%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO003-1 : 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 04:11:02 PM UTC 2026
% Result : Unsatisfiable 1.27s 2.66s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 42 ( 22 unt; 0 nHn; 22 RR)
% Number of literals : 84 ( 13 equ; 44 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 105 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity4) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
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/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity8) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse1) ).
cnf(multiplication_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
cnf(commutativity_of_multiplication,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(prove_both_equalities,negated_conjecture,
~ product(x,x,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_both_equalities) ).
cnf(c_0_11,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_12,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_13,plain,
( product(X1,X2,X3)
| ~ product(X4,X2,additive_identity)
| ~ product(X5,X2,X3)
| ~ sum(X4,X5,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_15,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_16,plain,
( product(X1,X2,X3)
| ~ product(X1,X2,additive_identity)
| ~ product(additive_identity,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
product(inverse(X1),X1,additive_identity),
multiplicative_inverse1 ).
cnf(c_0_18,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
multiplication_is_well_defined ).
cnf(c_0_19,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_20,axiom,
( product(X2,X1,X3)
| ~ product(X1,X2,X3) ),
commutativity_of_multiplication ).
cnf(c_0_21,plain,
( sum(X1,X2,X3)
| ~ product(X4,additive_identity,X1)
| ~ product(X5,X2,X3)
| ~ sum(X4,X2,X5) ),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_22,plain,
( product(inverse(X1),X1,X2)
| ~ product(additive_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( X1 = multiply(X2,X3)
| ~ product(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_25,plain,
( X1 = additive_identity
| ~ product(inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_26,plain,
( sum(X1,X2,X3)
| ~ product(additive_identity,additive_identity,X1)
| ~ product(X2,X2,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_12]) ).
cnf(c_0_27,plain,
product(inverse(X1),X1,multiply(additive_identity,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_28,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_30,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_31,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_32,plain,
( sum(X1,X2,multiply(X2,X2))
| ~ product(additive_identity,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_33,plain,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_27]),c_0_28]),c_0_29]) ).
cnf(c_0_34,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_12]) ).
cnf(c_0_35,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
sum(additive_identity,X1,multiply(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_19]),c_0_33]) ).
cnf(c_0_37,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_38,plain,
multiply(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_39,negated_conjecture,
~ product(x,x,x),
prove_both_equalities ).
cnf(c_0_40,plain,
product(X1,X1,X1),
inference(spm,[status(thm)],[c_0_19,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/1.05 % Problem : BOO003-1 : TPTP v9.2.1. Released v1.0.0.
% 0.11/1.05 % 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
% 0.11/1.26 % Computer : n027.cluster.edu
% 0.11/1.26 % Model : x86_64 x86_64
% 0.11/1.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/1.26 % Memory : 8042.1875MB
% 0.11/1.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/1.27 % CPULimit : 300
% 0.11/1.27 % WCLimit : 300
% 0.11/1.27 % DateTime : Tue May 5 10:45:06 EDT 2026
% 0.11/1.27 % CPUTime :
% 0.11/1.28 % start to proof: theBenchmark
% 1.27/2.66 % Version : CSE_E---1.7
% 1.27/2.66 % Problem : theBenchmark.p
% 1.27/2.66 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/2.66 % SZS output start CNFRefutation
% See solution above
% 1.27/2.66 % Total time : 1.372s
%------------------------------------------------------------------------------