%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP040-3 : 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 : n011.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 18.27s 5.33s
% Output : CNFRefutation 18.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of clauses : 72 ( 38 unt; 8 nHn; 51 RR)
% Number of literals : 134 ( 15 equ; 56 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 : 104 ( 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$uO2'(X0,X1),X1) ) ).
cnf(a_in_subgroup,hypothesis,
~ 'subgroup$umember'(a) ).
cnf(b_is_in_subgroup,hypothesis,
'subgroup$umember'(b) ).
cnf(d_in_subgroup,hypothesis,
~ 'subgroup$umember'(d) ).
cnf(b_times_a_inverse_is_c,hypothesis,
product(b,inverse(a),c) ).
cnf(a_times_c_is_d,hypothesis,
product(a,c,d) ).
cnf(prove_inverse_is_self_cancelling,negated_conjecture,
inverse(inverse(X0)) = X0 ).
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_product_and_inverse,axiom,
( 'subgroup$umember'(X2)
| ~ product(X0,inverse(X1),X2)
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ) ).
cnf(c0,plain,
( 'subgroup$umember'(X0)
| 'subgroup$umember'(X1)
| 'subgroup$umember'('element$uin$uO2'(X0,X1)) ),
inference(clausification,[status(esa)],[an_element_in_O2]) ).
cnf(c1,plain,
( 'subgroup$umember'(X0)
| 'subgroup$umember'(X1)
| product(X0,'element$uin$uO2'(X0,X1),X1) ),
inference(clausification,[status(esa)],[property_of_O2]) ).
cnf(c2,plain,
~ 'subgroup$umember'(a),
inference(clausification,[status(esa)],[a_in_subgroup]) ).
cnf(c3,plain,
'subgroup$umember'(b),
inference(clausification,[status(esa)],[b_is_in_subgroup]) ).
cnf(c4,plain,
~ 'subgroup$umember'(d),
inference(clausification,[status(esa)],[d_in_subgroup]) ).
cnf(c5,plain,
product(b,inverse(a),c),
inference(clausification,[status(esa)],[b_times_a_inverse_is_c]) ).
cnf(c6,plain,
product(a,c,d),
inference(clausification,[status(esa)],[a_times_c_is_d]) ).
cnf(c7,plain,
inverse(inverse(X0)) = X0,
inference(clausification,[status(esa)],[prove_inverse_is_self_cancelling]) ).
cnf(c8,plain,
product(identity,X0,X0),
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c9,plain,
product(X0,identity,X0),
inference(clausification,[status(esa)],[right_identity]) ).
cnf(c10,plain,
product(inverse(X0),X0,identity),
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c11,plain,
product(X0,inverse(X0),identity),
inference(clausification,[status(esa)],[right_inverse]) ).
cnf(c12,plain,
product(X0,X1,multiply(X0,X1)),
inference(clausification,[status(esa)],[total_function1]) ).
cnf(c13,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[total_function2]) ).
cnf(c14,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity1]) ).
cnf(c15,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(clausification,[status(esa)],[associativity2]) ).
cnf(c16,plain,
( 'subgroup$umember'(X2)
| ~ product(X0,inverse(X1),X2)
| ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(X0) ),
inference(clausification,[status(esa)],[closure_of_product_and_inverse]) ).
cnf(d0,plain,
( ~ 'subgroup$umember'(identity)
| ~ 'subgroup$umember'(X0)
| 'subgroup$umember'(inverse(X0)) ),
inference(resolution,[status(thm)],[c16,c8]) ).
cnf(d1,plain,
( ~ 'subgroup$umember'(X0)
| ~ 'subgroup$umember'(X0)
| 'subgroup$umember'(identity) ),
inference(resolution,[status(thm)],[c16,c11]) ).
cnf(d2,plain,
'subgroup$umember'(identity),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
( 'subgroup$umember'(inverse(X0))
| ~ 'subgroup$umember'(X0) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( ~ 'subgroup$umember'(X1)
| ~ 'subgroup$umember'(inverse(X0))
| 'subgroup$umember'(X2)
| ~ product(X1,X0,X2) ),
inference(superposition,[status(thm)],[c7,c16]) ).
cnf(d5,plain,
( ~ product(X1,X2,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[c13,c12]) ).
cnf(d6,plain,
X0 = multiply(identity,X0),
inference(resolution,[status(thm)],[d5,c8]) ).
cnf(d7,plain,
( ~ product(X4,X3,X1)
| ~ product(X0,X4,X2)
| product(X0,X1,multiply(X2,X3)) ),
inference(resolution,[status(thm)],[c14,c12]) ).
cnf(d8,plain,
( product(X0,X2,multiply(identity,X1))
| ~ product(inverse(X0),X1,X2) ),
inference(resolution,[status(thm)],[d7,c11]) ).
cnf(d9,plain,
( ~ product(inverse(X1),X0,X2)
| product(X1,X2,X0) ),
inference(demodulation,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
product(X0,multiply(inverse(X0),X1),X1),
inference(resolution,[status(thm)],[d9,c12]) ).
cnf(d11,plain,
product(inverse(X0),multiply(X0,X1),X1),
inference(superposition,[status(thm)],[c7,d10]) ).
cnf(d12,plain,
( ~ product(b,X2,X1)
| ~ product(inverse(a),X0,X2)
| product(c,X0,X1) ),
inference(resolution,[status(thm)],[c15,c5]) ).
cnf(d13,plain,
( product(c,a,X0)
| ~ product(b,identity,X0) ),
inference(resolution,[status(thm)],[d12,c10]) ).
cnf(d14,plain,
product(c,a,b),
inference(resolution,[status(thm)],[d13,c9]) ).
cnf(d15,plain,
b = multiply(c,a),
inference(resolution,[status(thm)],[d14,d5]) ).
cnf(d16,plain,
product(inverse(c),b,a),
inference(superposition,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
( ~ 'subgroup$umember'(inverse(b))
| ~ 'subgroup$umember'(inverse(c))
| 'subgroup$umember'(a) ),
inference(resolution,[status(thm)],[d16,d4]) ).
cnf(d18,plain,
( ~ 'subgroup$umember'(inverse(c))
| ~ 'subgroup$umember'(inverse(b)) ),
inference(resolution,[status(thm)],[c2,d17]) ).
cnf(d19,plain,
( ~ 'subgroup$umember'(c)
| ~ 'subgroup$umember'(inverse(b)) ),
inference(resolution,[status(thm)],[d18,d3]) ).
cnf(d20,plain,
( 'subgroup$umember'(X0)
| 'subgroup$umember'(X1)
| X0 = multiply(X1,'element$uin$uO2'(X1,X0)) ),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d21,plain,
( 'subgroup$umember'(X0)
| X0 = multiply(a,'element$uin$uO2'(a,X0)) ),
inference(resolution,[status(thm)],[d20,c2]) ).
cnf(d22,plain,
d = multiply(a,'element$uin$uO2'(a,d)),
inference(resolution,[status(thm)],[d21,c4]) ).
cnf(d23,plain,
product(a,'element$uin$uO2'(a,d),d),
inference(superposition,[status(thm)],[d22,c12]) ).
cnf(d24,plain,
( ~ product(a,c,X0)
| X0 = d ),
inference(resolution,[status(thm)],[c13,c6]) ).
cnf(d25,plain,
multiply(a,c) = d,
inference(resolution,[status(thm)],[d24,c12]) ).
cnf(d26,plain,
product(inverse(a),d,c),
inference(superposition,[status(thm)],[d25,d11]) ).
cnf(d27,plain,
( product(inverse(X0),X2,multiply(identity,X1))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d7,c10]) ).
cnf(d28,plain,
( product(inverse(X1),X2,X0)
| ~ product(X1,X0,X2) ),
inference(demodulation,[status(thm)],[d27,d6]) ).
cnf(d29,plain,
( ~ product(inverse(X0),X2,X3)
| X3 = X1
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[d28,c13]) ).
cnf(d30,plain,
( ~ product(a,X0,d)
| c = X0 ),
inference(resolution,[status(thm)],[d29,d26]) ).
cnf(d31,plain,
c = 'element$uin$uO2'(a,d),
inference(resolution,[status(thm)],[d30,d23]) ).
cnf(d32,plain,
( 'subgroup$umember'(a)
| 'subgroup$umember'(d)
| 'subgroup$umember'(c) ),
inference(superposition,[status(thm)],[d31,c0]) ).
cnf(d33,plain,
( 'subgroup$umember'(c)
| 'subgroup$umember'(d) ),
inference(resolution,[status(thm)],[c2,d32]) ).
cnf(d34,plain,
'subgroup$umember'(c),
inference(resolution,[status(thm)],[c4,d33]) ).
cnf(d35,plain,
~ 'subgroup$umember'(inverse(b)),
inference(resolution,[status(thm)],[d34,d19]) ).
cnf(d36,plain,
~ 'subgroup$umember'(b),
inference(resolution,[status(thm)],[d35,d3]) ).
cnf(d37,plain,
$false,
inference(resolution,[status(thm)],[c3,d36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP040-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 14:19:29 UTC 2026
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.27/5.33 % SZS status Unsatisfiable for theBenchmark.p
% 18.27/5.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------