%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO010-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 12:59:34 PM UTC 2026
% Result : Unsatisfiable 2.76s 0.79s
% Output : CNFRefutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 8 RR)
% Number of literals : 30 ( 29 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t9,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t61,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t11,axiom,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t36,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(add(X1,X3),X2),
inference(orient,[status(thm)],[t11]) ).
cnf(t3,axiom,
multiply(multiplicative_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t17,plain,
multiply(multiplicative_identity,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t40,plain,
multiply(add(multiplicative_identity,X1),X2) = add(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t36,t17]) ).
cnf(t76,plain,
add(X1,multiply(X2,X1)) = multiply(add(multiplicative_identity,X2),X1),
inference(orient,[status(thm)],[t40]) ).
cnf(t8,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t18,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t12,axiom,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t19,plain,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
cnf(t4,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t24,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(orient,[status(thm)],[t4]) ).
cnf(t26,plain,
add(X1,multiply(inverse(X1),X2)) = multiply(multiplicative_identity,add(X1,X2)),
inference(cp,[status(thm)],[t19,t24]) ).
cnf(t181,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(step,[status(thm)],[t26,t17]) ).
cnf(t152,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(orient,[status(thm)],[t181]) ).
cnf(t2,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t16,plain,
multiply(X1,multiplicative_identity) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t158,plain,
add(X1,multiplicative_identity) = add(X1,inverse(X1)),
inference(cp,[status(thm)],[t152,t16]) ).
cnf(t182,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(step,[status(thm)],[t158,t24]) ).
cnf(t168,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(orient,[status(thm)],[t182]) ).
cnf(goal_0,negated_conjecture,
add(a,multiply(a,b)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
add(a,multiply(a,b)) != add(a,multiply(b,a)),
inference(rw,[status(thm)],[goal_0,t61]) ).
cnf(g0_1,plain,
add(a,multiply(a,b)) != multiply(add(multiplicative_identity,b),a),
inference(rw,[status(thm)],[g0_0,t76]) ).
cnf(g0_2,plain,
add(a,multiply(a,b)) != multiply(add(b,multiplicative_identity),a),
inference(rw,[status(thm)],[g0_1,t18]) ).
cnf(g0_3,plain,
add(a,multiply(a,b)) != multiply(a,add(b,multiplicative_identity)),
inference(rw,[status(thm)],[g0_2,t61]) ).
cnf(g0_4,plain,
add(a,multiply(a,b)) != multiply(a,multiplicative_identity),
inference(rw,[status(thm)],[g0_3,t168]) ).
cnf(g0_5,plain,
add(a,multiply(a,b)) != a,
inference(rw,[status(thm)],[g0_4,t16]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO010-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 06:29:47 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.76/0.79 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.76/0.79 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------