%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP039-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 07:22:10 AM UTC 2026
% Result : Unsatisfiable 11.89s 4.26s
% Output : CNFRefutation 11.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of clauses : 84 ( 37 unt; 9 nHn; 61 RR)
% Number of literals : 165 ( 19 equ; 73 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(an_element_in_O2,axiom,
( 'subgroup$umember'(X0)
| 'subgroup$umember'(X1)
| 'subgroup$umember'('element$uin$uO2'(X0,X1)) ) ).
cnf(property_of_O2,axiom,
( 'subgroup$umember'(X0)
| 'subgroup$umember'(X1)
| product(X0,'element$uin$uO2'(X0,X1),X1) ) ).
cnf(b_is_in_subgroup,negated_conjecture,
'subgroup$umember'(b) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
product(b,inverse(a),c) ).
cnf(a_times_c_is_d,negated_conjecture,
product(a,c,d) ).
cnf(prove_d_is_in_subgroup,negated_conjecture,
~ 'subgroup$umember'(d) ).
cnf(left_identity,axiom,
product(identity,X0,X0) ).
cnf(right_identity,axiom,
product(X0,identity,X0) ).
cnf(left_inverse,axiom,
product(inverse(X0),X0,identity) ).
cnf(right_inverse,axiom,
product(X0,inverse(X0),identity) ).
cnf(total_function1,axiom,
product(X0,X1,multiply(X0,X1)) ).
cnf(total_function2,axiom,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ) ).
cnf(associativity1,axiom,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(associativity2,axiom,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ) ).
cnf(closure_of_inverse,axiom,
( 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(X0) ) ).
cnf(closure_of_product,axiom,
( 'subgroup$umember'(X2)
| ~ product(X0,X1,X2)
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ) ).
cnf(c1,plain,
( 'subgroup$umember'(X0)
| 'subgroup$umember'(X1)
| 'subgroup$umember'('element$uin$uO2'(X0,X1)) ),
inference(clausification,[status(esa)],[an_element_in_O2]) ).
cnf(c2,plain,
( 'subgroup$umember'(X0)
| 'subgroup$umember'(X1)
| product(X0,'element$uin$uO2'(X0,X1),X1) ),
inference(clausification,[status(esa)],[property_of_O2]) ).
cnf(c3,plain,
'subgroup$umember'(b),
inference(clausification,[status(esa)],[b_is_in_subgroup]) ).
cnf(c4,plain,
product(b,inverse(a),c),
inference(clausification,[status(esa)],[b_times_a_inverse_is_c]) ).
cnf(c5,plain,
product(a,c,d),
inference(clausification,[status(esa)],[a_times_c_is_d]) ).
cnf(c6,plain,
~ 'subgroup$umember'(d),
inference(clausification,[status(esa)],[prove_d_is_in_subgroup]) ).
cnf(c7,plain,
product(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c8,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c9,plain,
product(inverse(X0),X0,identity),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c10,plain,
product(X0,inverse(X0),identity),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c11,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[total_function1]) ).
cnf(c12,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[total_function2]) ).
cnf(c13,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity1]) ).
cnf(c14,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity2]) ).
cnf(c15,plain,
( 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[closure_of_inverse]) ).
cnf(c16,plain,
( 'subgroup$umember'(X2)
| ~ product(X0,X1,X2)
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[closure_of_product]) ).
cnf(d0,plain,
( ~ product(X1,X2,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[c12,c11]) ).
cnf(d1,plain,
X0 = multiply(identity,X0),
inference(resolution,[status(thm)],[d0,c7]) ).
cnf(d2,plain,
( product(X0,X4,X3)
| ~ product(X1,X2,X4)
| ~ product(multiply(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[c13,c11]) ).
cnf(d3,plain,
( product(X3,X2,multiply(multiply(X3,X0),X1))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d2,c11]) ).
cnf(d4,plain,
( ~ product(X1,inverse(X1),X0)
| X0 = identity ),
inference(resolution,[status(thm)],[c12,c10]) ).
cnf(d5,plain,
multiply(X0,inverse(X0)) = identity,
inference(resolution,[status(thm)],[d4,c11]) ).
cnf(d6,plain,
( ~ product(inverse(X0),X2,X1)
| product(X0,X1,multiply(identity,X2)) ),
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( ~ product(inverse(X1),X0,X2)
| product(X1,X2,X0) ),
inference(demodulation,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
product(X0,multiply(inverse(X0),X1),X1),
inference(resolution,[status(thm)],[d7,c11]) ).
cnf(d9,plain,
( ~ product(X1,identity,X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c12,c8]) ).
cnf(d10,plain,
( product(X2,X3,X1)
| ~ product(inverse(X2),X0,X3)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[c13,c10]) ).
cnf(d11,plain,
( ~ product(identity,inverse(inverse(X0)),X1)
| product(X0,identity,X1) ),
inference(resolution,[status(thm)],[d10,c10]) ).
cnf(d12,plain,
product(X0,identity,inverse(inverse(X0))),
inference(resolution,[status(thm)],[d11,c7]) ).
cnf(d13,plain,
inverse(inverse(X0)) = X0,
inference(resolution,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
product(inverse(X0),multiply(X0,X1),X1),
inference(superposition,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
( ~ product(a,c,X0)
| X0 = d ),
inference(resolution,[status(thm)],[c12,c5]) ).
cnf(d16,plain,
multiply(a,c) = d,
inference(resolution,[status(thm)],[d15,c11]) ).
cnf(d17,plain,
product(inverse(a),d,c),
inference(superposition,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
( product(inverse(X2),X3,X1)
| ~ product(X2,X0,X3)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[c13,c9]) ).
cnf(d19,plain,
( product(inverse(X0),X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d18,c7]) ).
cnf(d20,plain,
( ~ product(inverse(X0),X2,X3)
| X3 = X1
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d19,c12]) ).
cnf(d21,plain,
( ~ product(a,X0,d)
| c = X0 ),
inference(resolution,[status(thm)],[d20,d17]) ).
cnf(d22,plain,
( 'subgroup$umember'(X1)
| 'subgroup$umember'(X2)
| ~ product(X2,'element$uin$uO2'(X2,X1),X0)
| X0 = X1 ),
inference(resolution,[status(thm)],[c12,c2]) ).
cnf(d23,plain,
( 'subgroup$umember'(X1)
| 'subgroup$umember'(X0)
| multiply(X0,'element$uin$uO2'(X0,X1)) = X1 ),
inference(resolution,[status(thm)],[d22,c11]) ).
cnf(d24,plain,
( 'subgroup$umember'(X0)
| multiply(X0,'element$uin$uO2'(X0,d)) = d ),
inference(resolution,[status(thm)],[d23,c6]) ).
cnf(d25,plain,
( ~ 'subgroup$umember'(X0)
| ~ 'subgroup$umember'(X1)
| 'subgroup$umember'(multiply(X0,X1)) ),
inference(resolution,[status(thm)],[c16,c11]) ).
cnf(d26,plain,
( ~ product(X0,X4,X3)
| ~ product(X1,X2,X4)
| product(multiply(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[c14,c11]) ).
cnf(d27,plain,
( product(multiply(a,X0),X1,d)
| ~ product(X0,X1,c) ),
inference(resolution,[status(thm)],[d26,c5]) ).
cnf(d28,plain,
( ~ 'subgroup$umember'(multiply(a,X0))
| ~ 'subgroup$umember'(X1)
| 'subgroup$umember'(d)
| ~ product(X0,X1,c) ),
inference(resolution,[status(thm)],[d27,c16]) ).
cnf(d29,plain,
( ~ product(X1,X0,c)
| ~ 'subgroup$umember'(multiply(a,X1))
| ~ 'subgroup$umember'(X0) ),
inference(resolution,[status(thm)],[c6,d28]) ).
cnf(d30,plain,
( ~ 'subgroup$umember'(multiply(a,b))
| ~ 'subgroup$umember'(inverse(a)) ),
inference(resolution,[status(thm)],[d29,c4]) ).
cnf(d31,plain,
( ~ 'subgroup$umember'(a)
| ~ 'subgroup$umember'(b)
| ~ 'subgroup$umember'(inverse(a)) ),
inference(resolution,[status(thm)],[d30,d25]) ).
cnf(d32,plain,
( ~ 'subgroup$umember'(a)
| ~ 'subgroup$umember'(inverse(a)) ),
inference(resolution,[status(thm)],[c3,d31]) ).
cnf(d33,plain,
( ~ 'subgroup$umember'(a)
| ~ 'subgroup$umember'(a) ),
inference(resolution,[status(thm)],[d32,c15]) ).
cnf(d34,plain,
multiply(a,'element$uin$uO2'(a,d)) = d,
inference(resolution,[status(thm)],[d33,d24]) ).
cnf(d35,plain,
product(a,'element$uin$uO2'(a,d),d),
inference(superposition,[status(thm)],[d34,c11]) ).
cnf(d36,plain,
c = 'element$uin$uO2'(a,d),
inference(resolution,[status(thm)],[d35,d21]) ).
cnf(d37,plain,
( 'subgroup$umember'(a)
| 'subgroup$umember'(d)
| 'subgroup$umember'(c) ),
inference(superposition,[status(thm)],[d36,c1]) ).
cnf(d38,plain,
( 'subgroup$umember'(c)
| 'subgroup$umember'(a) ),
inference(resolution,[status(thm)],[c6,d37]) ).
cnf(d39,plain,
'subgroup$umember'(c),
inference(resolution,[status(thm)],[d33,d38]) ).
cnf(d40,plain,
( product(b,X2,X1)
| ~ product(inverse(a),X0,X2)
| ~ product(c,X0,X1) ),
inference(resolution,[status(thm)],[c13,c4]) ).
cnf(d41,plain,
( ~ product(c,a,X0)
| product(b,identity,X0) ),
inference(resolution,[status(thm)],[d40,c9]) ).
cnf(d42,plain,
product(b,identity,multiply(c,a)),
inference(resolution,[status(thm)],[d41,c11]) ).
cnf(d43,plain,
multiply(c,a) = b,
inference(resolution,[status(thm)],[d42,d9]) ).
cnf(d44,plain,
product(c,a,b),
inference(superposition,[status(thm)],[d43,c11]) ).
cnf(d45,plain,
b = multiply(c,a),
inference(resolution,[status(thm)],[d44,d0]) ).
cnf(d46,plain,
product(inverse(c),b,a),
inference(superposition,[status(thm)],[d45,d14]) ).
cnf(d47,plain,
( ~ 'subgroup$umember'(inverse(c))
| ~ 'subgroup$umember'(b)
| 'subgroup$umember'(a) ),
inference(resolution,[status(thm)],[d46,c16]) ).
cnf(d48,plain,
( 'subgroup$umember'(a)
| ~ 'subgroup$umember'(inverse(c)) ),
inference(resolution,[status(thm)],[c3,d47]) ).
cnf(d49,plain,
( ~ 'subgroup$umember'(c)
| 'subgroup$umember'(a) ),
inference(resolution,[status(thm)],[d48,c15]) ).
cnf(d50,plain,
~ 'subgroup$umember'(c),
inference(resolution,[status(thm)],[d33,d49]) ).
cnf(d51,plain,
$false,
inference(resolution,[status(thm)],[d50,d39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP039-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n014.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 14:19:02 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.89/4.26 % SZS status Unsatisfiable for theBenchmark.p
% 11.89/4.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------