%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO013-1 : 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 : n009.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 04:11:07 PM UTC 2026
% Result : Unsatisfiable 1.34s 1.74s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 36 ( 23 unt; 0 nHn; 27 RR)
% Number of literals : 61 ( 9 equ; 27 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity8,axiom,
( sum(X6,X2,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ product(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity8) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
cnf(sum_to_multiplicative_identity2,negated_conjecture,
sum(x,z,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_to_multiplicative_identity2) ).
cnf(product_to_additive_identity1,negated_conjecture,
product(x,y,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_additive_identity1) ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(sum_to_multiplicative_identity1,negated_conjecture,
sum(x,y,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_to_multiplicative_identity1) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_addition) ).
cnf(product_to_additive_identity2,negated_conjecture,
product(x,z,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_additive_identity2) ).
cnf(prove_both_inverse_are_equal,negated_conjecture,
y != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_both_inverse_are_equal) ).
cnf(c_0_11,axiom,
( sum(X6,X2,X7)
| ~ sum(X1,X2,X3)
| ~ sum(X4,X2,X5)
| ~ product(X1,X4,X6)
| ~ product(X3,X5,X7) ),
distributivity8 ).
cnf(c_0_12,axiom,
product(multiplicative_identity,X1,X1),
multiplicative_identity1 ).
cnf(c_0_13,plain,
( sum(X1,X2,X3)
| ~ product(X4,X5,X1)
| ~ sum(X4,X2,multiplicative_identity)
| ~ sum(X5,X2,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,negated_conjecture,
sum(x,z,multiplicative_identity),
sum_to_multiplicative_identity2 ).
cnf(c_0_15,negated_conjecture,
( sum(X1,z,X2)
| ~ product(x,X3,X1)
| ~ sum(X3,z,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,negated_conjecture,
product(x,y,additive_identity),
product_to_additive_identity1 ).
cnf(c_0_17,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_18,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_19,negated_conjecture,
sum(x,y,multiplicative_identity),
sum_to_multiplicative_identity1 ).
cnf(c_0_20,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_21,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_22,negated_conjecture,
( sum(additive_identity,z,X1)
| ~ sum(y,z,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( sum(X1,y,X2)
| ~ product(x,X3,X1)
| ~ sum(X3,y,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
product(x,z,additive_identity),
product_to_additive_identity2 ).
cnf(c_0_26,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_27,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
sum(additive_identity,z,add(y,z)),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_29,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_30,negated_conjecture,
( sum(additive_identity,y,X1)
| ~ sum(z,y,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
add(y,z) = z,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_28]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
sum(additive_identity,y,z),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_20]),c_0_31]),c_0_32]) ).
cnf(c_0_34,negated_conjecture,
y != z,
prove_both_inverse_are_equal ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_33]),c_0_29]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO013-1 : 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 : n009.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 10:44:11 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.34/1.74 % Version : CSE_E---1.7
% 1.34/1.74 % Problem : theBenchmark.p
% 1.34/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.34/1.74 % SZS output start CNFRefutation
% See solution above
% 1.34/1.74 % Total time : 1.372s
%------------------------------------------------------------------------------