%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP617-1 : TPTP v9.3.1. Released v3.1.0.
% 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 07:24:10 AM UTC 2026
% Result : Unsatisfiable 66.29s 13.70s
% Output : CNFRefutation 66.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 18
% Syntax : Number of clauses : 108 ( 57 unt; 0 nHn; 57 RR)
% Number of literals : 187 ( 31 equ; 82 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 211 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_inverse1,axiom,
( 'subgroup1$umember'(inverse(X0))
| ~ 'subgroup1$umember'(X0) ) ).
cnf(closure_of_product1,axiom,
( 'subgroup1$umember'(X2)
| ~ product(X0,X1,X2)
| ~ 'subgroup1$umember'(X1)
| ~ 'subgroup1$umember'(X0) ) ).
cnf(closure_of_inverse2,axiom,
( 'subgroup2$umember'(inverse(X0))
| ~ 'subgroup2$umember'(X0) ) ).
cnf(closure_of_product2,axiom,
( 'subgroup2$umember'(X2)
| ~ product(X0,X1,X2)
| ~ 'subgroup2$umember'(X1)
| ~ 'subgroup2$umember'(X0) ) ).
cnf(normality1,hypothesis,
( 'subgroup1$umember'(multiply(X1,multiply(X0,inverse(X1))))
| ~ 'subgroup1$umember'(X0) ) ).
cnf(normality2,hypothesis,
( 'subgroup2$umember'(multiply(X1,multiply(X0,inverse(X1))))
| ~ 'subgroup2$umember'(X0) ) ).
cnf(trivial_intersection,hypothesis,
( X0 = identity
| ~ 'subgroup2$umember'(X0)
| ~ 'subgroup1$umember'(X0) ) ).
cnf(v_in_G1,hypothesis,
'subgroup1$umember'(v) ).
cnf(u_in_G2,hypothesis,
'subgroup2$umember'(u) ).
cnf(prove_vu_equals_uv,negated_conjecture,
multiply(v,u) != multiply(u,v) ).
cnf(left_identity,axiom,
product(identity,X0,X0) ).
cnf(right_identity,axiom,
product(X0,identity,X0) ).
cnf(left_inverse,axiom,
product(inverse(X0),X0,identity) ).
cnf(right_inverse,axiom,
product(X0,inverse(X0),identity) ).
cnf(total_function1,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(total_function2,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(associativity1,axiom,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(associativity2,axiom,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(c0,plain,
( 'subgroup1$umember'(inverse(X0))
| ~ 'subgroup1$umember'(X0) ),
inference(clausification,[status(esa)],[closure_of_inverse1]) ).
cnf(c1,plain,
( 'subgroup1$umember'(X2)
| ~ 'subgroup1$umember'(X1)
| ~ 'subgroup1$umember'(X0)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[closure_of_product1]) ).
cnf(c2,plain,
( 'subgroup2$umember'(inverse(X0))
| ~ 'subgroup2$umember'(X0) ),
inference(clausification,[status(esa)],[closure_of_inverse2]) ).
cnf(c3,plain,
( 'subgroup2$umember'(X2)
| ~ 'subgroup2$umember'(X1)
| ~ 'subgroup2$umember'(X0)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[closure_of_product2]) ).
cnf(c4,plain,
( 'subgroup1$umember'(multiply(X1,multiply(X0,inverse(X1))))
| ~ 'subgroup1$umember'(X0) ),
inference(clausification,[status(esa)],[normality1]) ).
cnf(c5,plain,
( 'subgroup2$umember'(multiply(X1,multiply(X0,inverse(X1))))
| ~ 'subgroup2$umember'(X0) ),
inference(clausification,[status(esa)],[normality2]) ).
cnf(c6,plain,
( X0 = identity
| ~ 'subgroup1$umember'(X0)
| ~ 'subgroup2$umember'(X0) ),
inference(clausification,[status(esa)],[trivial_intersection]) ).
cnf(c7,plain,
'subgroup1$umember'(v),
inference(clausification,[status(esa)],[v_in_G1]) ).
cnf(c8,plain,
'subgroup2$umember'(u),
inference(clausification,[status(esa)],[u_in_G2]) ).
cnf(c9,plain,
multiply(u,v) != multiply(v,u),
inference(clausification,[status(esa)],[prove_vu_equals_uv]) ).
cnf(c10,plain,
product(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c11,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c12,plain,
product(inverse(X0),X0,identity),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c13,plain,
product(X0,inverse(X0),identity),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c14,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[total_function1]) ).
cnf(c15,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[total_function2]) ).
cnf(c16,plain,
( product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity1]) ).
cnf(c17,plain,
( product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity2]) ).
cnf(d0,plain,
( ~ product(X1,X2,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[c15,c14]) ).
cnf(d1,plain,
( ~ product(X1,identity,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c15,c11]) ).
cnf(d2,plain,
( ~ product(X3,inverse(X2),X1)
| ~ product(X0,X2,X3)
| product(X0,identity,X1) ),
inference(resolution,[status(thm)],[c16,c13]) ).
cnf(d3,plain,
( product(X0,identity,inverse(X1))
| ~ product(X0,X1,identity) ),
inference(resolution,[status(thm)],[d2,c10]) ).
cnf(d4,plain,
product(X0,identity,inverse(inverse(X0))),
inference(resolution,[status(thm)],[d3,c13]) ).
cnf(d5,plain,
inverse(inverse(X0)) = X0,
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( ~ product(X3,X1,X0)
| ~ product(X3,identity,X2)
| product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[c17,c13]) ).
cnf(d7,plain,
( product(multiply(X0,X2),inverse(X2),X1)
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[d6,c14]) ).
cnf(d8,plain,
product(multiply(X0,X1),inverse(X1),X0),
inference(resolution,[status(thm)],[d7,c11]) ).
cnf(d9,plain,
X0 = multiply(multiply(X0,X1),inverse(X1)),
inference(resolution,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
( ~ product(X4,X2,X3)
| ~ product(X0,X1,X4)
| product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[c16,c14]) ).
cnf(d11,plain,
( product(X0,multiply(X1,X2),X2)
| ~ product(X0,X1,identity) ),
inference(resolution,[status(thm)],[d10,c10]) ).
cnf(d12,plain,
product(inverse(X0),multiply(X0,X1),X1),
inference(resolution,[status(thm)],[d11,c12]) ).
cnf(d13,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(superposition,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
X0 = multiply(X0,identity),
inference(resolution,[status(thm)],[d0,c11]) ).
cnf(d16,plain,
( product(X0,identity,multiply(X2,inverse(X1)))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d2,c14]) ).
cnf(d17,plain,
product(X0,multiply(inverse(X0),X1),X1),
inference(resolution,[status(thm)],[d11,c13]) ).
cnf(d18,plain,
product(X0,identity,multiply(X1,inverse(multiply(inverse(X0),X1)))),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
( ~ product(X4,inverse(X1),X0)
| ~ product(X4,X2,X3)
| product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[d12,c17]) ).
cnf(d20,plain,
( product(X2,multiply(X1,identity),multiply(X3,inverse(multiply(inverse(X0),X3))))
| ~ product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
( ~ product(X3,inverse(X0),X1)
| product(X1,X0,multiply(X2,inverse(multiply(inverse(X3),X2)))) ),
inference(demodulation,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
( ~ product(X1,inverse(X3),X2)
| product(X2,X3,inverse(inverse(X1))) ),
inference(demodulation,[status(thm)],[d21,d14]) ).
cnf(d23,plain,
( ~ product(X0,inverse(X2),X1)
| product(X1,X2,X0) ),
inference(demodulation,[status(thm)],[d22,d5]) ).
cnf(d24,plain,
( ~ product(X3,X4,X0)
| ~ product(X3,multiply(X4,X1),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c17,c14]) ).
cnf(d25,plain,
( product(multiply(X0,X1),X2,X3)
| ~ product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[d24,c14]) ).
cnf(d26,plain,
( ~ product(X3,inverse(X1),X0)
| ~ product(X3,identity,X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c17,c12]) ).
cnf(d27,plain,
( product(X0,X1,X2)
| ~ product(multiply(X0,X1),identity,X2) ),
inference(resolution,[status(thm)],[d8,d26]) ).
cnf(d28,plain,
( product(X0,multiply(X1,X3),multiply(X2,X3))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d10,c14]) ).
cnf(d29,plain,
product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)),
inference(resolution,[status(thm)],[d28,c14]) ).
cnf(d30,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(resolution,[status(thm)],[d29,d0]) ).
cnf(d31,plain,
( product(multiply(X0,inverse(X2)),X2,X1)
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[d26,c14]) ).
cnf(d32,plain,
product(multiply(X0,inverse(X1)),X1,X0),
inference(resolution,[status(thm)],[d31,c11]) ).
cnf(d33,plain,
( product(X0,multiply(X1,multiply(inverse(X2),X3)),X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d17,d10]) ).
cnf(d34,plain,
product(multiply(X0,inverse(X1)),multiply(X1,multiply(inverse(X0),X2)),X2),
inference(resolution,[status(thm)],[d33,d32]) ).
cnf(d35,plain,
'subgroup2$umember'(inverse(u)),
inference(resolution,[status(thm)],[c2,c8]) ).
cnf(d36,plain,
'subgroup2$umember'(multiply(X0,multiply(inverse(u),inverse(X0)))),
inference(resolution,[status(thm)],[c5,d35]) ).
cnf(d37,plain,
'subgroup2$umember'(multiply(X0,multiply(multiply(X1,multiply(inverse(u),inverse(X1))),inverse(X0)))),
inference(resolution,[status(thm)],[d36,c5]) ).
cnf(d38,plain,
( ~ 'subgroup2$umember'(X1)
| ~ 'subgroup2$umember'(multiply(inverse(X1),X0))
| 'subgroup2$umember'(X0) ),
inference(resolution,[status(thm)],[d17,c3]) ).
cnf(d39,plain,
( ~ 'subgroup2$umember'(multiply(inverse(u),X0))
| 'subgroup2$umember'(X0) ),
inference(resolution,[status(thm)],[d38,c8]) ).
cnf(d40,plain,
'subgroup2$umember'(multiply(multiply(X0,multiply(inverse(u),inverse(X0))),inverse(inverse(u)))),
inference(resolution,[status(thm)],[d39,d37]) ).
cnf(d41,plain,
'subgroup2$umember'(multiply(X0,multiply(multiply(inverse(u),inverse(X0)),inverse(inverse(u))))),
inference(demodulation,[status(thm)],[d40,d30]) ).
cnf(d42,plain,
'subgroup2$umember'(multiply(X0,multiply(inverse(u),multiply(inverse(X0),inverse(inverse(u)))))),
inference(demodulation,[status(thm)],[d41,d30]) ).
cnf(d43,plain,
'subgroup2$umember'(multiply(X0,multiply(inverse(u),multiply(inverse(X0),u)))),
inference(demodulation,[status(thm)],[d42,d5]) ).
cnf(d44,plain,
X0 = multiply(multiply(X0,inverse(X1)),X1),
inference(resolution,[status(thm)],[d32,d0]) ).
cnf(d45,plain,
inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
inference(superposition,[status(thm)],[d9,d13]) ).
cnf(d46,plain,
inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[d45,d44]) ).
cnf(d47,plain,
X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(resolution,[status(thm)],[d17,d0]) ).
cnf(d48,plain,
multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[d47,d47]) ).
cnf(d49,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d48,d5]) ).
cnf(d50,plain,
multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(superposition,[status(thm)],[d9,d49]) ).
cnf(d51,plain,
multiply(inverse(X1),inverse(X0)) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[d45,d50]) ).
cnf(d52,plain,
( ~ product(v,X1,X0)
| ~ 'subgroup1$umember'(X1)
| 'subgroup1$umember'(X0) ),
inference(resolution,[status(thm)],[c1,c7]) ).
cnf(d53,plain,
'subgroup1$umember'(inverse(v)),
inference(resolution,[status(thm)],[c0,c7]) ).
cnf(d54,plain,
'subgroup1$umember'(multiply(X0,multiply(inverse(v),inverse(X0)))),
inference(resolution,[status(thm)],[c4,d53]) ).
cnf(d55,plain,
( ~ product(v,multiply(X1,multiply(inverse(v),inverse(X1))),X0)
| 'subgroup1$umember'(X0) ),
inference(resolution,[status(thm)],[d54,d52]) ).
cnf(d56,plain,
'subgroup1$umember'(multiply(v,multiply(X0,multiply(inverse(v),inverse(X0))))),
inference(resolution,[status(thm)],[d55,c14]) ).
cnf(d57,plain,
( ~ 'subgroup2$umember'(multiply(v,multiply(X0,multiply(inverse(v),inverse(X0)))))
| multiply(v,multiply(X0,multiply(inverse(v),inverse(X0)))) = identity ),
inference(resolution,[status(thm)],[d56,c6]) ).
cnf(d58,plain,
( multiply(v,multiply(inverse(X0),multiply(inverse(v),inverse(inverse(X0))))) = identity
| ~ 'subgroup2$umember'(multiply(v,multiply(inverse(X0),multiply(inverse(v),X0)))) ),
inference(superposition,[status(thm)],[d5,d57]) ).
cnf(d59,plain,
( ~ 'subgroup2$umember'(multiply(v,multiply(inverse(X0),multiply(inverse(v),X0))))
| multiply(v,multiply(inverse(X0),inverse(multiply(inverse(X0),v)))) = identity ),
inference(demodulation,[status(thm)],[d58,d51]) ).
cnf(d60,plain,
( ~ 'subgroup2$umember'(multiply(v,multiply(inverse(X0),multiply(inverse(v),X0))))
| multiply(v,inverse(multiply(multiply(inverse(X0),v),X0))) = identity ),
inference(demodulation,[status(thm)],[d59,d51]) ).
cnf(d61,plain,
( ~ 'subgroup2$umember'(multiply(v,multiply(inverse(X0),multiply(inverse(v),X0))))
| multiply(v,inverse(multiply(inverse(X0),multiply(v,X0)))) = identity ),
inference(demodulation,[status(thm)],[d60,d30]) ).
cnf(d62,plain,
( ~ 'subgroup2$umember'(multiply(v,multiply(inverse(X0),multiply(inverse(v),X0))))
| multiply(v,multiply(inverse(multiply(v,X0)),X0)) = identity ),
inference(demodulation,[status(thm)],[d61,d46]) ).
cnf(d63,plain,
multiply(v,multiply(inverse(multiply(v,u)),u)) = identity,
inference(resolution,[status(thm)],[d62,d43]) ).
cnf(d64,plain,
product(multiply(multiply(v,u),inverse(v)),identity,u),
inference(superposition,[status(thm)],[d63,d34]) ).
cnf(d65,plain,
product(multiply(v,multiply(u,inverse(v))),identity,u),
inference(demodulation,[status(thm)],[d64,d30]) ).
cnf(d66,plain,
product(v,multiply(u,inverse(v)),u),
inference(resolution,[status(thm)],[d65,d27]) ).
cnf(d67,plain,
product(multiply(v,u),inverse(v),u),
inference(resolution,[status(thm)],[d66,d25]) ).
cnf(d68,plain,
product(u,v,multiply(v,u)),
inference(resolution,[status(thm)],[d67,d23]) ).
cnf(d69,plain,
multiply(v,u) = multiply(u,v),
inference(resolution,[status(thm)],[d68,d0]) ).
cnf(d70,plain,
multiply(v,u) != multiply(v,u),
inference(demodulation,[status(thm)],[c9,d69]) ).
cnf(d71,plain,
$false,
inference(resolution,[status(thm)],[d49,d70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP617-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.52 % Computer : n012.cluster.edu
% 0.05/0.52 % Model : x86_64 x86_64
% 0.05/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.52 % Memory : 8046.5625MB
% 0.05/0.52 % OS : Linux 6.8.0-71-generic
% 0.05/0.52 % CPULimit : 300
% 0.05/0.52 % WCLimit : 300
% 0.05/0.52 % DateTime : Fri Sep 25 15:02:22 UTC 2026
% 0.05/0.52 % CPUTime :
% 0.05/0.52 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 66.29/13.70 % SZS status Unsatisfiable for theBenchmark.p
% 66.29/13.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------