%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG025-7 : 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 : n025.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 41.38s 30.86s
% Output : CNFRefutation 41.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of clauses : 49 ( 49 unt; 0 nHn; 5 RR)
% Number of literals : 49 ( 48 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 98 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_for_addition,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).
cnf(right_additive_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).
cnf(left_additive_identity,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).
cnf(distribute2,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute2) ).
cnf(right_alternative,axiom,
multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_alternative) ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',additive_inverse_additive_inverse) ).
cnf(left_alternative,axiom,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_alternative) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
cnf(inverse_product1,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product1) ).
cnf(inverse_product2,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product2) ).
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute1) ).
cnf(prove_flexible_law,negated_conjecture,
associator(x,y,x) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_flexible_law) ).
cnf(associator,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associator) ).
cnf(distributivity_of_difference2,axiom,
multiply(add(X1,additive_inverse(X2)),X3) = add(multiply(X1,X3),additive_inverse(multiply(X2,X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_of_difference2) ).
cnf(left_multiplicative_zero,axiom,
multiply(additive_identity,X1) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_multiplicative_zero) ).
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,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_19,axiom,
multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
right_alternative ).
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,plain,
add(multiply(X1,X2),multiply(X3,multiply(X2,X2))) = multiply(add(X1,multiply(X3,X2)),X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,axiom,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
left_alternative ).
cnf(c_0_24,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_26,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
inverse_product1 ).
cnf(c_0_27,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
inverse_product2 ).
cnf(c_0_28,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_29,plain,
add(multiply(X1,multiply(X1,X2)),multiply(X3,multiply(X2,X2))) = multiply(add(multiply(X1,X1),multiply(X3,X2)),X2),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
associator(x,y,x) != additive_identity,
prove_flexible_law ).
cnf(c_0_33,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
associator ).
cnf(c_0_34,plain,
multiply(multiply(X1,X2),additive_inverse(X2)) = multiply(X1,multiply(X2,additive_inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_27]),c_0_27]) ).
cnf(c_0_35,plain,
multiply(multiply(X1,add(X1,X2)),X2) = multiply(X1,multiply(add(X1,X2),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_28]),c_0_18]) ).
cnf(c_0_36,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_30]),c_0_25]) ).
cnf(c_0_37,plain,
multiply(multiply(X1,additive_inverse(X2)),X3) = multiply(multiply(X1,X2),additive_inverse(X3)),
inference(spm,[status(thm)],[c_0_31,c_0_27]) ).
cnf(c_0_38,axiom,
multiply(add(X1,additive_inverse(X2)),X3) = add(multiply(X1,X3),additive_inverse(multiply(X2,X3))),
distributivity_of_difference2 ).
cnf(c_0_39,negated_conjecture,
add(multiply(multiply(x,y),x),additive_inverse(multiply(x,multiply(y,x)))) != additive_identity,
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
add(multiply(X1,multiply(X2,additive_inverse(X2))),multiply(multiply(X1,X2),X3)) = multiply(multiply(X1,X2),add(additive_inverse(X2),X3)),
inference(spm,[status(thm)],[c_0_28,c_0_34]) ).
cnf(c_0_41,plain,
multiply(multiply(X1,X2),add(X1,X2)) = multiply(X1,multiply(X2,add(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_21]),c_0_31]),c_0_21]) ).
cnf(c_0_42,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_43,plain,
add(multiply(X1,X2),multiply(X3,additive_inverse(X2))) = multiply(add(X1,additive_inverse(X3)),X2),
inference(rw,[status(thm)],[c_0_38,c_0_27]) ).
cnf(c_0_44,negated_conjecture,
add(multiply(multiply(x,y),x),multiply(x,multiply(y,additive_inverse(x)))) != additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_27]),c_0_27]) ).
cnf(c_0_45,plain,
multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,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(spm,[status(thm)],[c_0_40,c_0_41]),c_0_28]),c_0_28]),c_0_42]),c_0_20]),c_0_42]),c_0_20]) ).
cnf(c_0_46,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_43,c_0_27]) ).
cnf(c_0_47,axiom,
multiply(additive_identity,X1) = additive_identity,
left_multiplicative_zero ).
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)],[c_0_44,c_0_45]),c_0_46]),c_0_16]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG025-7 : 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
% 0.15/0.32 % Computer : n025.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 01:46:43 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 41.38/30.86 % Version : CSE_E---1.7
% 41.38/30.86 % Problem : theBenchmark.p
% 41.38/30.86 % SZS status Unsatisfiable for theBenchmark.p
% 41.38/30.86 % SZS output start CNFRefutation
% See solution above
% 41.59/31.04 % Total time : 24.589s
%------------------------------------------------------------------------------