%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO013-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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 : n024.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 1.12s 1.61s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 12 RR)
% Number of literals : 22 ( 21 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity1,axiom,
add(multiply(X1,X2),X3) = multiply(add(X1,X3),add(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity1) ).
cnf(c_and_multiplicative_identity,hypothesis,
add(a,c) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_and_multiplicative_identity) ).
cnf(multiplicative_id2,axiom,
multiply(multiplicative_identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
cnf(b_and_multiplicative_identity,hypothesis,
add(a,b) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_and_multiplicative_identity) ).
cnf(b_a_additive_identity,hypothesis,
multiply(a,b) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_a_additive_identity) ).
cnf(additive_id1,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
cnf(c_a_additive_identity,hypothesis,
multiply(a,c) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_a_additive_identity) ).
cnf(prove_b_is_a,negated_conjecture,
b != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_is_a) ).
cnf(c_0_9,axiom,
add(multiply(X1,X2),X3) = multiply(add(X1,X3),add(X2,X3)),
distributivity1 ).
cnf(c_0_10,hypothesis,
add(a,c) = multiplicative_identity,
c_and_multiplicative_identity ).
cnf(c_0_11,axiom,
multiply(multiplicative_identity,X1) = X1,
multiplicative_id2 ).
cnf(c_0_12,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_13,hypothesis,
add(a,b) = multiplicative_identity,
b_and_multiplicative_identity ).
cnf(c_0_14,hypothesis,
add(c,multiply(a,X1)) = add(X1,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]) ).
cnf(c_0_15,hypothesis,
multiply(a,b) = additive_identity,
b_a_additive_identity ).
cnf(c_0_16,axiom,
add(X1,additive_identity) = X1,
additive_id1 ).
cnf(c_0_17,hypothesis,
add(b,multiply(a,X1)) = add(X1,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_13]),c_0_11]),c_0_12]) ).
cnf(c_0_18,hypothesis,
multiply(a,c) = additive_identity,
c_a_additive_identity ).
cnf(c_0_19,hypothesis,
add(b,c) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_20,negated_conjecture,
b != c,
prove_b_is_a ).
cnf(c_0_21,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_16]),c_0_12]),c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : BOO013-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.06 % 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
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue May 5 05:44:12 EDT 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.12/1.61 % Version : CSE_E---1.7
% 1.12/1.61 % Problem : theBenchmark.p
% 1.12/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 1.12/1.61 % SZS output start CNFRefutation
% See solution above
% 1.12/1.61 % Total time : 1.360s
%------------------------------------------------------------------------------