%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG005-1 : 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 : n018.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 05:04:57 PM UTC 2026
% Result : Unsatisfiable 1.39s 1.79s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of clauses : 63 ( 33 unt; 0 nHn; 43 RR)
% Number of literals : 125 ( 18 equ; 64 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 142 ( 0 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_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
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(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
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(a_times_b,hypothesis,
product(a,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
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(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(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(a_inverse_times_b,hypothesis,
product(additive_inverse(a),b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b) ).
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(prove_sum_is_additive_id,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum_is_additive_id) ).
cnf(c_0_16,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_17,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
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_16,c_0_17]) ).
cnf(c_0_21,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_22,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_23,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_25,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_26,hypothesis,
product(a,b,d),
a_times_b ).
cnf(c_0_27,plain,
( sum(X1,X2,X3)
| ~ sum(X3,additive_inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_21]),c_0_23]) ).
cnf(c_0_28,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_29,hypothesis,
( sum(X1,X2,d)
| ~ product(X3,b,X2)
| ~ product(X4,b,X1)
| ~ sum(X4,X3,a) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_31,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
distributivity4 ).
cnf(c_0_32,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_33,hypothesis,
product(additive_inverse(a),b,c),
a_inverse_times_b ).
cnf(c_0_34,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1 ).
cnf(c_0_35,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_36,plain,
sum(additive_identity,X1,additive_inverse(additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_37,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_38,hypothesis,
( sum(X1,d,d)
| ~ product(X2,b,X1)
| ~ sum(X2,a,a) ),
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_39,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_40,plain,
( X1 = additive_identity
| ~ sum(additive_inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_41,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_42,hypothesis,
( product(X1,b,X2)
| ~ product(X3,b,X4)
| ~ sum(X4,d,X2)
| ~ sum(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_26]) ).
cnf(c_0_43,hypothesis,
( X1 = c
| ~ product(additive_inverse(a),b,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_44,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X1,X3,additive_inverse(X4))
| ~ sum(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_19]) ).
cnf(c_0_45,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_46,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_47,hypothesis,
( sum(multiply(X1,b),d,d)
| ~ sum(X1,a,a) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_49,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,hypothesis,
( product(X1,b,X2)
| ~ sum(multiply(X3,b),d,X2)
| ~ sum(X3,a,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_39]) ).
cnf(c_0_51,hypothesis,
multiply(additive_inverse(a),b) = c,
inference(spm,[status(thm)],[c_0_43,c_0_39]) ).
cnf(c_0_52,plain,
( sum(X1,additive_identity,additive_identity)
| ~ sum(X1,X2,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_53,hypothesis,
sum(multiply(additive_identity,b),d,d),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_54,hypothesis,
( product(additive_identity,b,X1)
| ~ sum(c,d,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_19]),c_0_51]) ).
cnf(c_0_55,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_35,c_0_41]) ).
cnf(c_0_56,hypothesis,
sum(multiply(additive_identity,b),additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_39]) ).
cnf(c_0_58,hypothesis,
product(additive_identity,b,add(d,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_21]),c_0_55]) ).
cnf(c_0_59,hypothesis,
multiply(additive_identity,b) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_56]),c_0_23]) ).
cnf(c_0_60,hypothesis,
add(d,c) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_61,negated_conjecture,
~ sum(c,d,additive_identity),
prove_sum_is_additive_id ).
cnf(c_0_62,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_60]),c_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG005-1 : 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
% 0.12/0.32 % Computer : n018.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue May 5 01:46:02 EDT 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.33 % start to proof: theBenchmark
% 1.39/1.79 % Version : CSE_E---1.7
% 1.39/1.79 % Problem : theBenchmark.p
% 1.39/1.79 % SZS status Unsatisfiable for theBenchmark.p
% 1.39/1.79 % SZS output start CNFRefutation
% See solution above
% 1.39/1.79 % Total time : 1.374s
%------------------------------------------------------------------------------