%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP039-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 18.48s 4.52s
% Output : CNFRefutation 18.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of clauses : 75 ( 47 unt; 8 nHn; 46 RR)
% Number of literals : 120 ( 47 equ; 39 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
multiply(X0,identity) = X0 ).
cnf(right_inverse,axiom,
multiply(X0,inverse(X0)) = identity ).
cnf(an_element_in_O2,axiom,
( 'subgroup$umember'('element$uin$uO2'(X0,X1))
| 'subgroup$umember'(X1)
| 'subgroup$umember'(X0) ) ).
cnf(property_of_O2,axiom,
( multiply(X0,'element$uin$uO2'(X0,X1)) = X1
| 'subgroup$umember'(X1)
| 'subgroup$umember'(X0) ) ).
cnf(b_in_O2,negated_conjecture,
'subgroup$umember'(b) ).
cnf(b_times_a_inverse_is_c,negated_conjecture,
multiply(b,inverse(a)) = c ).
cnf(a_times_c_is_d,negated_conjecture,
multiply(a,c) = d ).
cnf(prove_d_in_O2,negated_conjecture,
~ 'subgroup$umember'(d) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(closure_of_inverse,axiom,
( 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(X0) ) ).
cnf(closure_of_multiply,axiom,
( 'subgroup$umember'(X2)
| multiply(X0,X1) != X2
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ) ).
cnf(c0,plain,
multiply(X0,identity) = X0,
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c1,plain,
multiply(X0,inverse(X0)) = identity,
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c2,plain,
( 'subgroup$umember'('element$uin$uO2'(X0,X1))
| 'subgroup$umember'(X1)
| 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[an_element_in_O2]) ).
cnf(c3,plain,
( multiply(X0,'element$uin$uO2'(X0,X1)) = X1
| 'subgroup$umember'(X1)
| 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[property_of_O2]) ).
cnf(c4,plain,
'subgroup$umember'(b),
inference(clausification,[status(esa)],[b_in_O2]) ).
cnf(c5,plain,
multiply(b,inverse(a)) = c,
inference(clausification,[status(esa)],[b_times_a_inverse_is_c]) ).
cnf(c6,plain,
multiply(a,c) = d,
inference(clausification,[status(esa)],[a_times_c_is_d]) ).
cnf(c7,plain,
~ 'subgroup$umember'(d),
inference(clausification,[status(esa)],[prove_d_in_O2]) ).
cnf(c8,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c9,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c10,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(c11,plain,
( 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[closure_of_inverse]) ).
cnf(c12,plain,
( 'subgroup$umember'(X2)
| multiply(X0,X1) != X2
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[closure_of_multiply]) ).
cnf(d0,plain,
multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[c9,c10]) ).
cnf(d1,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d0,c8]) ).
cnf(d2,plain,
multiply(identity,X1) = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[c1,c10]) ).
cnf(d3,plain,
X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(demodulation,[status(thm)],[d2,c8]) ).
cnf(d4,plain,
multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c10,c1]) ).
cnf(d5,plain,
multiply(X1,inverse(multiply(inverse(X0),X1))) = multiply(X0,identity),
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
multiply(X1,inverse(multiply(inverse(X0),X1))) = X0,
inference(demodulation,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
multiply(X0,multiply(X1,identity)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c10,c0]) ).
cnf(d8,plain,
multiply(X1,X0) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
c = multiply(inverse(a),d),
inference(superposition,[status(thm)],[c6,d1]) ).
cnf(d10,plain,
multiply(inverse(a),d) = c,
inference(superposition,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
multiply(d,inverse(c)) = a,
inference(superposition,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
inverse(c) = multiply(inverse(d),a),
inference(superposition,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
( 'subgroup$umember'(X0)
| multiply(d,'element$uin$uO2'(d,X0)) = X0 ),
inference(resolution,[status(thm)],[c3,c7]) ).
cnf(d14,plain,
( ~ 'subgroup$umember'(b)
| ~ 'subgroup$umember'(inverse(a))
| 'subgroup$umember'(X0)
| c != X0 ),
inference(superposition,[status(thm)],[c5,c12]) ).
cnf(d15,plain,
( ~ 'subgroup$umember'(inverse(a))
| 'subgroup$umember'(X0)
| c != X0 ),
inference(resolution,[status(thm)],[c4,d14]) ).
cnf(d16,plain,
( ~ 'subgroup$umember'(inverse(a))
| 'subgroup$umember'(c) ),
inference(equality_resolution,[status(thm)],[d15]) ).
cnf(d17,plain,
( ~ 'subgroup$umember'(a)
| 'subgroup$umember'(c) ),
inference(resolution,[status(thm)],[d16,c11]) ).
cnf(d18,plain,
( multiply(d,'element$uin$uO2'(d,a)) = a
| 'subgroup$umember'(c) ),
inference(resolution,[status(thm)],[d17,d13]) ).
cnf(d19,plain,
inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c1,d3]) ).
cnf(d20,plain,
inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[d19,c0]) ).
cnf(d21,plain,
multiply(c,X0) = multiply(b,multiply(inverse(a),X0)),
inference(superposition,[status(thm)],[c5,c10]) ).
cnf(d22,plain,
multiply(c,multiply(inverse(inverse(a)),X0)) = multiply(b,X0),
inference(superposition,[status(thm)],[d3,d21]) ).
cnf(d23,plain,
multiply(c,multiply(a,X0)) = multiply(b,X0),
inference(demodulation,[status(thm)],[d22,d20]) ).
cnf(d24,plain,
( ~ 'subgroup$umember'(X0)
| ~ 'subgroup$umember'(X1)
| 'subgroup$umember'(multiply(X0,X1)) ),
inference(equality_resolution,[status(thm)],[c12]) ).
cnf(d25,plain,
( ~ 'subgroup$umember'(b)
| ~ 'subgroup$umember'(multiply(inverse(a),X0))
| 'subgroup$umember'(multiply(c,X0)) ),
inference(superposition,[status(thm)],[d21,d24]) ).
cnf(d26,plain,
( 'subgroup$umember'(multiply(c,X0))
| ~ 'subgroup$umember'(multiply(inverse(a),X0)) ),
inference(resolution,[status(thm)],[c4,d25]) ).
cnf(d27,plain,
( 'subgroup$umember'(multiply(c,multiply(a,X0)))
| ~ 'subgroup$umember'(X0) ),
inference(superposition,[status(thm)],[d1,d26]) ).
cnf(d28,plain,
( 'subgroup$umember'(multiply(b,X0))
| ~ 'subgroup$umember'(X0) ),
inference(demodulation,[status(thm)],[d27,d23]) ).
cnf(d29,plain,
( ~ 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(multiply(X0,X1))
| 'subgroup$umember'(X1) ),
inference(superposition,[status(thm)],[d1,d24]) ).
cnf(d30,plain,
multiply(c,d) = multiply(b,c),
inference(superposition,[status(thm)],[d9,d21]) ).
cnf(d31,plain,
( ~ 'subgroup$umember'(inverse(c))
| 'subgroup$umember'(d)
| ~ 'subgroup$umember'(multiply(b,c)) ),
inference(superposition,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
( ~ 'subgroup$umember'(inverse(c))
| ~ 'subgroup$umember'(multiply(b,c)) ),
inference(resolution,[status(thm)],[c7,d31]) ).
cnf(d33,plain,
( ~ 'subgroup$umember'(c)
| ~ 'subgroup$umember'(inverse(c)) ),
inference(resolution,[status(thm)],[d32,d28]) ).
cnf(d34,plain,
( ~ 'subgroup$umember'(c)
| ~ 'subgroup$umember'(c) ),
inference(resolution,[status(thm)],[d33,c11]) ).
cnf(d35,plain,
multiply(d,'element$uin$uO2'(d,a)) = a,
inference(resolution,[status(thm)],[d34,d18]) ).
cnf(d36,plain,
'element$uin$uO2'(d,a) = multiply(inverse(d),a),
inference(superposition,[status(thm)],[d35,d1]) ).
cnf(d37,plain,
'element$uin$uO2'(d,a) = inverse(c),
inference(demodulation,[status(thm)],[d36,d12]) ).
cnf(d38,plain,
( 'subgroup$umember'(d)
| 'subgroup$umember'(a)
| 'subgroup$umember'(inverse(c)) ),
inference(superposition,[status(thm)],[d37,c2]) ).
cnf(d39,plain,
( 'subgroup$umember'(a)
| 'subgroup$umember'(inverse(c)) ),
inference(resolution,[status(thm)],[c7,d38]) ).
cnf(d40,plain,
~ 'subgroup$umember'(a),
inference(resolution,[status(thm)],[d34,d17]) ).
cnf(d41,plain,
'subgroup$umember'(inverse(c)),
inference(resolution,[status(thm)],[d40,d39]) ).
cnf(d42,plain,
multiply(c,a) = multiply(b,identity),
inference(superposition,[status(thm)],[c9,d21]) ).
cnf(d43,plain,
multiply(c,a) = b,
inference(demodulation,[status(thm)],[d42,c0]) ).
cnf(d44,plain,
a = multiply(inverse(c),b),
inference(superposition,[status(thm)],[d43,d1]) ).
cnf(d45,plain,
( ~ 'subgroup$umember'(inverse(c))
| ~ 'subgroup$umember'(b)
| 'subgroup$umember'(a) ),
inference(superposition,[status(thm)],[d44,d24]) ).
cnf(d46,plain,
( 'subgroup$umember'(a)
| ~ 'subgroup$umember'(inverse(c)) ),
inference(resolution,[status(thm)],[c4,d45]) ).
cnf(d47,plain,
~ 'subgroup$umember'(inverse(c)),
inference(resolution,[status(thm)],[d40,d46]) ).
cnf(d48,plain,
$false,
inference(resolution,[status(thm)],[d47,d41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n009.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Fri Sep 25 14:19:14 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.48/4.52 % SZS status Unsatisfiable for theBenchmark.p
% 18.48/4.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------