%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG016-6 : 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 : 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 05:05:00 PM UTC 2026
% Result : Unsatisfiable 2.22s 2.02s
% Output : CNFRefutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 5 RR)
% Number of literals : 39 ( 38 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 65 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_for_addition,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
cnf(right_additive_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).
cnf(left_additive_identity,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).
cnf(right_additive_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',additive_inverse_additive_inverse) ).
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute1) ).
cnf(right_multiplicative_zero,axiom,
multiply(X1,additive_identity) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_multiplicative_zero) ).
cnf(distribute2,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute2) ).
cnf(left_multiplicative_zero,axiom,
multiply(additive_identity,X1) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_multiplicative_zero) ).
cnf(prove_distributivity,negated_conjecture,
multiply(add(x,additive_inverse(y)),z) != add(multiply(x,z),additive_inverse(multiply(y,z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c_0_11,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
associativity_for_addition ).
cnf(c_0_12,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_additive_inverse ).
cnf(c_0_13,axiom,
add(additive_identity,X1) = X1,
left_additive_identity ).
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,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_16,axiom,
add(X1,additive_identity) = X1,
right_additive_identity ).
cnf(c_0_17,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_18,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_19,axiom,
additive_inverse(additive_inverse(X1)) = X1,
additive_inverse_additive_inverse ).
cnf(c_0_20,plain,
additive_inverse(add(additive_inverse(X1),additive_inverse(X2))) = add(X2,X1),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_21,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_22,plain,
add(additive_inverse(X1),additive_inverse(X2)) = additive_inverse(add(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_25,plain,
add(multiply(X1,X2),additive_inverse(multiply(X1,add(X2,X3)))) = additive_inverse(multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,axiom,
multiply(X1,additive_identity) = additive_identity,
right_multiplicative_zero ).
cnf(c_0_27,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_28,plain,
additive_inverse(multiply(X1,additive_inverse(X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_12]),c_0_26]),c_0_27]),c_0_16]) ).
cnf(c_0_29,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_30,plain,
additive_inverse(multiply(X1,X2)) = multiply(X1,additive_inverse(X2)),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_31,plain,
add(multiply(X1,X2),multiply(add(X1,X3),additive_inverse(X2))) = multiply(X3,additive_inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_29]),c_0_30]),c_0_30]) ).
cnf(c_0_32,axiom,
multiply(additive_identity,X1) = additive_identity,
left_multiplicative_zero ).
cnf(c_0_33,plain,
multiply(additive_inverse(X1),additive_inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_12]),c_0_32]),c_0_16]) ).
cnf(c_0_34,negated_conjecture,
multiply(add(x,additive_inverse(y)),z) != add(multiply(x,z),additive_inverse(multiply(y,z))),
prove_distributivity ).
cnf(c_0_35,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_33]),c_0_30]),c_0_19]) ).
cnf(c_0_36,negated_conjecture,
add(multiply(x,z),multiply(y,additive_inverse(z))) != multiply(add(x,additive_inverse(y)),z),
inference(rw,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_37,plain,
add(multiply(X1,X2),multiply(X3,additive_inverse(X2))) = multiply(add(X1,additive_inverse(X3)),X2),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG016-6 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % 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 01:46:51 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.22/2.02 % Version : CSE_E---1.7
% 2.22/2.02 % Problem : theBenchmark.p
% 2.22/2.02 % SZS status Unsatisfiable for theBenchmark.p
% 2.22/2.02 % SZS output start CNFRefutation
% See solution above
% 2.34/2.02 % Total time : 1.372s
%------------------------------------------------------------------------------