%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG009-5 : 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 : n016.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 05:04:59 PM UTC 2026
% Result : Unsatisfiable 6.23s 4.55s
% Output : CNFRefutation 6.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of clauses : 67 ( 67 unt; 0 nHn; 4 RR)
% Number of literals : 67 ( 66 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 142 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(commutative_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutative_addition) ).
cnf(associative_addition,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_addition) ).
cnf(right_additive_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_additive_inverse) ).
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute1) ).
cnf(x_cubed_is_x,hypothesis,
multiply(X1,multiply(X1,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_x) ).
cnf(associative_multiplication,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_multiplication) ).
cnf(distribute2,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute2) ).
cnf(prove_commutativity,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c_0_9,axiom,
add(X1,additive_identity) = X1,
right_identity ).
cnf(c_0_10,axiom,
add(X1,X2) = add(X2,X1),
commutative_addition ).
cnf(c_0_11,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associative_addition ).
cnf(c_0_12,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_additive_inverse ).
cnf(c_0_13,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
add(X1,add(additive_inverse(X1),X2)) = 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,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_16,hypothesis,
multiply(X1,multiply(X1,X1)) = X1,
x_cubed_is_x ).
cnf(c_0_17,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_12]),c_0_9]) ).
cnf(c_0_18,hypothesis,
multiply(X1,add(X2,multiply(X1,X1))) = add(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_10]) ).
cnf(c_0_19,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_20,hypothesis,
add(X1,multiply(X1,additive_identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_13]),c_0_16]) ).
cnf(c_0_21,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associative_multiplication ).
cnf(c_0_22,hypothesis,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_10]),c_0_12]) ).
cnf(c_0_23,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_24,hypothesis,
multiply(X1,multiply(additive_identity,X2)) = multiply(additive_identity,X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,hypothesis,
multiply(X1,multiply(X1,multiply(X1,X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_16]),c_0_21]) ).
cnf(c_0_26,hypothesis,
multiply(additive_identity,add(X1,X1)) = multiply(additive_identity,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_24]),c_0_15]),c_0_24]) ).
cnf(c_0_27,hypothesis,
multiply(X1,add(multiply(X1,multiply(X1,X2)),X3)) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_25]),c_0_15]) ).
cnf(c_0_28,hypothesis,
multiply(additive_identity,add(X1,add(X1,X2))) = multiply(additive_identity,add(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_26]),c_0_15]),c_0_11]) ).
cnf(c_0_29,hypothesis,
multiply(X1,add(X2,additive_inverse(multiply(X1,multiply(X1,X2))))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_12]),c_0_22]) ).
cnf(c_0_30,hypothesis,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_12]),c_0_9]),c_0_22]) ).
cnf(c_0_31,plain,
add(multiply(X1,X2),multiply(X3,multiply(X4,X2))) = multiply(add(X1,multiply(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_32,hypothesis,
multiply(X1,multiply(X2,multiply(X1,multiply(X2,multiply(X1,X2))))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_21]),c_0_21]) ).
cnf(c_0_33,hypothesis,
multiply(X1,multiply(add(X2,additive_inverse(multiply(X1,multiply(X1,X2)))),X3)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_29]),c_0_30]) ).
cnf(c_0_34,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_35,plain,
add(multiply(X1,X2),add(multiply(X3,X2),X4)) = add(multiply(add(X1,X3),X2),X4),
inference(spm,[status(thm)],[c_0_11,c_0_23]) ).
cnf(c_0_36,hypothesis,
multiply(add(X1,multiply(X2,X2)),X2) = add(X2,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_16]),c_0_10]) ).
cnf(c_0_37,hypothesis,
multiply(add(X1,additive_inverse(multiply(X2,multiply(X2,X1)))),X2) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_22]) ).
cnf(c_0_38,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_39,plain,
add(additive_inverse(multiply(X1,X2)),multiply(add(X1,X3),X2)) = multiply(X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_10]) ).
cnf(c_0_40,plain,
add(multiply(X1,X2),add(multiply(X1,X3),X4)) = add(multiply(X1,add(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_41,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_34,c_0_17]) ).
cnf(c_0_42,hypothesis,
multiply(add(multiply(X1,X1),X2),X1) = add(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_36,c_0_10]) ).
cnf(c_0_43,hypothesis,
multiply(add(X1,additive_inverse(multiply(X2,multiply(X2,X1)))),multiply(X3,X2)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_33]),c_0_22]),c_0_38]),c_0_9]),c_0_21]) ).
cnf(c_0_44,plain,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_12]),c_0_30]),c_0_9]) ).
cnf(c_0_45,plain,
add(additive_inverse(multiply(X1,X2)),multiply(X1,add(X2,X3))) = multiply(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_40]),c_0_10]) ).
cnf(c_0_46,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_41]),c_0_10]) ).
cnf(c_0_47,hypothesis,
add(multiply(X1,X2),additive_inverse(multiply(X2,multiply(X2,multiply(X1,X2))))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_21]),c_0_44]),c_0_21]),c_0_21]),c_0_21]),c_0_21]),c_0_21]),c_0_32]) ).
cnf(c_0_48,plain,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_12]),c_0_22]),c_0_9]) ).
cnf(c_0_49,plain,
add(multiply(X1,multiply(X2,X3)),multiply(X4,X3)) = multiply(add(multiply(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_50,hypothesis,
multiply(X1,multiply(X1,multiply(X2,X1))) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_38]),c_0_9]),c_0_17]) ).
cnf(c_0_51,hypothesis,
multiply(X1,multiply(add(additive_inverse(X2),multiply(X1,multiply(X1,X2))),X3)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_48]),c_0_48]),c_0_17]) ).
cnf(c_0_52,hypothesis,
multiply(add(X1,multiply(X2,X3)),multiply(X3,X3)) = multiply(add(multiply(X1,X3),X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_16]),c_0_49]) ).
cnf(c_0_53,hypothesis,
multiply(X1,multiply(X1,multiply(X2,multiply(X1,X3)))) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_50]),c_0_21]),c_0_21]),c_0_21]) ).
cnf(c_0_54,hypothesis,
multiply(X1,multiply(add(X1,additive_inverse(multiply(X2,multiply(X1,X2)))),multiply(X1,X2))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_44]),c_0_10]) ).
cnf(c_0_55,hypothesis,
multiply(add(X1,additive_inverse(multiply(X2,multiply(X1,X2)))),multiply(X1,X2)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_22]) ).
cnf(c_0_56,plain,
additive_inverse(add(additive_inverse(X1),X2)) = add(X1,additive_inverse(X2)),
inference(spm,[status(thm)],[c_0_14,c_0_46]) ).
cnf(c_0_57,hypothesis,
multiply(X1,add(multiply(X1,multiply(X2,X1)),X3)) = add(multiply(X2,X1),multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_15,c_0_50]) ).
cnf(c_0_58,hypothesis,
multiply(X1,multiply(X2,add(X1,additive_inverse(multiply(X2,multiply(X1,X2)))))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_55]),c_0_22]),c_0_38]),c_0_9]),c_0_21]) ).
cnf(c_0_59,hypothesis,
multiply(X1,add(X2,multiply(X1,multiply(X3,X1)))) = add(multiply(X1,X2),multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_50]) ).
cnf(c_0_60,plain,
additive_inverse(multiply(X1,add(additive_inverse(X2),X3))) = multiply(X1,add(X2,additive_inverse(X3))),
inference(spm,[status(thm)],[c_0_48,c_0_56]) ).
cnf(c_0_61,hypothesis,
multiply(X1,multiply(X1,add(multiply(X2,X1),X3))) = add(multiply(X2,X1),multiply(X1,multiply(X1,X3))),
inference(spm,[status(thm)],[c_0_57,c_0_15]) ).
cnf(c_0_62,hypothesis,
multiply(X1,add(multiply(X2,X1),additive_inverse(multiply(X1,X2)))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_58]),c_0_44]),c_0_48]),c_0_17]),c_0_59]),c_0_48]),c_0_60]) ).
cnf(c_0_63,hypothesis,
add(multiply(X1,X2),additive_inverse(multiply(X2,X1))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_22]),c_0_48]),c_0_48]),c_0_25]) ).
cnf(c_0_64,negated_conjecture,
multiply(a,b) != multiply(b,a),
prove_commutativity ).
cnf(c_0_65,hypothesis,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_63]),c_0_38]),c_0_9]),c_0_17]) ).
cnf(c_0_66,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG009-5 : 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 : n016.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 01:46:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 6.23/4.55 % Version : CSE_E---1.7
% 6.23/4.55 % Problem : theBenchmark.p
% 6.23/4.55 % SZS status Unsatisfiable for theBenchmark.p
% 6.23/4.55 % SZS output start CNFRefutation
% See solution above
% 6.23/4.57 % Total time : 3.371s
%------------------------------------------------------------------------------