%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG029-3 : TPTP v9.2.1. Bugfixed v2.4.0.
% 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 : n023.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 05:05:03 PM UTC 2026
% Result : Unsatisfiable 73.30s 42.95s
% Output : CNFRefutation 73.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 43 ( 39 unt; 0 nHn; 7 RR)
% Number of literals : 47 ( 46 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 109 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associator_skew_symmetry2,axiom,
associator(X1,X2,X3) = additive_inverse(associator(X3,X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator_skew_symmetry2) ).
cnf(associator,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator) ).
cnf(associator_skew_symmetry1,axiom,
associator(X1,X2,X3) = additive_inverse(associator(X2,X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associator_skew_symmetry1) ).
cnf(inverse_product2,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',inverse_product2) ).
cnf(inverse_product1,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',inverse_product1) ).
cnf(sum_of_inverses,axiom,
additive_inverse(add(X1,X2)) = add(additive_inverse(X1),additive_inverse(X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',sum_of_inverses) ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',additive_inverse_additive_inverse) ).
cnf(left_cancellation_for_addition,axiom,
( X1 = X3
| add(X1,X2) != add(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',left_cancellation_for_addition) ).
cnf(multiply_over_add1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',multiply_over_add1) ).
cnf(right_moufang,hypothesis,
multiply(X1,multiply(X2,multiply(X3,X2))) = multiply(multiply(multiply(X1,X2),X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_moufang) ).
cnf(left_moufang,hypothesis,
multiply(multiply(X1,multiply(X2,X1)),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_moufang) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG004-0.ax',commutativity_for_addition) ).
cnf(prove_middle_law,negated_conjecture,
multiply(multiply(cx,cy),multiply(cz,cx)) != multiply(cx,multiply(multiply(cy,cz),cx)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_middle_law) ).
cnf(c_0_13,axiom,
associator(X1,X2,X3) = additive_inverse(associator(X3,X2,X1)),
associator_skew_symmetry2 ).
cnf(c_0_14,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
associator ).
cnf(c_0_15,axiom,
associator(X1,X2,X3) = additive_inverse(associator(X2,X1,X3)),
associator_skew_symmetry1 ).
cnf(c_0_16,plain,
add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))) = additive_inverse(add(multiply(multiply(X3,X2),X1),additive_inverse(multiply(X3,multiply(X2,X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_17,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
inverse_product2 ).
cnf(c_0_18,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
inverse_product1 ).
cnf(c_0_19,plain,
add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))) = additive_inverse(add(multiply(multiply(X2,X1),X3),additive_inverse(multiply(X2,multiply(X1,X3))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_14]),c_0_14]) ).
cnf(c_0_20,plain,
additive_inverse(add(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,additive_inverse(X3))))) = add(multiply(multiply(X3,X2),X1),multiply(X3,multiply(X2,additive_inverse(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]),c_0_17]),c_0_17]) ).
cnf(c_0_21,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(rw,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_22,axiom,
additive_inverse(add(X1,X2)) = add(additive_inverse(X1),additive_inverse(X2)),
sum_of_inverses ).
cnf(c_0_23,axiom,
additive_inverse(additive_inverse(X1)) = X1,
additive_inverse_additive_inverse ).
cnf(c_0_24,axiom,
( X1 = X3
| add(X1,X2) != add(X3,X2) ),
left_cancellation_for_addition ).
cnf(c_0_25,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
multiply_over_add1 ).
cnf(c_0_26,hypothesis,
multiply(X1,multiply(X2,multiply(X3,X2))) = multiply(multiply(multiply(X1,X2),X3),X2),
right_moufang ).
cnf(c_0_27,plain,
add(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,additive_inverse(X3)))) = add(multiply(multiply(X2,X3),X1),multiply(X2,multiply(X3,additive_inverse(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_17]),c_0_17]),c_0_20]),c_0_17]),c_0_17]) ).
cnf(c_0_28,hypothesis,
multiply(multiply(X1,multiply(X2,X1)),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
left_moufang ).
cnf(c_0_29,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_30,plain,
multiply(multiply(X1,additive_inverse(X2)),X3) = multiply(multiply(X1,X2),additive_inverse(X3)),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_31,plain,
additive_inverse(add(X1,additive_inverse(X2))) = add(additive_inverse(X1),X2),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_32,plain,
( X1 = multiply(X2,X3)
| add(X1,multiply(X2,X4)) != multiply(X2,add(X3,X4)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,hypothesis,
additive_inverse(add(multiply(X1,multiply(X2,multiply(X3,X2))),multiply(multiply(X1,X2),multiply(X3,additive_inverse(X2))))) = add(multiply(multiply(X2,X3),multiply(X1,X2)),multiply(X2,multiply(X3,multiply(X1,additive_inverse(X2))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_26]),c_0_17]) ).
cnf(c_0_34,hypothesis,
add(multiply(X1,multiply(X2,multiply(X3,X2))),multiply(multiply(X1,X2),multiply(X3,additive_inverse(X2)))) = multiply(X2,add(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),additive_inverse(X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_26]),c_0_28]),c_0_25]) ).
cnf(c_0_35,plain,
additive_inverse(add(multiply(X1,multiply(X2,X3)),multiply(multiply(X1,X2),additive_inverse(X3)))) = add(multiply(X3,multiply(X2,X1)),multiply(multiply(X3,X2),additive_inverse(X1))),
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_20,c_0_23]),c_0_21]),c_0_21]),c_0_17]),c_0_23]),c_0_29]),c_0_30]),c_0_29]) ).
cnf(c_0_36,plain,
additive_inverse(add(X1,multiply(X2,additive_inverse(X3)))) = add(additive_inverse(X1),multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_37,plain,
( X1 = multiply(X2,multiply(multiply(X3,X4),X5))
| add(X1,multiply(X2,multiply(X3,multiply(X4,additive_inverse(X5))))) != multiply(X2,add(multiply(multiply(X4,X5),X3),multiply(X4,multiply(X5,additive_inverse(X3))))) ),
inference(spm,[status(thm)],[c_0_32,c_0_27]) ).
cnf(c_0_38,hypothesis,
add(multiply(multiply(X1,X2),multiply(X3,X1)),multiply(X1,multiply(X2,multiply(X3,additive_inverse(X1))))) = multiply(X1,add(multiply(X2,multiply(X1,X3)),multiply(multiply(X2,X1),additive_inverse(X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_17]),c_0_35]) ).
cnf(c_0_39,plain,
add(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,additive_inverse(X3)))) = add(multiply(X3,multiply(X2,X1)),multiply(multiply(X3,X2),additive_inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_17]),c_0_17]),c_0_29]) ).
cnf(c_0_40,negated_conjecture,
multiply(multiply(cx,cy),multiply(cz,cx)) != multiply(cx,multiply(multiply(cy,cz),cx)),
prove_middle_law ).
cnf(c_0_41,hypothesis,
multiply(multiply(X1,X2),multiply(X3,X1)) = multiply(X1,multiply(multiply(X2,X3),X1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG029-3 : TPTP v9.2.1. Bugfixed v2.4.0.
% 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 : n023.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 01:48:23 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 73.30/42.95 % Version : CSE_E---1.7
% 73.30/42.95 % Problem : theBenchmark.p
% 73.30/42.95 % SZS status Unsatisfiable for theBenchmark.p
% 73.30/42.95 % SZS output start CNFRefutation
% See solution above
% 73.60/43.23 % Total time : 32.268s
%------------------------------------------------------------------------------