%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG001-10 : TPTP v9.2.1. Released v7.3.0.
% 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 : n026.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 05:04:45 PM UTC 2026
% Result : Unsatisfiable 27.36s 16.71s
% Output : CNFRefutation 27.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of clauses : 76 ( 76 unt; 0 nHn; 4 RR)
% Number of literals : 76 ( 75 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 214 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_addition2,axiom,
ifeq(sum(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X1,X6),true,sum(X6,X2,X5),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
cnf(ifeq_axiom_001,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(distributivity4,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,X5),true,ifeq(sum(X5,X3,X6),true,ifeq(sum(X4,X1,X7),true,product(X7,X2,X6),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(addition_is_well_defined,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X1,X2,X4),true,X4,X3),X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(ifeq_axiom,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(commutativity_of_addition,axiom,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(associativity_of_multiplication2,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X3,X5),true,ifeq(product(X4,X1,X6),true,product(X6,X2,X5),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(cancellation2,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X4,X2,X3),true,X4,X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation2) ).
cnf(multiplication_is_well_defined,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
cnf(distributivity2,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X4,X5),true,ifeq(sum(X5,X3,X6),true,ifeq(sum(X4,X2,X7),true,product(X1,X7,X6),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(prove_a_times_additive_id_is_additive_id,negated_conjecture,
product(a,additive_identity,additive_identity) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).
cnf(c_0_17,axiom,
ifeq(sum(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X1,X6),true,sum(X6,X2,X5),true),true),true) = true,
associativity_of_addition2 ).
cnf(c_0_18,axiom,
sum(X1,additive_identity,X1) = true,
additive_identity2 ).
cnf(c_0_19,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_20,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,X5),true,ifeq(sum(X5,X3,X6),true,ifeq(sum(X4,X1,X7),true,product(X7,X2,X6),true),true),true),true) = true,
distributivity4 ).
cnf(c_0_21,axiom,
sum(additive_identity,X1,X1) = true,
additive_identity1 ).
cnf(c_0_22,plain,
ifeq(sum(X1,X2,additive_identity),true,ifeq(sum(X3,X1,X4),true,sum(X4,X2,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,axiom,
sum(additive_inverse(X1),X1,additive_identity) = true,
left_inverse ).
cnf(c_0_24,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X1,X2,X4),true,X4,X3),X3) = X3,
addition_is_well_defined ).
cnf(c_0_25,axiom,
sum(X1,X2,add(X1,X2)) = true,
closure_of_addition ).
cnf(c_0_26,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_27,axiom,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
commutativity_of_addition ).
cnf(c_0_28,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(additive_identity,X2,X4),true,ifeq(sum(X4,X3,X5),true,product(X1,X2,X5),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]) ).
cnf(c_0_29,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X3,X5),true,ifeq(product(X4,X1,X6),true,product(X6,X2,X5),true),true),true) = true,
associativity_of_multiplication2 ).
cnf(c_0_30,axiom,
product(X1,X2,multiply(X1,X2)) = true,
closure_of_multiplication ).
cnf(c_0_31,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X4,X2,X3),true,X4,X1),X1) = X1,
cancellation2 ).
cnf(c_0_32,plain,
ifeq(sum(X1,additive_inverse(X2),X3),true,sum(X3,X2,X1),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_19]) ).
cnf(c_0_33,plain,
ifeq2(sum(X1,X2,X3),true,add(X1,X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_34,plain,
sum(X1,X2,add(X2,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_19]) ).
cnf(c_0_35,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(additive_identity,X2,X4),true,product(X1,X2,add(X4,X3)),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_25]),c_0_19]) ).
cnf(c_0_36,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X3,X5),true,product(multiply(X4,X1),X2,X5),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_19]) ).
cnf(c_0_37,plain,
ifeq2(sum(X1,X2,add(X3,X2)),true,X3,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_25]),c_0_26]) ).
cnf(c_0_38,plain,
sum(add(X1,additive_inverse(X2)),X2,X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_19]) ).
cnf(c_0_39,plain,
add(X1,X2) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_26]) ).
cnf(c_0_40,plain,
ifeq2(sum(X1,X2,add(X2,X3)),true,X3,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_34]),c_0_26]) ).
cnf(c_0_41,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
multiplication_is_well_defined ).
cnf(c_0_42,plain,
ifeq(product(X1,X2,X3),true,product(X1,X2,add(multiply(additive_identity,X2),X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_19]) ).
cnf(c_0_43,plain,
ifeq(product(X1,X2,X3),true,product(multiply(X4,X1),X2,multiply(X4,X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_30]),c_0_19]) ).
cnf(c_0_44,plain,
add(additive_inverse(X1),add(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_26]),c_0_39]) ).
cnf(c_0_45,plain,
add(additive_inverse(X1),add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_38]),c_0_26]),c_0_39]) ).
cnf(c_0_46,plain,
ifeq2(product(X1,X2,X3),true,multiply(X1,X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_30]),c_0_26]) ).
cnf(c_0_47,plain,
product(X1,X2,add(multiply(additive_identity,X2),multiply(X1,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_30]),c_0_19]) ).
cnf(c_0_48,plain,
ifeq2(sum(additive_inverse(X1),X1,X2),true,additive_identity,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_26]) ).
cnf(c_0_49,axiom,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X4,X5),true,ifeq(sum(X5,X3,X6),true,ifeq(sum(X4,X2,X7),true,product(X1,X7,X6),true),true),true),true) = true,
distributivity2 ).
cnf(c_0_50,plain,
product(multiply(X1,X2),X3,multiply(X1,multiply(X2,X3))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_30]),c_0_19]) ).
cnf(c_0_51,plain,
ifeq2(sum(X1,X2,additive_identity),true,additive_inverse(X2),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_23]),c_0_26]) ).
cnf(c_0_52,axiom,
sum(X1,additive_inverse(X1),additive_identity) = true,
right_inverse ).
cnf(c_0_53,plain,
add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_39]) ).
cnf(c_0_54,plain,
add(multiply(additive_identity,X1),multiply(X2,X1)) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_26]) ).
cnf(c_0_55,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_34]),c_0_26]) ).
cnf(c_0_56,plain,
ifeq2(sum(X1,X2,X2),true,additive_identity,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_21]),c_0_26]) ).
cnf(c_0_57,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,additive_identity,X4),true,ifeq(sum(X4,X3,X5),true,product(X1,X2,X5),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_21]),c_0_19]) ).
cnf(c_0_58,plain,
ifeq2(product(multiply(X1,X2),X3,X4),true,multiply(X1,multiply(X2,X3)),X4) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_50]),c_0_26]) ).
cnf(c_0_59,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_50]),c_0_26]) ).
cnf(c_0_60,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_26]) ).
cnf(c_0_61,plain,
additive_inverse(multiply(additive_identity,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_62,plain,
additive_inverse(additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_23]),c_0_26]) ).
cnf(c_0_63,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,additive_identity,X4),true,product(X1,X2,add(X4,X3)),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_25]),c_0_19]) ).
cnf(c_0_64,plain,
ifeq2(product(multiply(X1,multiply(X2,X3)),X4,X5),true,multiply(X1,multiply(X2,multiply(X3,X4))),X5) = X5,
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_65,plain,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_66,plain,
ifeq(product(X1,X2,X3),true,product(X1,X2,add(multiply(X1,additive_identity),X3)),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_30]),c_0_19]) ).
cnf(c_0_67,plain,
ifeq2(product(multiply(X1,additive_identity),X2,X3),true,multiply(X1,additive_identity),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_65]) ).
cnf(c_0_68,plain,
product(X1,X2,add(multiply(X1,additive_identity),multiply(X1,X2))) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_30]),c_0_19]) ).
cnf(c_0_69,plain,
add(X1,additive_inverse(add(X1,X2))) = additive_inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_44]),c_0_39]) ).
cnf(c_0_70,plain,
add(multiply(X1,additive_identity),multiply(X1,additive_identity)) = multiply(X1,additive_identity),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_59]),c_0_65]),c_0_59]),c_0_65]),c_0_26]),c_0_59]),c_0_65]),c_0_59]),c_0_65]) ).
cnf(c_0_71,plain,
additive_inverse(multiply(X1,additive_identity)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_55]) ).
cnf(c_0_72,plain,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_71]),c_0_62]) ).
cnf(c_0_73,negated_conjecture,
product(a,additive_identity,additive_identity) != true,
prove_a_times_additive_id_is_additive_id ).
cnf(c_0_74,plain,
product(X1,additive_identity,additive_identity) = true,
inference(spm,[status(thm)],[c_0_30,c_0_72]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG001-10 : TPTP v9.2.1. Released v7.3.0.
% 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 : n026.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 01:45:23 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 27.36/16.71 % Version : CSE_E---1.7
% 27.36/16.71 % Problem : theBenchmark.p
% 27.36/16.71 % SZS status Unsatisfiable for theBenchmark.p
% 27.36/16.71 % SZS output start CNFRefutation
% See solution above
% 27.47/16.82 % Total time : 12.395s
%------------------------------------------------------------------------------