%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG040-1 : 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 : n008.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 05:05:05 PM UTC 2026
% Result : Unsatisfiable 2.81s 5.61s
% Output : CNFRefutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 45
% Syntax : Number of clauses : 73 ( 29 unt; 4 nHn; 51 RR)
% Number of literals : 175 ( 32 equ; 100 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 216 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity2,axiom,
( product(X1,X6,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity2) ).
cnf(distributivity4,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity4) ).
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(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(associativity_of_multiplication1,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication1) ).
cnf(associativity_of_multiplication2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication2) ).
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(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(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
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(product_symmetry,hypothesis,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_symmetry) ).
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_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(prove_equation,negated_conjecture,
~ sum(l,n,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
cnf(clause31,hypothesis,
( product(h(X1),X1,multiplicative_identity)
| X1 = additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause31) ).
cnf(clause30,hypothesis,
( product(X1,h(X1),multiplicative_identity)
| X1 = additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause30) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
cnf(left_multiplicative_identity,hypothesis,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_multiplicative_identity) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(right_multiplicative_identity,hypothesis,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_multiplicative_identity) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
cnf(d_plus_a,negated_conjecture,
product(d,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_plus_a) ).
cnf(c_plus_a,negated_conjecture,
product(c,a,n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_plus_a) ).
cnf(b_plus_a,negated_conjecture,
product(b,a,l),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_a) ).
cnf(b_plus_c,negated_conjecture,
sum(b,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_c) ).
cnf(i_0_27,axiom,
( product(X1,X6,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ sum(X3,X5,X7) ),
distributivity2,
[final] ).
cnf(i_0_28,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
distributivity4,
[final] ).
cnf(i_0_29,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
distributivity3,
[final] ).
cnf(i_0_30,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
distributivity1,
[final] ).
cnf(i_0_31,axiom,
( product(X1,X5,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X3,X4,X6) ),
associativity_of_multiplication1,
[final] ).
cnf(i_0_32,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity_of_multiplication2,
[final] ).
cnf(i_0_33,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1,
[final] ).
cnf(i_0_34,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2,
[final] ).
cnf(i_0_35,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined,
[final] ).
cnf(i_0_36,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined,
[final] ).
cnf(i_0_37,hypothesis,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
product_symmetry,
[final] ).
cnf(i_0_38,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition,
[final] ).
cnf(i_0_39,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication,
[final] ).
cnf(i_0_40,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition,
[final] ).
cnf(i_0_41,negated_conjecture,
~ sum(l,n,additive_identity),
prove_equation,
[final] ).
cnf(i_0_42,hypothesis,
( product(h(X1),X1,multiplicative_identity)
| X1 = additive_identity ),
clause31,
[final] ).
cnf(i_0_43,hypothesis,
( product(X1,h(X1),multiplicative_identity)
| X1 = additive_identity ),
clause30,
[final] ).
cnf(i_0_44,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse,
[final] ).
cnf(i_0_45,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse,
[final] ).
cnf(i_0_46,hypothesis,
product(multiplicative_identity,X1,X1),
left_multiplicative_identity,
[final] ).
cnf(i_0_47,axiom,
sum(additive_identity,X1,X1),
additive_identity1,
[final] ).
cnf(i_0_48,hypothesis,
product(X1,multiplicative_identity,X1),
right_multiplicative_identity,
[final] ).
cnf(i_0_49,axiom,
sum(X1,additive_identity,X1),
additive_identity2,
[final] ).
cnf(i_0_50,negated_conjecture,
product(d,a,additive_identity),
d_plus_a,
[final] ).
cnf(i_0_51,negated_conjecture,
product(c,a,n),
c_plus_a,
[final] ).
cnf(i_0_52,negated_conjecture,
product(b,a,l),
b_plus_a,
[final] ).
cnf(i_0_53,negated_conjecture,
sum(b,c,d),
b_plus_c,
[final] ).
cnf(i_0_54,axiom,
X1 = X1 ).
cnf(i_0_55,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_56,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_57,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_58,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_59,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_60,axiom,
( X1 != X2
| ~ sum(X1,X3,X4)
| sum(X2,X3,X4) ) ).
cnf(i_0_61,axiom,
( X1 != X2
| ~ sum(X3,X1,X4)
| sum(X3,X2,X4) ) ).
cnf(i_0_62,axiom,
( X1 != X2
| ~ sum(X3,X4,X1)
| sum(X3,X4,X2) ) ).
cnf(i_0_54_001,axiom,
X1 = X1 ).
cnf(i_0_55_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_56_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_57_004,axiom,
( X1 != X2
| ~ product(X1,X3,X4)
| product(X2,X3,X4) ) ).
cnf(i_0_58_005,axiom,
( X1 != X2
| ~ product(X3,X1,X4)
| product(X3,X2,X4) ) ).
cnf(i_0_59_006,axiom,
( X1 != X2
| ~ product(X3,X4,X1)
| product(X3,X4,X2) ) ).
cnf(i_0_60_007,axiom,
( X1 != X2
| ~ sum(X1,X3,X4)
| sum(X2,X3,X4) ) ).
cnf(i_0_61_008,axiom,
( X1 != X2
| ~ sum(X3,X1,X4)
| sum(X3,X2,X4) ) ).
cnf(i_0_62_009,axiom,
( X1 != X2
| ~ sum(X3,X4,X1)
| sum(X3,X4,X2) ) ).
cnf(i_0_63,plain,
$false,
inference(scs_inference,[],[i_0_41,i_0_52,i_0_51,i_0_53,i_0_50,i_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG040-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n008.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:47:58 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 2.81/5.61 % Version : CSE_E---1.7
% 2.81/5.61 % Problem : theBenchmark.p
% 2.81/5.61 % SZS status Unsatisfiable for theBenchmark.p
% 2.81/5.61 % SZS output start CNFRefutation
% See solution above
% 2.81/5.63 % Total time : 5.280s
%------------------------------------------------------------------------------