%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG037-1 : 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 : n012.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 05:05:05 PM UTC 2026
% Result : Unsatisfiable 1.23s 1.70s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 63 ( 35 unt; 0 nHn; 40 RR)
% Number of literals : 115 ( 18 equ; 54 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 141 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(addition_is_well_defined,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
cnf(associativity_of_addition2,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(distributivity1,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity1) ).
cnf(a_times_b,hypothesis,
product(a,b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
cnf(commutativity_of_addition,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
cnf(a_inverse_times_b,hypothesis,
product(a,additive_inverse(b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(associativity_of_addition1,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition1) ).
cnf(prove_sum_is_additive_identity,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sum_is_additive_identity) ).
cnf(c_0_13,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_14,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_15,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2 ).
cnf(c_0_16,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_17,plain,
( X1 = X2
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_19,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ sum(X4,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_22,plain,
( sum(X1,X2,X3)
| ~ sum(X3,additive_inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_20]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_24,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X5)
| ~ sum(X2,X4,X6)
| ~ product(X1,X6,X7) ),
distributivity1 ).
cnf(c_0_25,hypothesis,
product(a,b,d),
a_times_b ).
cnf(c_0_26,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_27,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_28,plain,
sum(additive_identity,X1,additive_inverse(additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_29,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_30,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_31,hypothesis,
( sum(X1,X2,d)
| ~ product(a,X3,X2)
| ~ product(a,X4,X1)
| ~ sum(X4,X3,b) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,hypothesis,
product(a,additive_inverse(b),c),
a_inverse_times_b ).
cnf(c_0_33,plain,
( X1 = X2
| ~ sum(add(X2,additive_inverse(X3)),X3,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_26]) ).
cnf(c_0_34,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_35,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_18]) ).
cnf(c_0_36,hypothesis,
( sum(X1,c,d)
| ~ product(a,X2,X1)
| ~ sum(X2,additive_inverse(b),b) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_38,plain,
( X1 = X2
| ~ sum(add(X2,X3),additive_inverse(X3),X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_27,c_0_35]) ).
cnf(c_0_40,hypothesis,
( sum(multiply(a,X1),c,d)
| ~ sum(X1,additive_inverse(b),b) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
sum(add(additive_inverse(X1),X2),X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_35]) ).
cnf(c_0_42,axiom,
( sum(X1,X5,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X3,X4,X6) ),
associativity_of_addition1 ).
cnf(c_0_43,plain,
( sum(X1,additive_inverse(X2),X3)
| ~ sum(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_44,plain,
( sum(X1,X2,multiply(X3,X4))
| ~ product(X3,X5,X2)
| ~ product(X3,X6,X1)
| ~ sum(X6,X5,X4) ),
inference(spm,[status(thm)],[c_0_24,c_0_37]) ).
cnf(c_0_45,plain,
( X1 = X2
| ~ sum(add(X3,X2),additive_inverse(X3),X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,hypothesis,
sum(multiply(a,add(b,b)),c,d),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_34]) ).
cnf(c_0_47,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X1,X3,additive_inverse(X4))
| ~ sum(X3,X4,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_16]) ).
cnf(c_0_48,plain,
sum(add(X1,X2),additive_inverse(X1),X2),
inference(spm,[status(thm)],[c_0_43,c_0_35]) ).
cnf(c_0_49,hypothesis,
( sum(X1,d,multiply(a,X2))
| ~ product(a,X3,X1)
| ~ sum(X3,b,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_25]) ).
cnf(c_0_50,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_18]),c_0_39]) ).
cnf(c_0_51,hypothesis,
add(c,multiply(a,add(b,b))) = d,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_46]),c_0_39]) ).
cnf(c_0_52,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_26]),c_0_39]) ).
cnf(c_0_53,plain,
( sum(X1,X2,additive_identity)
| ~ sum(X1,add(X3,X2),X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_34]) ).
cnf(c_0_54,hypothesis,
( sum(d,d,multiply(a,X1))
| ~ sum(b,b,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_25]) ).
cnf(c_0_55,hypothesis,
multiply(a,add(b,b)) = add(d,additive_inverse(c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_39]) ).
cnf(c_0_56,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_52,c_0_34]) ).
cnf(c_0_57,plain,
( sum(X1,add(X2,additive_inverse(X3)),additive_identity)
| ~ sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_52]) ).
cnf(c_0_58,hypothesis,
sum(d,d,add(d,additive_inverse(c))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_18]),c_0_55]) ).
cnf(c_0_59,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_56]),c_0_39]) ).
cnf(c_0_60,hypothesis,
sum(d,c,additive_identity),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_34]) ).
cnf(c_0_61,negated_conjecture,
~ sum(c,d,additive_identity),
prove_sum_is_additive_identity ).
cnf(c_0_62,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_60]),c_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : RNG037-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.10 % 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
% 0.06/0.30 % Computer : n012.cluster.edu
% 0.06/0.30 % Model : x86_64 x86_64
% 0.06/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.30 % Memory : 8042.1875MB
% 0.06/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.30 % CPULimit : 300
% 0.06/0.30 % WCLimit : 300
% 0.06/0.30 % DateTime : Tue May 5 01:47:01 EDT 2026
% 0.06/0.30 % CPUTime :
% 0.06/0.31 % start to proof: theBenchmark
% 1.23/1.70 % Version : CSE_E---1.7
% 1.23/1.70 % Problem : theBenchmark.p
% 1.23/1.70 % SZS status Unsatisfiable for theBenchmark.p
% 1.23/1.70 % SZS output start CNFRefutation
% See solution above
% 1.23/1.70 % Total time : 1.361s
%------------------------------------------------------------------------------