%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG008-7 : 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 : n017.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 1.34s 1.75s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of clauses : 53 ( 53 unt; 0 nHn; 12 RR)
% Number of literals : 53 ( 52 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 : 72 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_for_addition,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',associativity_for_addition) ).
cnf(right_additive_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',right_additive_inverse) ).
cnf(left_additive_identity,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',left_additive_identity) ).
cnf(right_additive_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',right_additive_identity) ).
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',distribute1) ).
cnf(boolean_ring,hypothesis,
multiply(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolean_ring) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',commutativity_for_addition) ).
cnf(distribute2,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',distribute2) ).
cnf(associativity_for_multiplication,axiom,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',associativity_for_multiplication) ).
cnf(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(prove_commutativity,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
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,axiom,
add(X1,additive_identity) = X1,
right_additive_identity ).
cnf(c_0_16,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_17,hypothesis,
multiply(X1,X1) = X1,
boolean_ring ).
cnf(c_0_18,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_19,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_12]),c_0_15]) ).
cnf(c_0_20,hypothesis,
multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_21,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_22,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_23,hypothesis,
add(X1,multiply(X1,additive_identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_13]),c_0_17]) ).
cnf(c_0_24,hypothesis,
multiply(add(X1,X2),X2) = add(X2,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_18]) ).
cnf(c_0_25,hypothesis,
multiply(X1,add(X1,X2)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_26,hypothesis,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_18]),c_0_12]) ).
cnf(c_0_27,axiom,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
associativity_for_multiplication ).
cnf(c_0_28,negated_conjecture,
multiply(a,b) = c,
a_times_b_is_c ).
cnf(c_0_29,hypothesis,
add(X1,multiply(additive_identity,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_13]),c_0_17]) ).
cnf(c_0_30,hypothesis,
add(X1,multiply(X1,additive_inverse(X1))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_12]),c_0_26]) ).
cnf(c_0_31,negated_conjecture,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,hypothesis,
multiply(add(X1,X2),X1) = add(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_33,hypothesis,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_29]),c_0_18]),c_0_12]) ).
cnf(c_0_34,hypothesis,
multiply(additive_inverse(X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_30]),c_0_15]),c_0_19]) ).
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_27,c_0_20]) ).
cnf(c_0_36,hypothesis,
multiply(c,b) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_17]),c_0_28]) ).
cnf(c_0_37,hypothesis,
add(X1,X1) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_12]),c_0_33]),c_0_34]) ).
cnf(c_0_38,hypothesis,
multiply(X1,multiply(X2,multiply(X1,X2))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
cnf(c_0_39,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_37]),c_0_33]) ).
cnf(c_0_40,hypothesis,
add(X1,add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_37]),c_0_13]) ).
cnf(c_0_41,hypothesis,
add(c,multiply(b,c)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_26]),c_0_24]) ).
cnf(c_0_42,hypothesis,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_43,hypothesis,
multiply(b,c) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_15]) ).
cnf(c_0_44,hypothesis,
multiply(add(X1,multiply(X2,X1)),X3) = multiply(add(X2,X1),multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_45,negated_conjecture,
multiply(a,c) = c,
inference(spm,[status(thm)],[c_0_42,c_0_28]) ).
cnf(c_0_46,negated_conjecture,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(spm,[status(thm)],[c_0_38,c_0_31]) ).
cnf(c_0_47,hypothesis,
multiply(b,multiply(c,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_27,c_0_43]) ).
cnf(c_0_48,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_44,c_0_45]),c_0_37]),c_0_33]) ).
cnf(c_0_49,negated_conjecture,
multiply(c,a) = multiply(b,a),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,hypothesis,
add(c,multiply(b,a)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_48]),c_0_26]),c_0_20]),c_0_49]) ).
cnf(c_0_51,negated_conjecture,
multiply(b,a) != c,
prove_commutativity ).
cnf(c_0_52,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_50]),c_0_15]),c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG008-7 : 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
% 0.16/0.33 % Computer : n017.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 01:44:28 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.34/1.75 % Version : CSE_E---1.7
% 1.34/1.75 % Problem : theBenchmark.p
% 1.34/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 1.34/1.75 % SZS output start CNFRefutation
% See solution above
% 1.34/1.75 % Total time : 1.371s
%------------------------------------------------------------------------------