%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG008-3 : 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 : n009.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 05:04:58 PM UTC 2026
% Result : Unsatisfiable 1.27s 1.73s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 12 RR)
% Number of literals : 52 ( 51 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 : 71 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distribute2,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',distribute2) ).
cnf(boolean_ring,hypothesis,
multiply(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',boolean_ring) ).
cnf(commutative_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',commutative_addition) ).
cnf(associative_multiplication,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',associative_multiplication) ).
cnf(multiply_additive_inverse2,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse2) ).
cnf(multiply_additive_inverse1,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse1) ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',additive_inverse_additive_inverse) ).
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',distribute1) ).
cnf(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(right_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
cnf(multiply_additive_id2,axiom,
multiply(additive_identity,X1) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_id2) ).
cnf(associative_addition,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',associative_addition) ).
cnf(left_identity,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',left_identity) ).
cnf(multiply_additive_id1,axiom,
multiply(X1,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_id1) ).
cnf(right_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(prove_commutativity,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c_0_16,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_17,hypothesis,
multiply(X1,X1) = X1,
boolean_ring ).
cnf(c_0_18,axiom,
add(X1,X2) = add(X2,X1),
commutative_addition ).
cnf(c_0_19,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associative_multiplication ).
cnf(c_0_20,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
multiply_additive_inverse2 ).
cnf(c_0_21,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
multiply_additive_inverse1 ).
cnf(c_0_22,axiom,
additive_inverse(additive_inverse(X1)) = X1,
additive_inverse_additive_inverse ).
cnf(c_0_23,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_24,negated_conjecture,
multiply(a,b) = c,
a_times_b_is_c ).
cnf(c_0_25,hypothesis,
multiply(add(X1,X2),X2) = add(X2,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_26,hypothesis,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_27,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_inverse ).
cnf(c_0_28,hypothesis,
additive_inverse(X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_21]),c_0_17]),c_0_22]) ).
cnf(c_0_29,hypothesis,
multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_17]),c_0_18]) ).
cnf(c_0_30,negated_conjecture,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
cnf(c_0_31,hypothesis,
multiply(add(X1,multiply(X2,X1)),X3) = multiply(add(X2,X1),multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_32,negated_conjecture,
multiply(a,c) = c,
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_33,plain,
add(X1,X1) = additive_identity,
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,axiom,
multiply(additive_identity,X1) = additive_identity,
multiply_additive_id2 ).
cnf(c_0_35,hypothesis,
multiply(add(X1,multiply(X1,X2)),X3) = multiply(X1,multiply(add(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_19,c_0_29]) ).
cnf(c_0_36,hypothesis,
multiply(c,b) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_17]),c_0_24]) ).
cnf(c_0_37,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associative_addition ).
cnf(c_0_38,axiom,
add(additive_identity,X1) = X1,
left_identity ).
cnf(c_0_39,hypothesis,
multiply(X1,multiply(X2,multiply(X1,X2))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_40,negated_conjecture,
multiply(add(a,c),multiply(c,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34]) ).
cnf(c_0_41,axiom,
multiply(X1,additive_identity) = additive_identity,
multiply_additive_id1 ).
cnf(c_0_42,hypothesis,
multiply(c,multiply(add(b,c),X1)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_33]),c_0_34]) ).
cnf(c_0_43,plain,
add(X1,add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_33]),c_0_38]) ).
cnf(c_0_44,hypothesis,
add(c,multiply(c,a)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_29]) ).
cnf(c_0_45,axiom,
add(X1,additive_identity) = X1,
right_identity ).
cnf(c_0_46,hypothesis,
add(c,multiply(b,c)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_42]),c_0_41]),c_0_25]) ).
cnf(c_0_47,negated_conjecture,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(spm,[status(thm)],[c_0_39,c_0_30]) ).
cnf(c_0_48,hypothesis,
multiply(c,a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_49,hypothesis,
multiply(b,c) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_46]),c_0_45]) ).
cnf(c_0_50,negated_conjecture,
multiply(b,a) != c,
prove_commutativity ).
cnf(c_0_51,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG008-3 : 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
% 0.16/0.33 % Computer : n009.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 01:45:41 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.27/1.73 % Version : CSE_E---1.7
% 1.27/1.73 % Problem : theBenchmark.p
% 1.27/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/1.73 % SZS output start CNFRefutation
% See solution above
% 1.27/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------