%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO013-4 : TPTP v9.2.1. Released v1.1.0.
% 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 : n026.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 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 10 RR)
% Number of literals : 42 ( 41 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity1,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity1) ).
cnf(additive_inverse1,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
cnf(multiplicative_inverse1,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).
cnf(additive_id1,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_id1) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_multiply) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_add) ).
cnf(distributivity2,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity2) ).
cnf(b_a_multiplicative_identity,hypothesis,
add(a,b) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_a_multiplicative_identity) ).
cnf(b_an_additive_identity,hypothesis,
multiply(a,b) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_an_additive_identity) ).
cnf(prove_a_inverse_is_b,negated_conjecture,
b != inverse(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_inverse_is_b) ).
cnf(c_0_11,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
distributivity1 ).
cnf(c_0_12,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
additive_inverse1 ).
cnf(c_0_13,axiom,
multiply(X1,multiplicative_identity) = X1,
multiplicative_id1 ).
cnf(c_0_14,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_15,axiom,
multiply(X1,inverse(X1)) = additive_identity,
multiplicative_inverse1 ).
cnf(c_0_16,axiom,
add(X1,additive_identity) = X1,
additive_id1 ).
cnf(c_0_17,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_18,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_19,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_20,plain,
multiply(X1,add(X1,X2)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_21,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_22,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distributivity2 ).
cnf(c_0_23,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_19]),c_0_12]) ).
cnf(c_0_24,hypothesis,
add(a,b) = multiplicative_identity,
b_a_multiplicative_identity ).
cnf(c_0_25,plain,
multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_13]),c_0_23]),c_0_13]),c_0_21]) ).
cnf(c_0_27,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_19]) ).
cnf(c_0_28,hypothesis,
add(a,multiply(b,X1)) = add(a,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_24]),c_0_19]) ).
cnf(c_0_29,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_30,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_15]),c_0_16]) ).
cnf(c_0_32,hypothesis,
multiply(a,b) = additive_identity,
b_an_additive_identity ).
cnf(c_0_33,hypothesis,
add(a,inverse(b)) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_15]),c_0_16]) ).
cnf(c_0_34,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_15]),c_0_29]) ).
cnf(c_0_35,plain,
multiply(X1,inverse(inverse(X1))) = inverse(inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_17]) ).
cnf(c_0_36,hypothesis,
multiply(a,add(b,X1)) = multiply(a,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_32]),c_0_29]) ).
cnf(c_0_37,hypothesis,
multiply(a,inverse(b)) = inverse(b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_33]),c_0_17]) ).
cnf(c_0_38,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_12]),c_0_13]),c_0_35]) ).
cnf(c_0_39,hypothesis,
inverse(b) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_12]),c_0_13]),c_0_37]) ).
cnf(c_0_40,negated_conjecture,
b != inverse(a),
prove_a_inverse_is_b ).
cnf(c_0_41,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO013-4 : TPTP v9.2.1. Released v1.1.0.
% 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
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 10:44:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.372s
%------------------------------------------------------------------------------