%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG025-6 : 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 : n011.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 7.23s 5.56s
% Output : CNFRefutation 7.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 44 ( 44 unt; 0 nHn; 6 RR)
% Number of literals : 44 ( 43 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 : 79 ( 2 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(right_additive_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).
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(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(right_alternative,axiom,
multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_alternative) ).
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(left_alternative,axiom,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',left_alternative) ).
cnf(right_multiplicative_zero,axiom,
multiply(X1,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',right_multiplicative_zero) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).
cnf(prove_flexible_law,negated_conjecture,
associator(x,y,x) != additive_identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/RNG003-0.ax',associator) ).
cnf(c_0_13,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
associativity_for_addition ).
cnf(c_0_14,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_additive_inverse ).
cnf(c_0_15,axiom,
add(additive_identity,X1) = X1,
left_additive_identity ).
cnf(c_0_16,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_17,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_18,axiom,
add(X1,additive_identity) = X1,
right_additive_identity ).
cnf(c_0_19,plain,
add(X1,additive_inverse(add(additive_inverse(X2),X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_20,axiom,
additive_inverse(additive_inverse(X1)) = X1,
additive_inverse_additive_inverse ).
cnf(c_0_21,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_22,axiom,
multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
right_alternative ).
cnf(c_0_23,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_25,plain,
add(multiply(X1,X2),multiply(X3,multiply(X2,X2))) = multiply(add(X1,multiply(X3,X2)),X2),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
left_alternative ).
cnf(c_0_27,plain,
add(multiply(X1,X2),additive_inverse(multiply(X1,add(X3,X2)))) = additive_inverse(multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,axiom,
multiply(X1,additive_identity) = additive_identity,
right_multiplicative_zero ).
cnf(c_0_29,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_30,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_25,c_0_26]) ).
cnf(c_0_31,plain,
additive_inverse(multiply(X1,X2)) = multiply(X1,additive_inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_14]),c_0_28]),c_0_29]),c_0_18]) ).
cnf(c_0_32,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_24,c_0_30]),c_0_24]),c_0_21]) ).
cnf(c_0_33,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_34,negated_conjecture,
associator(x,y,x) != additive_identity,
prove_flexible_law ).
cnf(c_0_35,axiom,
associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
associator ).
cnf(c_0_36,plain,
add(multiply(multiply(X1,X2),X3),multiply(X1,multiply(X2,X2))) = multiply(multiply(X1,X2),add(X3,X2)),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_37,plain,
multiply(multiply(X1,add(X1,X2)),additive_inverse(X2)) = multiply(X1,multiply(add(X1,X2),additive_inverse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_31]),c_0_31]) ).
cnf(c_0_38,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(spm,[status(thm)],[c_0_33,c_0_13]) ).
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_34,c_0_35]) ).
cnf(c_0_40,plain,
multiply(multiply(X1,add(X1,X2)),X1) = multiply(X1,multiply(add(X1,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_36,c_0_37]),c_0_24]),c_0_24]),c_0_38]),c_0_16]),c_0_38]),c_0_16]) ).
cnf(c_0_41,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_31]),c_0_31]) ).
cnf(c_0_42,plain,
multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_40,c_0_16]) ).
cnf(c_0_43,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)],[c_0_41,c_0_42]),c_0_24]),c_0_24]),c_0_14]),c_0_28]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG025-6 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % 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 : n011.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 01:46:17 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 7.23/5.56 % Version : CSE_E---1.7
% 7.23/5.56 % Problem : theBenchmark.p
% 7.23/5.56 % SZS status Unsatisfiable for theBenchmark.p
% 7.23/5.56 % SZS output start CNFRefutation
% See solution above
% 7.23/5.58 % Total time : 4.371s
%------------------------------------------------------------------------------