%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO008-2 : 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 : 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 04:11:05 PM UTC 2026
% Result : Unsatisfiable 3.72s 3.17s
% Output : CNFRefutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 4 RR)
% Number of literals : 45 ( 44 equ; 3 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 87 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity2,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity2) ).
cnf(additive_inverse1,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
cnf(multiplicative_inverse1,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
cnf(additive_id1,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
cnf(multiplicative_id2,axiom,
multiply(multiplicative_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).
cnf(distributivity4,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity4) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
cnf(distributivity1,axiom,
add(multiply(X1,X2),X3) = multiply(add(X1,X3),add(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity1) ).
cnf(prove_associativity,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity) ).
cnf(c_0_11,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
distributivity2 ).
cnf(c_0_12,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
additive_inverse1 ).
cnf(c_0_13,axiom,
multiply(X1,multiplicative_identity) = X1,
multiplicative_id1 ).
cnf(c_0_14,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,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,inverse(X1)) = additive_identity,
multiplicative_inverse1 ).
cnf(c_0_16,axiom,
add(X1,additive_identity) = X1,
additive_id1 ).
cnf(c_0_17,axiom,
multiply(multiplicative_identity,X1) = X1,
multiplicative_id2 ).
cnf(c_0_18,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_19,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_20,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distributivity4 ).
cnf(c_0_21,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_17]),c_0_12]) ).
cnf(c_0_22,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_23,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_24,plain,
add(X1,multiply(X2,X1)) = multiply(X1,add(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_18]),c_0_19]) ).
cnf(c_0_25,plain,
multiply(X1,add(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_13]),c_0_21]),c_0_13]),c_0_22]),c_0_23]) ).
cnf(c_0_26,plain,
add(X1,multiply(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,plain,
add(X1,add(X1,X2)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_25]),c_0_22]) ).
cnf(c_0_28,plain,
add(X1,multiply(add(X1,X2),X3)) = add(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_27]),c_0_11]) ).
cnf(c_0_29,axiom,
add(multiply(X1,X2),X3) = multiply(add(X1,X3),add(X2,X3)),
distributivity1 ).
cnf(c_0_30,plain,
multiply(X1,add(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_22]) ).
cnf(c_0_31,plain,
multiply(add(X1,X2),add(X2,X3)) = add(X2,multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_11,c_0_22]) ).
cnf(c_0_32,plain,
add(X1,add(multiply(X1,X2),X3)) = add(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_33,plain,
multiply(X1,multiply(X2,X1)) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_26]),c_0_19]) ).
cnf(c_0_34,plain,
add(X1,add(X2,multiply(X1,X3))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_31]),c_0_25]) ).
cnf(c_0_35,plain,
add(X1,add(multiply(X2,X1),X3)) = add(X1,X3),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
add(X1,add(X2,multiply(X3,X1))) = add(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_33]) ).
cnf(c_0_37,plain,
add(add(X1,X2),add(X2,X3)) = add(add(X1,X2),X3),
inference(spm,[status(thm)],[c_0_35,c_0_30]) ).
cnf(c_0_38,plain,
add(add(X1,X2),add(X3,X1)) = add(add(X1,X2),X3),
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_39,plain,
add(add(X1,X2),X3) = add(add(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_37]),c_0_38]) ).
cnf(c_0_40,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
prove_associativity ).
cnf(c_0_41,plain,
add(add(X1,X2),X3) = add(X2,add(X3,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
add(c,add(a,b)) != add(a,add(b,c)),
inference(rw,[status(thm)],[c_0_40,c_0_22]) ).
cnf(c_0_43,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_41]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO008-2 : 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 : n013.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 10:44:26 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 3.72/3.17 % Version : CSE_E---1.7
% 3.72/3.17 % Problem : theBenchmark.p
% 3.72/3.17 % SZS status Unsatisfiable for theBenchmark.p
% 3.72/3.17 % SZS output start CNFRefutation
% See solution above
% 3.72/3.18 % Total time : 2.369s
%------------------------------------------------------------------------------