%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG004-1 : 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 : n029.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 05:04:56 PM UTC 2026
% Result : Unsatisfiable 1.56s 1.83s
% Output : CNFRefutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 15
% Syntax : Number of clauses : 74 ( 45 unt; 0 nHn; 49 RR)
% Number of literals : 140 ( 26 equ; 68 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 : 149 ( 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(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(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,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_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(distributivity4,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity4) ).
cnf(a_inverse_times_b_inverse,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).
cnf(distributivity3,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity3) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
cnf(prove_c_equals_d,negated_conjecture,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(c_0_15,axiom,
( X3 = X4
| ~ sum(X1,X2,X3)
| ~ sum(X1,X2,X4) ),
addition_is_well_defined ).
cnf(c_0_16,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_17,axiom,
( sum(X3,X4,X6)
| ~ sum(X1,X2,X3)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X5,X6) ),
associativity_of_addition2 ).
cnf(c_0_18,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_19,plain,
( X1 = X2
| ~ sum(X2,additive_identity,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_21,plain,
( sum(X1,X2,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| ~ sum(X4,additive_identity,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,axiom,
( sum(X2,X1,X3)
| ~ sum(X1,X2,X3) ),
commutativity_of_addition ).
cnf(c_0_24,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_25,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_26,hypothesis,
product(a,b,c),
a_times_b ).
cnf(c_0_27,plain,
( sum(X1,X2,X3)
| ~ sum(X3,additive_inverse(X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_22]) ).
cnf(c_0_28,plain,
( X1 = add(X2,X3)
| ~ sum(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_29,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ sum(additive_identity,X2,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
cnf(c_0_31,hypothesis,
( sum(X1,X2,c)
| ~ product(a,X3,X2)
| ~ product(a,X4,X1)
| ~ sum(X4,X3,b) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_33,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
sum(additive_identity,X1,additive_inverse(additive_inverse(X1))),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_35,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_36,hypothesis,
( sum(X1,c,c)
| ~ product(a,X2,X1)
| ~ sum(X2,b,b) ),
inference(spm,[status(thm)],[c_0_31,c_0_26]) ).
cnf(c_0_37,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_38,plain,
( X1 = additive_identity
| ~ sum(additive_inverse(X2),X2,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_39,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_32]),c_0_33]) ).
cnf(c_0_40,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_34]),c_0_35]) ).
cnf(c_0_41,hypothesis,
( sum(multiply(a,X1),c,c)
| ~ sum(X1,b,b) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_38,c_0_29]) ).
cnf(c_0_43,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,hypothesis,
sum(multiply(a,additive_identity),c,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_32]),c_0_42]) ).
cnf(c_0_45,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_43]),c_0_33]) ).
cnf(c_0_46,hypothesis,
add(c,multiply(a,additive_identity)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_44]),c_0_33]) ).
cnf(c_0_47,hypothesis,
additive_inverse(multiply(a,additive_identity)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_42]) ).
cnf(c_0_48,hypothesis,
multiply(a,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_47]),c_0_22]) ).
cnf(c_0_49,hypothesis,
product(a,additive_identity,additive_identity),
inference(spm,[status(thm)],[c_0_37,c_0_48]) ).
cnf(c_0_50,hypothesis,
( sum(X1,X2,additive_identity)
| ~ product(a,X3,X2)
| ~ product(a,X4,X1)
| ~ sum(X4,X3,additive_identity) ),
inference(spm,[status(thm)],[c_0_25,c_0_49]) ).
cnf(c_0_51,hypothesis,
( sum(X1,c,additive_identity)
| ~ product(a,X2,X1)
| ~ sum(X2,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_50,c_0_26]) ).
cnf(c_0_52,hypothesis,
( sum(multiply(a,X1),c,additive_identity)
| ~ sum(X1,b,additive_identity) ),
inference(spm,[status(thm)],[c_0_51,c_0_37]) ).
cnf(c_0_53,axiom,
( product(X6,X2,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ sum(X3,X5,X7) ),
distributivity4 ).
cnf(c_0_54,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
a_inverse_times_b_inverse ).
cnf(c_0_55,hypothesis,
sum(multiply(a,additive_inverse(b)),c,additive_identity),
inference(spm,[status(thm)],[c_0_52,c_0_18]) ).
cnf(c_0_56,hypothesis,
( product(X1,additive_inverse(b),X2)
| ~ product(X3,additive_inverse(b),X4)
| ~ sum(X3,additive_inverse(a),X1)
| ~ sum(X4,d,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_43,c_0_33]) ).
cnf(c_0_58,hypothesis,
add(c,multiply(a,additive_inverse(b))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_55]),c_0_33]) ).
cnf(c_0_59,axiom,
( sum(X3,X5,X7)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X5)
| ~ sum(X1,X4,X6)
| ~ product(X6,X2,X7) ),
distributivity3 ).
cnf(c_0_60,hypothesis,
( product(X1,additive_inverse(b),X2)
| ~ sum(multiply(X3,additive_inverse(b)),d,X2)
| ~ sum(X3,additive_inverse(a),X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_37]) ).
cnf(c_0_61,hypothesis,
multiply(a,additive_inverse(b)) = additive_inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_22]) ).
cnf(c_0_62,hypothesis,
( sum(X1,X2,d)
| ~ product(X3,additive_inverse(b),X2)
| ~ product(X4,additive_inverse(b),X1)
| ~ sum(X4,X3,additive_inverse(a)) ),
inference(spm,[status(thm)],[c_0_59,c_0_54]) ).
cnf(c_0_63,hypothesis,
( product(additive_identity,additive_inverse(b),X1)
| ~ sum(additive_inverse(c),d,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_18]),c_0_40]),c_0_61]) ).
cnf(c_0_64,hypothesis,
( sum(X1,d,d)
| ~ product(X2,additive_inverse(b),X1)
| ~ sum(X2,additive_inverse(a),additive_inverse(a)) ),
inference(spm,[status(thm)],[c_0_62,c_0_54]) ).
cnf(c_0_65,hypothesis,
product(additive_identity,additive_inverse(b),add(d,additive_inverse(c))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_20]),c_0_33]) ).
cnf(c_0_66,hypothesis,
sum(add(d,additive_inverse(c)),d,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_24])]) ).
cnf(c_0_67,hypothesis,
add(d,add(d,additive_inverse(c))) = d,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_66]),c_0_33]) ).
cnf(c_0_68,plain,
additive_inverse(add(X1,additive_inverse(X2))) = add(X2,additive_inverse(X1)),
inference(spm,[status(thm)],[c_0_45,c_0_39]) ).
cnf(c_0_69,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_70,hypothesis,
add(c,additive_inverse(d)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_67]),c_0_42]),c_0_68]) ).
cnf(c_0_71,plain,
additive_inverse(additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_30,c_0_69]) ).
cnf(c_0_72,negated_conjecture,
c != d,
prove_c_equals_d ).
cnf(c_0_73,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_70]),c_0_71]),c_0_22]),c_0_40]),c_0_72]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG004-1 : 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
% 0.14/0.33 % Computer : n029.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 01:45:44 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.56/1.83 % Version : CSE_E---1.7
% 1.56/1.83 % Problem : theBenchmark.p
% 1.56/1.83 % SZS status Unsatisfiable for theBenchmark.p
% 1.56/1.83 % SZS output start CNFRefutation
% See solution above
% 1.56/1.84 % Total time : 1.368s
%------------------------------------------------------------------------------