%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : BOO017-10 : TPTP v9.2.1. Released v7.5.0.
% 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 : n002.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 04:11:09 PM UTC 2026
% Result : Unsatisfiable 1.93s 1.91s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 5 RR)
% Number of literals : 37 ( 36 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 94 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
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(ifeq_axiom_001,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_inverse1) ).
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(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(ifeq_axiom,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(commutativity_of_multiplication,axiom,
ifeq(product(X1,X2,X3),true,product(X2,X1,X3),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiplication) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
cnf(distributivity5,axiom,
ifeq(product(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X2,X6),true,ifeq(sum(X4,X1,X7),true,product(X7,X6,X5),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity5) ).
cnf(x_plus_y,hypothesis,
sum(x,y,z) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_plus_y) ).
cnf(prove_product,negated_conjecture,
product(x,z,x) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product) ).
cnf(c_0_12,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_13,axiom,
sum(additive_identity,X1,X1) = true,
additive_identity1 ).
cnf(c_0_14,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_15,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X4,X2,additive_identity),true,ifeq(sum(X4,X1,X5),true,product(X5,X2,X3),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_16,axiom,
product(inverse(X1),X1,additive_identity) = true,
multiplicative_inverse1 ).
cnf(c_0_17,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
multiplication_is_well_defined ).
cnf(c_0_18,axiom,
product(X1,X2,multiply(X1,X2)) = true,
closure_of_multiplication ).
cnf(c_0_19,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_20,axiom,
ifeq(product(X1,X2,X3),true,product(X2,X1,X3),true) = true,
commutativity_of_multiplication ).
cnf(c_0_21,plain,
ifeq(product(X1,X2,X3),true,ifeq(sum(inverse(X2),X1,X4),true,product(X4,X2,X3),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_14]) ).
cnf(c_0_22,axiom,
sum(X1,additive_identity,X1) = true,
additive_identity2 ).
cnf(c_0_23,plain,
ifeq2(product(X1,X2,X3),true,multiply(X1,X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_24,plain,
product(X1,X2,multiply(X2,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_18]),c_0_14]) ).
cnf(c_0_25,plain,
ifeq(product(additive_identity,X1,X2),true,product(inverse(X1),X1,X2),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_14]) ).
cnf(c_0_26,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_19]) ).
cnf(c_0_27,plain,
product(inverse(X1),X1,multiply(additive_identity,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_14]) ).
cnf(c_0_28,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_16]),c_0_19]),c_0_26]) ).
cnf(c_0_29,axiom,
ifeq(product(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X2,X6),true,ifeq(sum(X4,X1,X7),true,product(X7,X6,X5),true),true),true),true) = true,
distributivity5 ).
cnf(c_0_30,plain,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_27]),c_0_26]),c_0_28]),c_0_19]) ).
cnf(c_0_31,plain,
ifeq(product(additive_identity,X1,X2),true,ifeq(sum(X3,X2,X4),true,ifeq(sum(X3,X1,X5),true,product(X3,X5,X4),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_22]),c_0_14]) ).
cnf(c_0_32,plain,
product(additive_identity,X1,additive_identity) = true,
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_33,plain,
ifeq(sum(X1,X2,X3),true,product(X1,X3,X1),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_22]),c_0_32]),c_0_14]),c_0_14]) ).
cnf(c_0_34,hypothesis,
sum(x,y,z) = true,
x_plus_y ).
cnf(c_0_35,negated_conjecture,
product(x,z,x) != true,
prove_product ).
cnf(c_0_36,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_14]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO017-10 : TPTP v9.2.1. Released v7.5.0.
% 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
% 0.16/0.33 % Computer : n002.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 10:44:31 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.93/1.91 % Version : CSE_E---1.7
% 1.93/1.91 % Problem : theBenchmark.p
% 1.93/1.91 % SZS status Unsatisfiable for theBenchmark.p
% 1.93/1.91 % SZS output start CNFRefutation
% See solution above
% 1.93/1.92 % Total time : 1.368s
%------------------------------------------------------------------------------