%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG006-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 08:25:33 AM UTC 2026
% Result : Unsatisfiable 46.34s 48.82s
% Output : CNFRefutation 46.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of clauses : 106 ( 106 unt; 0 nHn; 30 RR)
% Number of literals : 106 ( 105 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 196 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq2(X0,X0,X1,X2) = X1 ).
cnf(ifeq_axiom_001,axiom,
ifeq(X0,X0,X1,X2) = X1 ).
cnf(additive_identity2,axiom,
sum(X0,'additive$uidentity',X0) = true ).
cnf(closure_of_multiplication,axiom,
product(X0,X1,multiply(X0,X1)) = true ).
cnf(closure_of_addition,axiom,
sum(X0,X1,add(X0,X1)) = true ).
cnf(right_inverse,axiom,
sum(X0,'additive$uinverse'(X0),'additive$uidentity') = true ).
cnf(associativity_of_addition1,axiom,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X4),true,ifeq(sum(X5,X3,X0),true,sum(X5,X4,X2),true),true),true) = true ).
cnf(commutativity_of_addition,axiom,
ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true ).
cnf(distributivity1,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true) = true ).
cnf(addition_is_well_defined,axiom,
ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2) = X2 ).
cnf(multiplication_is_well_defined,axiom,
ifeq2(product(X0,X1,X2),true,ifeq2(product(X0,X1,X3),true,X3,X2),X2) = X2 ).
cnf(b_plus_inverse_c,hypothesis,
sum(b,'additive$uinverse'(c),'bS$uIc') = true ).
cnf(a_times_b,hypothesis,
product(a,b,aPb) = true ).
cnf(a_times_c,hypothesis,
product(a,c,aPc) = true ).
cnf(aPb_plus_IaPc,hypothesis,
sum(aPb,'additive$uinverse'(aPc),'aPb$uS$uIaPc') = true ).
cnf(prove_a_times_bS_Ic_is_aPb_S__IaPc,negated_conjecture,
product(a,'bS$uIc','aPb$uS$uIaPc') != true ).
cnf(c0,plain,
ifeq2(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom]) ).
cnf(c1,plain,
ifeq(X0,X0,X1,X2) = X1,
inference(clausification,[status(esa)],[ifeq_axiom_001]) ).
cnf(c3,plain,
sum(X0,'additive$uidentity',X0) = true,
inference(clausification,[status(esa)],[additive_identity2]) ).
cnf(c4,plain,
product(X0,X1,multiply(X0,X1)) = true,
inference(clausification,[status(esa)],[closure_of_multiplication]) ).
cnf(c5,plain,
sum(X0,X1,add(X0,X1)) = true,
inference(clausification,[status(esa)],[closure_of_addition]) ).
cnf(c7,plain,
sum(X0,'additive$uinverse'(X0),'additive$uidentity') = true,
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c8,plain,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X4),true,ifeq(sum(X5,X3,X0),true,sum(X5,X4,X2),true),true),true) = true,
inference(clausification,[status(esa)],[associativity_of_addition1]) ).
cnf(c10,plain,
ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(clausification,[status(esa)],[commutativity_of_addition]) ).
cnf(c13,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(c17,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(c18,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(c19,plain,
sum(b,'additive$uinverse'(c),'bS$uIc') = true,
inference(clausification,[status(esa)],[b_plus_inverse_c]) ).
cnf(c20,plain,
product(a,b,aPb) = true,
inference(clausification,[status(esa)],[a_times_b]) ).
cnf(c21,plain,
product(a,c,aPc) = true,
inference(clausification,[status(esa)],[a_times_c]) ).
cnf(c22,plain,
sum(aPb,'additive$uinverse'(aPc),'aPb$uS$uIaPc') = true,
inference(clausification,[status(esa)],[aPb_plus_IaPc]) ).
cnf(c23,plain,
product(a,'bS$uIc','aPb$uS$uIaPc') != true,
inference(clausification,[status(esa)],[prove_a_times_bS_Ic_is_aPb_S__IaPc]) ).
cnf(d0,plain,
ifeq2(true,true,ifeq2(sum(aPb,'additive$uinverse'(aPc),X0),true,X0,'aPb$uS$uIaPc'),'aPb$uS$uIaPc') = 'aPb$uS$uIaPc',
inference(superposition,[status(thm)],[c22,c17]) ).
cnf(d1,plain,
ifeq2(sum(aPb,'additive$uinverse'(aPc),X0),true,X0,'aPb$uS$uIaPc') = 'aPb$uS$uIaPc',
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
ifeq2(true,true,add(aPb,'additive$uinverse'(aPc)),'aPb$uS$uIaPc') = 'aPb$uS$uIaPc',
inference(superposition,[status(thm)],[c5,d1]) ).
cnf(d3,plain,
add(aPb,'additive$uinverse'(aPc)) = 'aPb$uS$uIaPc',
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
ifeq2(true,true,ifeq2(sum(X0,X1,X2),true,X2,add(X0,X1)),add(X0,X1)) = add(X0,X1),
inference(superposition,[status(thm)],[c5,c17]) ).
cnf(d5,plain,
ifeq2(sum(X0,X1,X2),true,X2,add(X0,X1)) = add(X0,X1),
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
ifeq(true,true,sum(X1,X0,add(X0,X1)),true) = true,
inference(superposition,[status(thm)],[c5,c10]) ).
cnf(d7,plain,
sum(X0,X1,add(X1,X0)) = true,
inference(demodulation,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
ifeq2(true,true,add(X1,X0),add(X0,X1)) = add(X0,X1),
inference(superposition,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
add(X0,X1) = add(X1,X0),
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
ifeq2(true,true,ifeq2(sum(X0,'additive$uidentity',X1),true,X1,X0),X0) = X0,
inference(superposition,[status(thm)],[c3,c17]) ).
cnf(d11,plain,
ifeq2(sum(X0,'additive$uidentity',X1),true,X1,X0) = X0,
inference(demodulation,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
ifeq2(true,true,add('additive$uidentity',X0),X0) = X0,
inference(superposition,[status(thm)],[d7,d11]) ).
cnf(d13,plain,
add('additive$uidentity',X0) = X0,
inference(demodulation,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
ifeq(true,true,ifeq(sum(X2,X1,X3),true,ifeq(sum(X4,X2,X0),true,sum(X4,X3,add(X0,X1)),true),true),true) = true,
inference(superposition,[status(thm)],[c5,c8]) ).
cnf(d15,plain,
ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X0,X4),true,sum(X3,X2,add(X4,X1)),true),true) = true,
inference(demodulation,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
ifeq(sum('additive$uinverse'(X0),X1,X2),true,ifeq(true,true,sum(X0,X2,add('additive$uidentity',X1)),true),true) = true,
inference(superposition,[status(thm)],[c7,d15]) ).
cnf(d17,plain,
ifeq(sum('additive$uinverse'(X0),X2,X1),true,sum(X0,X1,add('additive$uidentity',X2)),true) = true,
inference(demodulation,[status(thm)],[d16,c1]) ).
cnf(d18,plain,
ifeq(sum('additive$uinverse'(X1),X0,X2),true,sum(X1,X2,X0),true) = true,
inference(demodulation,[status(thm)],[d17,d13]) ).
cnf(d19,plain,
ifeq(true,true,sum(X0,'additive$uidentity','additive$uinverse'('additive$uinverse'(X0))),true) = true,
inference(superposition,[status(thm)],[c7,d18]) ).
cnf(d20,plain,
sum(X0,'additive$uidentity','additive$uinverse'('additive$uinverse'(X0))) = true,
inference(demodulation,[status(thm)],[d19,c1]) ).
cnf(d21,plain,
ifeq2(true,true,'additive$uinverse'('additive$uinverse'(X0)),X0) = X0,
inference(superposition,[status(thm)],[d20,d11]) ).
cnf(d22,plain,
'additive$uinverse'('additive$uinverse'(X0)) = X0,
inference(demodulation,[status(thm)],[d21,c0]) ).
cnf(d23,plain,
ifeq2(sum(X0,X1,X2),true,ifeq2(true,true,add(X1,X0),X2),X2) = X2,
inference(superposition,[status(thm)],[d7,c17]) ).
cnf(d24,plain,
ifeq2(sum(X1,X0,X2),true,add(X0,X1),X2) = X2,
inference(demodulation,[status(thm)],[d23,c0]) ).
cnf(d25,plain,
ifeq(true,true,ifeq(sum(X2,X0,X3),true,sum(X2,add(X0,X1),add(X3,X1)),true),true) = true,
inference(superposition,[status(thm)],[c5,d15]) ).
cnf(d26,plain,
ifeq(sum(X0,X1,X2),true,sum(X0,add(X1,X3),add(X2,X3)),true) = true,
inference(demodulation,[status(thm)],[d25,c1]) ).
cnf(d27,plain,
ifeq(true,true,sum(X0,add('additive$uinverse'(X0),X1),add('additive$uidentity',X1)),true) = true,
inference(superposition,[status(thm)],[c7,d26]) ).
cnf(d28,plain,
sum(X0,add('additive$uinverse'(X0),X1),add('additive$uidentity',X1)) = true,
inference(demodulation,[status(thm)],[d27,c1]) ).
cnf(d29,plain,
sum(X1,add('additive$uinverse'(X1),X0),X0) = true,
inference(demodulation,[status(thm)],[d28,d13]) ).
cnf(d30,plain,
ifeq2(true,true,add(add('additive$uinverse'(X0),X1),X0),X1) = X1,
inference(superposition,[status(thm)],[d29,d24]) ).
cnf(d31,plain,
add(add('additive$uinverse'(X0),X1),X0) = X1,
inference(demodulation,[status(thm)],[d30,c0]) ).
cnf(d32,plain,
add(X0,add('additive$uinverse'(X0),X1)) = X1,
inference(demodulation,[status(thm)],[d31,d9]) ).
cnf(d33,plain,
add(X0,add(X1,'additive$uinverse'(X0))) = X1,
inference(superposition,[status(thm)],[d9,d32]) ).
cnf(d34,plain,
add('additive$uinverse'(X0),add(X1,X0)) = X1,
inference(superposition,[status(thm)],[d22,d33]) ).
cnf(d35,plain,
add('additive$uinverse'(add(X1,X0)),X1) = 'additive$uinverse'(X0),
inference(superposition,[status(thm)],[d34,d34]) ).
cnf(d36,plain,
add(X0,'additive$uinverse'(add(X0,X1))) = 'additive$uinverse'(X1),
inference(demodulation,[status(thm)],[d35,d9]) ).
cnf(d37,plain,
add(X0,'additive$uinverse'(X1)) = 'additive$uinverse'(add('additive$uinverse'(X0),X1)),
inference(superposition,[status(thm)],[d36,d32]) ).
cnf(d38,plain,
'additive$uinverse'(add(X0,'additive$uinverse'(X1))) = add('additive$uinverse'(X0),X1),
inference(superposition,[status(thm)],[d37,d22]) ).
cnf(d39,plain,
add('additive$uinverse'(X0),add(X0,X1)) = X1,
inference(superposition,[status(thm)],[d22,d32]) ).
cnf(d40,plain,
add('additive$uinverse'(add(X0,X1)),X1) = 'additive$uinverse'(X0),
inference(superposition,[status(thm)],[d39,d34]) ).
cnf(d41,plain,
add(X1,'additive$uinverse'(add(X0,X1))) = 'additive$uinverse'(X0),
inference(demodulation,[status(thm)],[d40,d9]) ).
cnf(d42,plain,
'additive$uinverse'('additive$uinverse'(X1)) = add('additive$uinverse'(X0),add(X1,X0)),
inference(superposition,[status(thm)],[d41,d38]) ).
cnf(d43,plain,
X0 = add('additive$uinverse'(X1),add(X0,X1)),
inference(demodulation,[status(thm)],[d42,d22]) ).
cnf(d44,plain,
X0 = add('additive$uinverse'(X1),add(X1,X0)),
inference(superposition,[status(thm)],[d9,d43]) ).
cnf(d45,plain,
ifeq2(true,true,ifeq2(product(a,b,X0),true,X0,aPb),aPb) = aPb,
inference(superposition,[status(thm)],[c20,c18]) ).
cnf(d46,plain,
ifeq2(product(a,b,X0),true,X0,aPb) = aPb,
inference(demodulation,[status(thm)],[d45,c0]) ).
cnf(d47,plain,
ifeq2(true,true,multiply(a,b),aPb) = aPb,
inference(superposition,[status(thm)],[c4,d46]) ).
cnf(d48,plain,
multiply(a,b) = aPb,
inference(demodulation,[status(thm)],[d47,c0]) ).
cnf(d49,plain,
ifeq(true,true,ifeq(product(X0,X2,X3),true,ifeq(product(X0,X4,X5),true,ifeq(sum(X4,X2,X1),true,sum(X5,X3,multiply(X0,X1)),true),true),true),true) = true,
inference(superposition,[status(thm)],[c4,c13]) ).
cnf(d50,plain,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X3,X1,X5),true,sum(X4,X2,multiply(X0,X5)),true),true),true) = true,
inference(demodulation,[status(thm)],[d49,c1]) ).
cnf(d51,plain,
ifeq(true,true,ifeq(product(a,X0,X1),true,ifeq(sum(X0,c,X2),true,sum(X1,aPc,multiply(a,X2)),true),true),true) = true,
inference(superposition,[status(thm)],[c21,d50]) ).
cnf(d52,plain,
ifeq(product(a,X0,X1),true,ifeq(sum(X0,c,X2),true,sum(X1,aPc,multiply(a,X2)),true),true) = true,
inference(demodulation,[status(thm)],[d51,c1]) ).
cnf(d53,plain,
ifeq2(sum(X0,X1,X2),true,ifeq2(true,true,add(X0,X1),X2),X2) = X2,
inference(superposition,[status(thm)],[c5,c17]) ).
cnf(d54,plain,
ifeq2(sum(X0,X1,X2),true,add(X0,X1),X2) = X2,
inference(demodulation,[status(thm)],[d53,c0]) ).
cnf(d55,plain,
ifeq(true,true,sum('additive$uinverse'(c),b,'bS$uIc'),true) = true,
inference(superposition,[status(thm)],[c19,c10]) ).
cnf(d56,plain,
sum('additive$uinverse'(c),b,'bS$uIc') = true,
inference(demodulation,[status(thm)],[d55,c1]) ).
cnf(d57,plain,
ifeq(true,true,sum(c,'bS$uIc',b),true) = true,
inference(superposition,[status(thm)],[d56,d18]) ).
cnf(d58,plain,
sum(c,'bS$uIc',b) = true,
inference(demodulation,[status(thm)],[d57,c1]) ).
cnf(d59,plain,
ifeq2(true,true,add(c,'bS$uIc'),b) = b,
inference(superposition,[status(thm)],[d58,d54]) ).
cnf(d60,plain,
add(c,'bS$uIc') = b,
inference(demodulation,[status(thm)],[d59,c0]) ).
cnf(d61,plain,
sum('bS$uIc',c,b) = true,
inference(superposition,[status(thm)],[d60,d7]) ).
cnf(d62,plain,
ifeq(product(a,'bS$uIc',X0),true,ifeq(true,true,sum(X0,aPc,multiply(a,b)),true),true) = true,
inference(superposition,[status(thm)],[d61,d52]) ).
cnf(d63,plain,
ifeq(product(a,'bS$uIc',X0),true,sum(X0,aPc,multiply(a,b)),true) = true,
inference(demodulation,[status(thm)],[d62,c1]) ).
cnf(d64,plain,
ifeq(product(a,'bS$uIc',X0),true,sum(X0,aPc,aPb),true) = true,
inference(demodulation,[status(thm)],[d63,d48]) ).
cnf(d65,plain,
ifeq(true,true,sum(multiply(a,'bS$uIc'),aPc,aPb),true) = true,
inference(superposition,[status(thm)],[c4,d64]) ).
cnf(d66,plain,
sum(multiply(a,'bS$uIc'),aPc,aPb) = true,
inference(demodulation,[status(thm)],[d65,c1]) ).
cnf(d67,plain,
ifeq2(true,true,add(aPc,multiply(a,'bS$uIc')),aPb) = aPb,
inference(superposition,[status(thm)],[d66,d24]) ).
cnf(d68,plain,
add(aPc,multiply(a,'bS$uIc')) = aPb,
inference(demodulation,[status(thm)],[d67,c0]) ).
cnf(d69,plain,
multiply(a,'bS$uIc') = add('additive$uinverse'(aPc),aPb),
inference(superposition,[status(thm)],[d68,d44]) ).
cnf(d70,plain,
multiply(a,'bS$uIc') = add(aPb,'additive$uinverse'(aPc)),
inference(demodulation,[status(thm)],[d69,d9]) ).
cnf(d71,plain,
multiply(a,'bS$uIc') = 'aPb$uS$uIaPc',
inference(demodulation,[status(thm)],[d70,d3]) ).
cnf(d72,plain,
product(a,'bS$uIc','aPb$uS$uIaPc') = true,
inference(superposition,[status(thm)],[d71,c4]) ).
cnf(d73,plain,
$false,
inference(resolution,[status(thm)],[c23,d72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG006-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 05:47:28 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.34/48.82 % SZS status Unsatisfiable for theBenchmark.p
% 46.34/48.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------