.32 % Computer : n013.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Sun Aug 27 01:44:17 EDT 2023
% 0.13/0.32 % CPUTime :
% 0.16/0.54 start to proof: theBenchmark
% 28.73/28.93 % Version : CSE_E---1.5
% 28.73/28.93 % Problem : theBenchmark.p
% 28.73/28.93 % Proof found
% 28.73/28.93 % SZS status Theorem for theBenchmark.p
% 28.73/28.93 % SZS output start Proof
% See solution above
% 28.73/28.94 % Total time : 28.392000 s
% 28.73/28.94 % SZS output end Proof
% 28.73/28.94 % Total time : 28.396000 s
%------------------------------------------------------------------------------