%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG038-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/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 05:05:05 PM UTC 2026
% Result : Unsatisfiable 1.24s 1.72s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 48 ( 24 unt; 0 nHn; 31 RR)
% Number of literals : 95 ( 18 equ; 49 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 109 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
cnf(some_property,hypothesis,
( product(X1,h(X1,X2),X2)
| X1 != additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',some_property) ).
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,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
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(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
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_multiplication2,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication2) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(prove_b_is_additive_identity,negated_conjecture,
b != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_is_additive_identity) ).
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(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_15,hypothesis,
( product(X1,h(X1,X2),X2)
| X1 != additive_identity ),
some_property ).
cnf(c_0_16,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_17,hypothesis,
product(a,b,additive_identity),
a_times_b ).
cnf(c_0_18,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2 ).
cnf(c_0_19,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_20,plain,
( X1 = X2
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_22,axiom,
( product(X3,X4,X6)
| ~ product(X1,X2,X3)
| ~ product(X2,X4,X5)
| ~ product(X1,X5,X6) ),
associativity_of_multiplication2 ).
cnf(c_0_23,hypothesis,
product(additive_identity,h(additive_identity,X1),X1),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_24,hypothesis,
( sum(X1,X2,additive_identity)
| ~ product(a,X3,X2)
| ~ product(a,X4,X1)
| ~ sum(X4,X3,b) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ sum(X4,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_28,hypothesis,
( product(X1,h(additive_identity,X2),X3)
| ~ product(X4,additive_identity,X1)
| ~ product(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,hypothesis,
( sum(X1,additive_identity,additive_identity)
| ~ product(a,X2,X1)
| ~ sum(X2,b,b) ),
inference(spm,[status(thm)],[c_0_24,c_0_17]) ).
cnf(c_0_30,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_31,plain,
( sum(X1,X2,X3)
| ~ sum(X3,additive_inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_21]),c_0_26]) ).
cnf(c_0_32,plain,
( X1 = additive_identity
| ~ sum(X2,additive_inverse(X2),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_27]) ).
cnf(c_0_33,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_34,hypothesis,
( product(X1,h(additive_identity,b),additive_identity)
| ~ product(a,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_17]) ).
cnf(c_0_35,hypothesis,
( sum(multiply(a,X1),additive_identity,additive_identity)
| ~ sum(X1,b,b) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_37,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_32,c_0_21]) ).
cnf(c_0_38,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_39,hypothesis,
product(multiply(a,additive_identity),h(additive_identity,b),additive_identity),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_40,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_41,hypothesis,
sum(multiply(a,additive_identity),additive_identity,additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_42,hypothesis,
( X1 = X2
| ~ product(additive_identity,h(additive_identity,X2),X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_43,hypothesis,
multiply(multiply(a,additive_identity),h(additive_identity,b)) = additive_identity,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,hypothesis,
multiply(a,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_26]) ).
cnf(c_0_45,hypothesis,
multiply(additive_identity,h(additive_identity,X1)) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_30]) ).
cnf(c_0_46,negated_conjecture,
b != additive_identity,
prove_b_is_additive_identity ).
cnf(c_0_47,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG038-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n027.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 01:47:20 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.24/1.72 % Version : CSE_E---1.7
% 1.24/1.72 % Problem : theBenchmark.p
% 1.24/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.24/1.72 % SZS output start CNFRefutation
% See solution above
% 1.24/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------