%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG025-1 : 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 : 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 215.34s 64.61s
% Output : CNFRefutation 215.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of clauses : 43 ( 40 unt; 0 nHn; 6 RR)
% Number of literals : 46 ( 45 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply_over_add2,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',multiply_over_add2) ).
cnf(right_alternative,axiom,
multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',right_alternative) ).
cnf(add_inverse,axiom,
add(additive_inverse(X1),X1) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',add_inverse) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',commutativity_for_addition) ).
cnf(left_alternative,axiom,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',left_alternative) ).
cnf(associativity_for_addition,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',associativity_for_addition) ).
cnf(left_additive_identity,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',left_additive_identity) ).
cnf(inverse_product1,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',inverse_product1) ).
cnf(inverse_product2,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',inverse_product2) ).
cnf(multiply_over_add1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',multiply_over_add1) ).
cnf(sum_of_inverses,axiom,
additive_inverse(add(X1,X2)) = add(additive_inverse(X1),additive_inverse(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',sum_of_inverses) ).
cnf(right_cancellation_for_addition,axiom,
( X2 = X3
| add(X1,X2) != add(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',right_cancellation_for_addition) ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG004-0.ax',additive_inverse_additive_inverse) ).
cnf(prove_middle_law,negated_conjecture,
multiply(multiply(cy,cx),cy) != multiply(cy,multiply(cx,cy)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_middle_law) ).
cnf(c_0_14,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
multiply_over_add2 ).
cnf(c_0_15,axiom,
multiply(multiply(X1,X2),X2) = multiply(X1,multiply(X2,X2)),
right_alternative ).
cnf(c_0_16,axiom,
add(additive_inverse(X1),X1) = additive_identity,
add_inverse ).
cnf(c_0_17,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_18,plain,
add(multiply(X1,X2),multiply(X3,multiply(X2,X2))) = multiply(add(X1,multiply(X3,X2)),X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,axiom,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
left_alternative ).
cnf(c_0_20,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
associativity_for_addition ).
cnf(c_0_21,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,axiom,
add(additive_identity,X1) = X1,
left_additive_identity ).
cnf(c_0_23,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
inverse_product1 ).
cnf(c_0_24,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
inverse_product2 ).
cnf(c_0_25,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
multiply_over_add1 ).
cnf(c_0_26,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_18,c_0_19]) ).
cnf(c_0_27,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_28,axiom,
additive_inverse(add(X1,X2)) = add(additive_inverse(X1),additive_inverse(X2)),
sum_of_inverses ).
cnf(c_0_29,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,axiom,
( X2 = X3
| add(X1,X2) != add(X1,X3) ),
right_cancellation_for_addition ).
cnf(c_0_31,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_24,c_0_15]),c_0_24]),c_0_24]) ).
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_25,c_0_26]),c_0_25]),c_0_14]) ).
cnf(c_0_33,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
multiply(multiply(X1,additive_inverse(X2)),X3) = multiply(multiply(X1,X2),additive_inverse(X3)),
inference(spm,[status(thm)],[c_0_29,c_0_24]) ).
cnf(c_0_35,axiom,
additive_inverse(additive_inverse(X1)) = X1,
additive_inverse_additive_inverse ).
cnf(c_0_36,plain,
( X1 = X2
| add(X3,X1) != add(X2,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_17]) ).
cnf(c_0_37,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_25,c_0_31]) ).
cnf(c_0_38,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_32,c_0_33]),c_0_34]),c_0_35]),c_0_29]),c_0_35]) ).
cnf(c_0_39,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_27])]) ).
cnf(c_0_40,negated_conjecture,
multiply(multiply(cy,cx),cy) != multiply(cy,multiply(cx,cy)),
prove_middle_law ).
cnf(c_0_41,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(spm,[status(thm)],[c_0_37,c_0_38]),c_0_25]),c_0_25]),c_0_39]),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 : RNG025-1 : 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
% 0.14/0.32 % 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 01:46:08 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 215.34/64.61 % Version : CSE_E---1.7
% 215.34/64.61 % Problem : theBenchmark.p
% 215.34/64.61 % SZS status Unsatisfiable for theBenchmark.p
% 215.34/64.61 % SZS output start CNFRefutation
% See solution above
% 215.64/64.95 % Total time : 51.690s
%------------------------------------------------------------------------------