%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : BOO004-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:54:36 AM UTC 2026
% Result : Unsatisfiable 1.60s 12.26s
% Output : CNFRefutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of clauses : 65 ( 65 unt; 0 nHn; 3 RR)
% Number of literals : 65 ( 64 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 164 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq2(X0,X0,X1,X2) = X1 ).
cnf(ifeq_axiom_001,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(closure_of_addition,axiom,
sum(X0,X1,add(X0,X1)) = true ).
cnf(closure_of_multiplication,axiom,
product(X0,X1,multiply(X0,X1)) = true ).
cnf(commutativity_of_multiplication,axiom,
ifeq(product(X0,X1,X2),true,product(X1,X0,X2),true) = true ).
cnf(additive_identity1,axiom,
sum('additive$uidentity',X0,X0) = true ).
cnf(additive_identity2,axiom,
sum(X0,'additive$uidentity',X0) = true ).
cnf(multiplicative_identity2,axiom,
product(X0,'multiplicative$uidentity',X0) = true ).
cnf(distributivity1,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true) = true ).
cnf(distributivity7,axiom,
ifeq(product(X0,X1,X2),true,ifeq(sum(X2,X3,X4),true,ifeq(sum(X1,X3,X5),true,ifeq(sum(X0,X3,X6),true,product(X6,X5,X4),true),true),true),true) = true ).
cnf(multiplicative_inverse2,axiom,
product(X0,inverse(X0),'additive$uidentity') = true ).
cnf(addition_is_well_defined,axiom,
ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2) = X2 ).
cnf(multiplication_is_well_defined,axiom,
ifeq2(product(X0,X1,X2),true,ifeq2(product(X0,X1,X3),true,X3,X2),X2) = X2 ).
cnf(prove_both_equalities,negated_conjecture,
sum(x,x,x) != true ).
cnf(c0,plain,
ifeq2(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom]) ).
cnf(c1,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom_001]) ).
cnf(c2,plain,
sum(X0,X1,add(X0,X1)) = true,
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c3,plain,
product(X0,X1,multiply(X0,X1)) = true,
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c5,plain,
ifeq(product(X0,X1,X2),true,product(X1,X0,X2),true) = true,
inference(clausification,[status(esa)],[commutativity_of_multiplication]) ).
cnf(c6,plain,
sum('additive$uidentity',X0,X0) = true,
inference(clausification,[status(esa)],[additive_identity1]) ).
cnf(c7,plain,
sum(X0,'additive$uidentity',X0) = true,
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c9,plain,
product(X0,'multiplicative$uidentity',X0) = true,
inference(clausification,[status(esa)],[multiplicative_identity2]) ).
cnf(c10,plain,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true) = true,
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c16,plain,
ifeq(product(X0,X1,X2),true,ifeq(sum(X2,X3,X4),true,ifeq(sum(X1,X3,X5),true,ifeq(sum(X0,X3,X6),true,product(X6,X5,X4),true),true),true),true) = true,
inference(clausification,[status(esa)],[distributivity7]) ).
cnf(c21,plain,
product(X0,inverse(X0),'additive$uidentity') = true,
inference(clausification,[status(esa)],[multiplicative_inverse2]) ).
cnf(c22,plain,
ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2) = X2,
inference(clausification,[status(esa)],[addition_is_well_defined]) ).
cnf(c23,plain,
ifeq2(product(X0,X1,X2),true,ifeq2(product(X0,X1,X3),true,X3,X2),X2) = X2,
inference(clausification,[status(esa)],[multiplication_is_well_defined]) ).
cnf(c24,plain,
sum(x,x,x) != true,
inference(clausification,[status(esa)],[prove_both_equalities]) ).
cnf(d0,plain,
ifeq2(product(X0,'multiplicative$uidentity',X1),true,ifeq2(true,true,X0,X1),X1) = X1,
inference(superposition,[status(thm)],[c9,c23]) ).
cnf(d1,plain,
ifeq2(product(X0,'multiplicative$uidentity',X1),true,X0,X1) = X1,
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
ifeq(true,true,product(X1,X0,multiply(X0,X1)),true) = true,
inference(superposition,[status(thm)],[c3,c5]) ).
cnf(d3,plain,
product(X0,X1,multiply(X1,X0)) = true,
inference(demodulation,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
ifeq2(sum(X0,'additive$uidentity',X1),true,ifeq2(true,true,X0,X1),X1) = X1,
inference(superposition,[status(thm)],[c7,c22]) ).
cnf(d5,plain,
ifeq2(sum(X0,'additive$uidentity',X1),true,X0,X1) = X1,
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
ifeq(true,true,ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X3,X1,inverse(X0)),true,sum(X4,X2,'additive$uidentity'),true),true),true),true) = true,
inference(superposition,[status(thm)],[c21,c10]) ).
cnf(d7,plain,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X3,X1,inverse(X0)),true,sum(X4,X2,'additive$uidentity'),true),true),true) = true,
inference(demodulation,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
ifeq(true,true,ifeq(product(X0,X1,X2),true,ifeq(sum(X1,inverse(X0),inverse(X0)),true,sum(X2,'additive$uidentity','additive$uidentity'),true),true),true) = true,
inference(superposition,[status(thm)],[c21,d7]) ).
cnf(d9,plain,
ifeq(product(X0,X1,X2),true,ifeq(sum(X1,inverse(X0),inverse(X0)),true,sum(X2,'additive$uidentity','additive$uidentity'),true),true) = true,
inference(demodulation,[status(thm)],[d8,c1]) ).
cnf(d10,plain,
ifeq(product(X0,'additive$uidentity',X1),true,ifeq(true,true,sum(X1,'additive$uidentity','additive$uidentity'),true),true) = true,
inference(superposition,[status(thm)],[c6,d9]) ).
cnf(d11,plain,
ifeq(product(X1,'additive$uidentity',X0),true,sum(X0,'additive$uidentity','additive$uidentity'),true) = true,
inference(demodulation,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
ifeq(true,true,sum(multiply('additive$uidentity',X0),'additive$uidentity','additive$uidentity'),true) = true,
inference(superposition,[status(thm)],[d3,d11]) ).
cnf(d13,plain,
sum(multiply('additive$uidentity',X0),'additive$uidentity','additive$uidentity') = true,
inference(demodulation,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
ifeq2(true,true,multiply('additive$uidentity',X0),'additive$uidentity') = 'additive$uidentity',
inference(superposition,[status(thm)],[d13,d5]) ).
cnf(d15,plain,
multiply('additive$uidentity',X0) = 'additive$uidentity',
inference(demodulation,[status(thm)],[d14,c0]) ).
cnf(d16,plain,
product(X0,'additive$uidentity','additive$uidentity') = true,
inference(superposition,[status(thm)],[d15,d3]) ).
cnf(d17,plain,
ifeq(product(X1,X2,'additive$uidentity'),true,ifeq(true,true,ifeq(sum(X2,X0,X3),true,ifeq(sum(X1,X0,X4),true,product(X4,X3,X0),true),true),true),true) = true,
inference(superposition,[status(thm)],[c6,c16]) ).
cnf(d18,plain,
ifeq(product(X3,X0,'additive$uidentity'),true,ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X4),true,product(X4,X2,X1),true),true),true) = true,
inference(demodulation,[status(thm)],[d17,c1]) ).
cnf(d19,plain,
ifeq(product(X1,'additive$uidentity','additive$uidentity'),true,ifeq(true,true,ifeq(sum(X1,X0,X2),true,product(X2,X0,X0),true),true),true) = true,
inference(superposition,[status(thm)],[c6,d18]) ).
cnf(d20,plain,
ifeq(true,true,ifeq(true,true,ifeq(sum(X0,X1,X2),true,product(X2,X1,X1),true),true),true) = true,
inference(demodulation,[status(thm)],[d19,d16]) ).
cnf(d21,plain,
ifeq(true,true,ifeq(sum(X0,X1,X2),true,product(X2,X1,X1),true),true) = true,
inference(demodulation,[status(thm)],[d20,c1]) ).
cnf(d22,plain,
ifeq(sum(X0,X1,X2),true,product(X2,X1,X1),true) = true,
inference(demodulation,[status(thm)],[d21,c1]) ).
cnf(d23,plain,
ifeq(true,true,product(add(X0,X1),X1,X1),true) = true,
inference(superposition,[status(thm)],[c2,d22]) ).
cnf(d24,plain,
product(add(X0,X1),X1,X1) = true,
inference(demodulation,[status(thm)],[d23,c1]) ).
cnf(d25,plain,
ifeq2(true,true,add(X0,'multiplicative$uidentity'),'multiplicative$uidentity') = 'multiplicative$uidentity',
inference(superposition,[status(thm)],[d24,d1]) ).
cnf(d26,plain,
add(X0,'multiplicative$uidentity') = 'multiplicative$uidentity',
inference(demodulation,[status(thm)],[d25,c0]) ).
cnf(d27,plain,
sum(X0,'multiplicative$uidentity','multiplicative$uidentity') = true,
inference(superposition,[status(thm)],[d26,c2]) ).
cnf(d28,plain,
ifeq(true,true,ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X3,X1,'multiplicative$uidentity'),true,sum(X4,X2,X0),true),true),true),true) = true,
inference(superposition,[status(thm)],[c9,c10]) ).
cnf(d29,plain,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X3,X1,'multiplicative$uidentity'),true,sum(X4,X2,X0),true),true),true) = true,
inference(demodulation,[status(thm)],[d28,c1]) ).
cnf(d30,plain,
ifeq(true,true,ifeq(product(X0,X1,X2),true,ifeq(sum(X1,'multiplicative$uidentity','multiplicative$uidentity'),true,sum(X2,X0,X0),true),true),true) = true,
inference(superposition,[status(thm)],[c9,d29]) ).
cnf(d31,plain,
ifeq(product(X0,X1,X2),true,ifeq(sum(X1,'multiplicative$uidentity','multiplicative$uidentity'),true,sum(X2,X0,X0),true),true) = true,
inference(demodulation,[status(thm)],[d30,c1]) ).
cnf(d32,plain,
ifeq(true,true,ifeq(sum('multiplicative$uidentity','multiplicative$uidentity','multiplicative$uidentity'),true,sum(X0,X0,X0),true),true) = true,
inference(superposition,[status(thm)],[c9,d31]) ).
cnf(d33,plain,
ifeq(sum('multiplicative$uidentity','multiplicative$uidentity','multiplicative$uidentity'),true,sum(X0,X0,X0),true) = true,
inference(demodulation,[status(thm)],[d32,c1]) ).
cnf(d34,plain,
ifeq(true,true,sum(X0,X0,X0),true) = true,
inference(demodulation,[status(thm)],[d33,d27]) ).
cnf(d35,plain,
sum(X0,X0,X0) = true,
inference(demodulation,[status(thm)],[d34,c1]) ).
cnf(d36,plain,
$false,
inference(resolution,[status(thm)],[d35,c24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : BOO004-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 26 22:34:04 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.60/12.26 % SZS status Unsatisfiable for theBenchmark.p
% 1.60/12.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------