%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP039-7 : TPTP v9.3.1. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 07:22:11 AM UTC 2026
% Result : Unsatisfiable 17.51s 2.63s
% Output : CNFRefutation 17.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of clauses : 64 ( 38 unt; 8 nHn; 37 RR)
% Number of literals : 106 ( 39 equ; 35 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 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 : 60 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
multiply(X0,identity) = X0 ).
cnf(right_inverse,axiom,
multiply(X0,inverse(X0)) = identity ).
cnf(inverse_inverse,axiom,
inverse(inverse(X0)) = X0 ).
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,
inverse(inverse(X0)) = X0,
inference(clausification,[status(esa)],[inverse_inverse]) ).
cnf(c5,plain,
( 'subgroup$umember'('element$uin$uO2'(X0,X1))
| 'subgroup$umember'(X1)
| 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[an_element_in_O2]) ).
cnf(c6,plain,
( multiply(X0,'element$uin$uO2'(X0,X1)) = X1
| 'subgroup$umember'(X1)
| 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[property_of_O2]) ).
cnf(c7,plain,
'subgroup$umember'(b),
inference(clausification,[status(esa)],[b_in_O2]) ).
cnf(c8,plain,
multiply(b,inverse(a)) = c,
inference(clausification,[status(esa)],[b_times_a_inverse_is_c]) ).
cnf(c9,plain,
multiply(a,c) = d,
inference(clausification,[status(esa)],[a_times_c_is_d]) ).
cnf(c10,plain,
~ 'subgroup$umember'(d),
inference(clausification,[status(esa)],[prove_d_in_O2]) ).
cnf(c11,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c12,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c13,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(c14,plain,
( 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[closure_of_inverse]) ).
cnf(c15,plain,
( 'subgroup$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)],[c12,c13]) ).
cnf(d1,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d0,c11]) ).
cnf(d2,plain,
c = multiply(inverse(a),d),
inference(superposition,[status(thm)],[c9,d1]) ).
cnf(d3,plain,
( 'subgroup$umember'(X0)
| multiply(X0,'element$uin$uO2'(X0,d)) = d ),
inference(resolution,[status(thm)],[c6,c10]) ).
cnf(d4,plain,
( ~ 'subgroup$umember'(b)
| ~ 'subgroup$umember'(inverse(a))
| 'subgroup$umember'(X0)
| c != X0 ),
inference(superposition,[status(thm)],[c8,c15]) ).
cnf(d5,plain,
( ~ 'subgroup$umember'(inverse(a))
| 'subgroup$umember'(X0)
| c != X0 ),
inference(resolution,[status(thm)],[c7,d4]) ).
cnf(d6,plain,
( ~ 'subgroup$umember'(inverse(a))
| 'subgroup$umember'(c) ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( ~ 'subgroup$umember'(a)
| 'subgroup$umember'(c) ),
inference(resolution,[status(thm)],[d6,c14]) ).
cnf(d8,plain,
( multiply(a,'element$uin$uO2'(a,d)) = d
| 'subgroup$umember'(c) ),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
multiply(c,X0) = multiply(b,multiply(inverse(a),X0)),
inference(superposition,[status(thm)],[c8,c13]) ).
cnf(d10,plain,
multiply(identity,X1) = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[c1,c13]) ).
cnf(d11,plain,
X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(demodulation,[status(thm)],[d10,c11]) ).
cnf(d12,plain,
multiply(c,multiply(inverse(inverse(a)),X0)) = multiply(b,X0),
inference(superposition,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
multiply(c,multiply(a,X0)) = multiply(b,X0),
inference(demodulation,[status(thm)],[d12,c2]) ).
cnf(d14,plain,
( ~ 'subgroup$umember'(X0)
| ~ 'subgroup$umember'(X1)
| 'subgroup$umember'(multiply(X0,X1)) ),
inference(equality_resolution,[status(thm)],[c15]) ).
cnf(d15,plain,
( ~ 'subgroup$umember'(b)
| ~ 'subgroup$umember'(multiply(inverse(a),X0))
| 'subgroup$umember'(multiply(c,X0)) ),
inference(superposition,[status(thm)],[d9,d14]) ).
cnf(d16,plain,
( 'subgroup$umember'(multiply(c,X0))
| ~ 'subgroup$umember'(multiply(inverse(a),X0)) ),
inference(resolution,[status(thm)],[c7,d15]) ).
cnf(d17,plain,
multiply(X0,multiply(X1,identity)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c13,c0]) ).
cnf(d18,plain,
multiply(X1,X0) = multiply(X1,X0),
inference(demodulation,[status(thm)],[d17,c0]) ).
cnf(d19,plain,
multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[d1,d18]) ).
cnf(d20,plain,
( 'subgroup$umember'(multiply(c,multiply(a,X0)))
| ~ 'subgroup$umember'(X0) ),
inference(superposition,[status(thm)],[d19,d16]) ).
cnf(d21,plain,
( 'subgroup$umember'(multiply(b,X0))
| ~ 'subgroup$umember'(X0) ),
inference(demodulation,[status(thm)],[d20,d13]) ).
cnf(d22,plain,
( ~ 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(multiply(X0,X1))
| 'subgroup$umember'(X1) ),
inference(superposition,[status(thm)],[d1,d14]) ).
cnf(d23,plain,
multiply(c,d) = multiply(b,c),
inference(superposition,[status(thm)],[d2,d9]) ).
cnf(d24,plain,
( ~ 'subgroup$umember'(inverse(c))
| 'subgroup$umember'(d)
| ~ 'subgroup$umember'(multiply(b,c)) ),
inference(superposition,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
( ~ 'subgroup$umember'(inverse(c))
| ~ 'subgroup$umember'(multiply(b,c)) ),
inference(resolution,[status(thm)],[c10,d24]) ).
cnf(d26,plain,
( ~ 'subgroup$umember'(c)
| ~ 'subgroup$umember'(inverse(c)) ),
inference(resolution,[status(thm)],[d25,d21]) ).
cnf(d27,plain,
( ~ 'subgroup$umember'(c)
| ~ 'subgroup$umember'(c) ),
inference(resolution,[status(thm)],[d26,c14]) ).
cnf(d28,plain,
multiply(a,'element$uin$uO2'(a,d)) = d,
inference(resolution,[status(thm)],[d27,d8]) ).
cnf(d29,plain,
'element$uin$uO2'(a,d) = multiply(inverse(a),d),
inference(superposition,[status(thm)],[d28,d1]) ).
cnf(d30,plain,
'element$uin$uO2'(a,d) = c,
inference(demodulation,[status(thm)],[d29,d2]) ).
cnf(d31,plain,
( 'subgroup$umember'(a)
| 'subgroup$umember'(d)
| 'subgroup$umember'(c) ),
inference(superposition,[status(thm)],[d30,c5]) ).
cnf(d32,plain,
( 'subgroup$umember'(c)
| 'subgroup$umember'(a) ),
inference(resolution,[status(thm)],[c10,d31]) ).
cnf(d33,plain,
'subgroup$umember'(a),
inference(resolution,[status(thm)],[d27,d32]) ).
cnf(d34,plain,
~ 'subgroup$umember'(a),
inference(resolution,[status(thm)],[d27,d7]) ).
cnf(d35,plain,
$false,
inference(resolution,[status(thm)],[d34,d33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-7 : TPTP v9.3.1. Bugfixed v1.0.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 14:22:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.51/2.63 % SZS status Unsatisfiable for theBenchmark.p
% 17.51/2.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------