%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO015-4 : TPTP v9.2.1. Released v1.1.0.
% 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 : n013.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 04:11:08 PM UTC 2026
% Result : Unsatisfiable 2.21s 1.94s
% Output : CNFRefutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of clauses : 58 ( 58 unt; 0 nHn; 3 RR)
% Number of literals : 58 ( 57 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 109 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity1,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',distributivity1) ).
cnf(additive_inverse1,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',additive_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
cnf(multiplicative_inverse1,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).
cnf(additive_id1,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',additive_id1) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',commutativity_of_multiply) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/BOO004-0.ax',distributivity2) ).
cnf(prove_c_inverse_is_d,negated_conjecture,
inverse(multiply(a,b)) != add(inverse(a),inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_inverse_is_d) ).
cnf(c_0_9,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
distributivity1 ).
cnf(c_0_10,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
additive_inverse1 ).
cnf(c_0_11,axiom,
multiply(X1,multiplicative_identity) = X1,
multiplicative_id1 ).
cnf(c_0_12,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_13,axiom,
multiply(X1,inverse(X1)) = additive_identity,
multiplicative_inverse1 ).
cnf(c_0_14,axiom,
add(X1,additive_identity) = X1,
additive_id1 ).
cnf(c_0_15,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_16,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_17,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_18,plain,
multiply(X1,add(X1,X2)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_16]) ).
cnf(c_0_19,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_20,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distributivity2 ).
cnf(c_0_21,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_17]),c_0_10]) ).
cnf(c_0_22,plain,
multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,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_20,c_0_11]),c_0_21]),c_0_11]),c_0_19]) ).
cnf(c_0_24,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_15]) ).
cnf(c_0_26,plain,
multiply(X1,add(multiply(X1,X2),X3)) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_20]) ).
cnf(c_0_27,plain,
add(multiply(X1,X2),multiply(X2,X3)) = multiply(X2,add(X1,X3)),
inference(spm,[status(thm)],[c_0_20,c_0_15]) ).
cnf(c_0_28,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_29,plain,
multiply(X1,multiply(X2,add(X1,X3))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23]) ).
cnf(c_0_30,plain,
add(X1,add(X2,X1)) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_24]),c_0_19]) ).
cnf(c_0_31,plain,
multiply(X1,multiply(X2,add(X3,X1))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,plain,
multiply(X1,multiply(add(X2,X1),X3)) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_31,c_0_15]) ).
cnf(c_0_33,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_17]) ).
cnf(c_0_34,plain,
multiply(multiply(X1,X2),multiply(X3,X1)) = multiply(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_35,plain,
multiply(multiply(X1,X2),multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_36,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_37,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_13]),c_0_14]) ).
cnf(c_0_38,plain,
multiply(multiply(X1,X2),X3) = multiply(multiply(X2,X3),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_34]),c_0_35]) ).
cnf(c_0_39,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_13]),c_0_36]) ).
cnf(c_0_40,plain,
multiply(X1,inverse(inverse(X1))) = inverse(inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_37]),c_0_15]) ).
cnf(c_0_41,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_15,c_0_38]) ).
cnf(c_0_42,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_10]),c_0_11]),c_0_40]) ).
cnf(c_0_43,plain,
multiply(X1,multiply(X2,inverse(multiply(X1,X2)))) = additive_identity,
inference(spm,[status(thm)],[c_0_13,c_0_41]) ).
cnf(c_0_44,plain,
add(inverse(X1),multiply(X2,X1)) = add(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_12,c_0_42]) ).
cnf(c_0_45,plain,
multiply(X1,multiply(inverse(X1),X2)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_23]),c_0_13]) ).
cnf(c_0_46,plain,
multiply(X1,multiply(X2,inverse(X1))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_28]),c_0_13]) ).
cnf(c_0_47,plain,
multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_20]) ).
cnf(c_0_48,plain,
add(X1,multiply(X2,inverse(multiply(inverse(X1),X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_43]),c_0_14]) ).
cnf(c_0_49,plain,
add(X1,inverse(multiply(inverse(X1),X2))) = inverse(multiply(inverse(X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_14]),c_0_19]) ).
cnf(c_0_50,plain,
multiply(inverse(X1),multiply(X2,X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_46,c_0_42]) ).
cnf(c_0_51,plain,
add(inverse(X1),multiply(X1,X2)) = add(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_33,c_0_42]) ).
cnf(c_0_52,plain,
multiply(X1,inverse(multiply(inverse(X2),X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_53,plain,
add(inverse(X1),inverse(multiply(X2,X1))) = inverse(multiply(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_50]),c_0_14]),c_0_19]) ).
cnf(c_0_54,plain,
inverse(multiply(inverse(X1),X2)) = add(inverse(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_51]),c_0_53]) ).
cnf(c_0_55,negated_conjecture,
inverse(multiply(a,b)) != add(inverse(a),inverse(b)),
prove_c_inverse_is_d ).
cnf(c_0_56,plain,
add(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_54,c_0_42]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : BOO015-4 : TPTP v9.2.1. Released v1.1.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n013.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 10:44:11 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 2.21/1.94 % Version : CSE_E---1.7
% 2.21/1.94 % Problem : theBenchmark.p
% 2.21/1.94 % SZS status Unsatisfiable for theBenchmark.p
% 2.21/1.94 % SZS output start CNFRefutation
% See solution above
% 2.21/1.95 % Total time : 1.371s
%------------------------------------------------------------------------------