%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG026-7 : 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 : n007.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 05:05:02 PM UTC 2026
% Result : Unsatisfiable 1.66s 1.84s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of clauses : 49 ( 49 unt; 0 nHn; 7 RR)
% Number of literals : 49 ( 48 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 95 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_for_addition,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
cnf(right_additive_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).
cnf(left_additive_identity,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).
cnf(prove_teichmuller_identity,negated_conjecture,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_teichmuller_identity) ).
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/Axioms/RNG003-0.ax',associator) ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',additive_inverse_additive_inverse) ).
cnf(inverse_product2,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product2) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',distribute1) ).
cnf(inverse_product1,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product1) ).
cnf(distributivity_of_difference2,axiom,
multiply(add(X1,additive_inverse(X2)),X3) = add(multiply(X1,X3),additive_inverse(multiply(X2,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_of_difference2) ).
cnf(right_multiplicative_zero,axiom,
multiply(X1,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/RNG003-0.ax',distribute2) ).
cnf(left_multiplicative_zero,axiom,
multiply(additive_identity,X1) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',left_multiplicative_zero) ).
cnf(right_additive_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
cnf(c_0_15,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
associativity_for_addition ).
cnf(c_0_16,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_additive_inverse ).
cnf(c_0_17,axiom,
add(additive_identity,X1) = X1,
left_additive_identity ).
cnf(c_0_18,negated_conjecture,
add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
prove_teichmuller_identity ).
cnf(c_0_19,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
associator ).
cnf(c_0_20,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,axiom,
additive_inverse(additive_inverse(X1)) = X1,
additive_inverse_additive_inverse ).
cnf(c_0_22,negated_conjecture,
add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),additive_inverse(add(add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d)))))),multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d)))) != additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_23,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
inverse_product2 ).
cnf(c_0_24,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_25,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
add(multiply(multiply(multiply(a,b),c),d),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),add(multiply(multiply(a,b),multiply(c,d)),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),additive_inverse(add(multiply(multiply(a,multiply(b,c)),d),add(multiply(a,multiply(multiply(b,c),additive_inverse(d))),add(multiply(a,add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))),multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d))))))))) != additive_identity,
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(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_15]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_15]),c_0_23]),c_0_23]),c_0_15]),c_0_15]),c_0_15]),c_0_15]),c_0_15]) ).
cnf(c_0_27,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_28,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_29,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
inverse_product1 ).
cnf(c_0_30,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_31,axiom,
multiply(add(X1,additive_inverse(X2)),X3) = add(multiply(X1,X3),additive_inverse(multiply(X2,X3))),
distributivity_of_difference2 ).
cnf(c_0_32,negated_conjecture,
add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(multiply(a,multiply(b,c)),d),add(multiply(a,multiply(multiply(b,c),additive_inverse(d))),add(multiply(a,add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))),multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d))))))))) != additive_identity,
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(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)],[c_0_26,c_0_27]),c_0_15]),c_0_24]),c_0_27]),c_0_15]),c_0_15]),c_0_24]),c_0_27]),c_0_24]),c_0_27]),c_0_15]),c_0_24]),c_0_27]),c_0_24]) ).
cnf(c_0_33,plain,
add(multiply(X1,X2),add(multiply(X1,X3),X4)) = add(multiply(X1,add(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_15,c_0_28]) ).
cnf(c_0_34,axiom,
multiply(X1,additive_identity) = additive_identity,
right_multiplicative_zero ).
cnf(c_0_35,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_36,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(rw,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_37,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_24]) ).
cnf(c_0_38,plain,
add(X1,add(X2,X3)) = add(X3,add(X2,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_39,plain,
add(multiply(X1,X2),multiply(X3,additive_inverse(X2))) = multiply(add(X1,additive_inverse(X3)),X2),
inference(rw,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_40,negated_conjecture,
add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(multiply(a,multiply(b,c)),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d)))))))) != additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]),c_0_24]),c_0_16]),c_0_34]),c_0_17]) ).
cnf(c_0_41,plain,
add(multiply(X1,X2),add(X3,multiply(X4,X2))) = add(X3,multiply(add(X4,X1),X2)),
inference(spm,[status(thm)],[c_0_27,c_0_35]) ).
cnf(c_0_42,plain,
add(multiply(X1,additive_inverse(X2)),multiply(X3,X2)) = multiply(add(additive_inverse(X1),X3),X2),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,axiom,
multiply(additive_identity,X1) = additive_identity,
left_multiplicative_zero ).
cnf(c_0_44,axiom,
add(X1,additive_identity) = X1,
right_additive_identity ).
cnf(c_0_45,plain,
add(X1,add(X2,additive_inverse(add(X3,X1)))) = add(X2,additive_inverse(X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_37]),c_0_38]) ).
cnf(c_0_46,plain,
add(multiply(X1,X2),add(X3,multiply(X1,X4))) = add(X3,multiply(X1,add(X4,X2))),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_47,plain,
add(multiply(X1,multiply(X2,X3)),multiply(X4,multiply(X2,additive_inverse(X3)))) = multiply(add(X1,additive_inverse(X4)),multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_39,c_0_23]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[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(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(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_15]),c_0_28]),c_0_42]),c_0_24]),c_0_16]),c_0_43]),c_0_34]),c_0_44]),c_0_24]),c_0_45]),c_0_23]),c_0_46]),c_0_24]),c_0_16]),c_0_34]),c_0_44]),c_0_47]),c_0_23]),c_0_28]),c_0_16]),c_0_34]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG026-7 : 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
% 0.14/0.32 % Computer : n007.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:45:54 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.66/1.84 % Version : CSE_E---1.7
% 1.66/1.84 % Problem : theBenchmark.p
% 1.66/1.84 % SZS status Unsatisfiable for theBenchmark.p
% 1.66/1.84 % SZS output start CNFRefutation
% See solution above
% 1.66/1.85 % Total time : 1.371s
%------------------------------------------------------------------------------