%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG007-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 : Tue May 5 05:04:58 PM UTC 2026
% Result : Unsatisfiable 1.45s 1.79s
% Output : CNFRefutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of clauses : 70 ( 36 unt; 0 nHn; 36 RR)
% Number of literals : 142 ( 12 equ; 74 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 179 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity1) ).
cnf(x_squared_is_x,hypothesis,
product(X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_squared_is_x) ).
cnf(associativity_of_addition1,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
cnf(distributivity3,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity3) ).
cnf(prove_a_plus_a_is_id,negated_conjecture,
~ sum(a,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_plus_a_is_id) ).
cnf(c_0_13,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_14,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_15,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_16,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_17,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2 ).
cnf(c_0_18,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_19,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ sum(X4,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,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_24,hypothesis,
product(X1,X1,X1),
x_squared_is_x ).
cnf(c_0_25,plain,
( sum(X1,X2,X3)
| ~ sum(X3,additive_inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_16]),c_0_22]) ).
cnf(c_0_26,hypothesis,
( sum(X1,X2,X3)
| ~ product(X3,X4,X2)
| ~ product(X3,X5,X1)
| ~ sum(X5,X4,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1 ).
cnf(c_0_28,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_29,plain,
sum(additive_identity,X1,additive_inverse(additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_30,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_31,hypothesis,
( sum(X1,X2,X2)
| ~ product(X2,X3,X1)
| ~ sum(X3,X2,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_32,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_33,plain,
( X1 = additive_identity
| ~ sum(additive_inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_34,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X1,X3,additive_inverse(X4))
| ~ sum(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_35,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_36,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_37,hypothesis,
( sum(multiply(X1,X2),X1,X1)
| ~ sum(X2,X1,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_25,c_0_16]) ).
cnf(c_0_39,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
cnf(c_0_40,plain,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,X2,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_41,hypothesis,
sum(multiply(X1,additive_identity),X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_42,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
distributivity3 ).
cnf(c_0_43,hypothesis,
sum(multiply(X1,additive_identity),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,hypothesis,
( sum(X1,X2,X3)
| ~ product(X4,X3,X2)
| ~ product(X5,X3,X1)
| ~ sum(X5,X4,X3) ),
inference(spm,[status(thm)],[c_0_42,c_0_24]) ).
cnf(c_0_45,hypothesis,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_43]),c_0_22]) ).
cnf(c_0_46,hypothesis,
( sum(X1,X2,X2)
| ~ product(X3,X2,X1)
| ~ sum(X3,X2,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_24]) ).
cnf(c_0_47,hypothesis,
product(X1,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_45]) ).
cnf(c_0_48,hypothesis,
( sum(multiply(X1,X2),X2,X2)
| ~ sum(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_32]) ).
cnf(c_0_49,hypothesis,
( sum(X1,X2,additive_identity)
| ~ product(X3,X4,X2)
| ~ product(X3,X5,X1)
| ~ sum(X5,X4,additive_identity) ),
inference(spm,[status(thm)],[c_0_23,c_0_47]) ).
cnf(c_0_50,plain,
( sum(X1,X2,X3)
| ~ sum(X1,X4,additive_identity)
| ~ sum(X4,X3,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_14]) ).
cnf(c_0_51,hypothesis,
sum(multiply(additive_identity,X1),X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_38]),c_0_39]) ).
cnf(c_0_52,hypothesis,
( sum(X1,X2,additive_identity)
| ~ product(X2,X3,X1)
| ~ sum(X3,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_49,c_0_24]) ).
cnf(c_0_53,plain,
( sum(X1,add(X2,X3),X3)
| ~ sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_50,c_0_16]) ).
cnf(c_0_54,hypothesis,
sum(multiply(additive_identity,X1),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_40,c_0_51]) ).
cnf(c_0_55,plain,
( sum(X1,X2,add(X3,X4))
| ~ sum(X5,X3,X2)
| ~ sum(X1,X5,X4) ),
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_56,hypothesis,
( sum(multiply(X1,X2),X1,additive_identity)
| ~ sum(X2,X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_52,c_0_32]) ).
cnf(c_0_57,plain,
sum(additive_inverse(X1),add(X1,X2),X2),
inference(spm,[status(thm)],[c_0_53,c_0_18]) ).
cnf(c_0_58,hypothesis,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_54]),c_0_22]) ).
cnf(c_0_59,plain,
( sum(X1,additive_identity,add(X2,X3))
| ~ sum(X1,additive_inverse(X2),X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_18]) ).
cnf(c_0_60,hypothesis,
sum(multiply(X1,additive_inverse(X1)),X1,additive_identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_22]),c_0_22]) ).
cnf(c_0_61,hypothesis,
product(additive_identity,X1,additive_identity),
inference(spm,[status(thm)],[c_0_32,c_0_58]) ).
cnf(c_0_62,hypothesis,
sum(multiply(additive_inverse(X1),X1),additive_identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_36]),c_0_22]) ).
cnf(c_0_63,hypothesis,
( sum(X1,X2,additive_identity)
| ~ product(X3,X4,X2)
| ~ product(X5,X4,X1)
| ~ sum(X5,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_42,c_0_61]) ).
cnf(c_0_64,hypothesis,
multiply(additive_inverse(X1),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_62]),c_0_22]) ).
cnf(c_0_65,hypothesis,
( sum(X1,X2,additive_identity)
| ~ product(X3,X2,X1)
| ~ sum(X3,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_63,c_0_24]) ).
cnf(c_0_66,hypothesis,
product(additive_inverse(X1),X1,X1),
inference(spm,[status(thm)],[c_0_32,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
~ sum(a,a,additive_identity),
prove_a_plus_a_is_id ).
cnf(c_0_68,hypothesis,
sum(X1,X1,additive_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_18])]) ).
cnf(c_0_69,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG007-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:46:20 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.45/1.79 % Version : CSE_E---1.7
% 1.45/1.79 % Problem : theBenchmark.p
% 1.45/1.79 % SZS status Unsatisfiable for theBenchmark.p
% 1.45/1.79 % SZS output start CNFRefutation
% See solution above
% 1.55/1.80 % Total time : 1.369s
%------------------------------------------------------------------------------