%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO009-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 4.71s 1.12s
% Output : CNFRefutation 4.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of clauses : 65 ( 65 unt; 0 nHn; 8 RR)
% Number of literals : 65 ( 64 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 89 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t61,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t10,axiom,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t19,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t6,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t24,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t6]) ).
cnf(t27,plain,
multiply(X1,add(X2,inverse(X1))) = add(multiply(X1,X2),additive_identity),
inference(cp,[status(thm)],[t19,t24]) ).
cnf(t0,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t16,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t287,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(step,[status(thm)],[t27,t16]) ).
cnf(t174,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(orient,[status(thm)],[t287]) ).
cnf(t4,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t68,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(orient,[status(thm)],[t4]) ).
cnf(t176,plain,
multiply(X1,X1) = multiply(X1,multiplicative_identity),
inference(cp,[status(thm)],[t174,t68]) ).
cnf(t2,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t14,plain,
multiply(X1,multiplicative_identity) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t288,plain,
multiply(X1,X1) = X1,
inference(step,[status(thm)],[t176,t14]) ).
cnf(t183,plain,
multiply(X1,X1) = X1,
inference(orient,[status(thm)],[t288]) ).
cnf(t185,plain,
multiply(X1,add(X2,X1)) = add(multiply(X1,X2),X1),
inference(cp,[status(thm)],[t19,t183]) ).
cnf(t299,plain,
multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
inference(step,[status(thm)],[t185,t61]) ).
cnf(t20,plain,
multiply(X1,add(multiplicative_identity,X2)) = add(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t19,t14]) ).
cnf(t76,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(multiplicative_identity,X2)),
inference(orient,[status(thm)],[t20]) ).
cnf(t300,plain,
multiply(X1,add(X2,X1)) = multiply(X1,add(multiplicative_identity,X2)),
inference(step,[status(thm)],[t299,t76]) ).
cnf(t214,plain,
multiply(X1,add(X2,X1)) = multiply(X1,add(multiplicative_identity,X2)),
inference(orient,[status(thm)],[t300]) ).
cnf(t9,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t18,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(t28,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(t15,plain,
multiply(multiplicative_identity,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t31,plain,
multiply(add(multiplicative_identity,X1),X2) = add(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t28,t15]) ).
cnf(t109,plain,
add(X1,multiply(X2,X1)) = multiply(add(multiplicative_identity,X2),X1),
inference(orient,[status(thm)],[t31]) ).
cnf(t80,plain,
multiply(X1,add(multiplicative_identity,inverse(X1))) = add(X1,additive_identity),
inference(cp,[status(thm)],[t76,t24]) ).
cnf(t276,plain,
multiply(X1,add(multiplicative_identity,inverse(X1))) = X1,
inference(step,[status(thm)],[t80,t16]) ).
cnf(t102,plain,
multiply(X1,add(multiplicative_identity,inverse(X1))) = X1,
inference(orient,[status(thm)],[t276]) ).
cnf(t113,plain,
multiply(add(multiplicative_identity,X1),add(multiplicative_identity,inverse(X1))) = add(add(multiplicative_identity,inverse(X1)),X1),
inference(cp,[status(thm)],[t109,t102]) ).
cnf(t12,axiom,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t48,plain,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
cnf(t277,plain,
add(multiplicative_identity,multiply(X1,inverse(X1))) = add(add(multiplicative_identity,inverse(X1)),X1),
inference(step,[status(thm)],[t113,t48]) ).
cnf(t278,plain,
add(multiplicative_identity,additive_identity) = add(add(multiplicative_identity,inverse(X1)),X1),
inference(step,[status(thm)],[t277,t24]) ).
cnf(t279,plain,
multiplicative_identity = add(add(multiplicative_identity,inverse(X1)),X1),
inference(step,[status(thm)],[t278,t16]) ).
cnf(t280,plain,
multiplicative_identity = add(X1,add(multiplicative_identity,inverse(X1))),
inference(step,[status(thm)],[t279,t61]) ).
cnf(t125,plain,
add(X1,add(multiplicative_identity,inverse(X1))) = multiplicative_identity,
inference(orient,[status(thm)],[t280]) ).
cnf(t189,plain,
multiply(add(X1,X2),X2) = add(multiply(X1,X2),X2),
inference(cp,[status(thm)],[t28,t183]) ).
cnf(t301,plain,
multiply(X2,add(X1,X2)) = add(multiply(X1,X2),X2),
inference(step,[status(thm)],[t189,t18]) ).
cnf(t302,plain,
multiply(X2,add(X1,X2)) = add(X2,multiply(X1,X2)),
inference(step,[status(thm)],[t301,t61]) ).
cnf(t303,plain,
multiply(X2,add(X1,X2)) = multiply(add(multiplicative_identity,X1),X2),
inference(step,[status(thm)],[t302,t109]) ).
cnf(t238,plain,
multiply(X1,add(X2,X1)) = multiply(add(multiplicative_identity,X2),X1),
inference(orient,[status(thm)],[t303]) ).
cnf(t243,plain,
multiply(add(multiplicative_identity,X1),add(multiplicative_identity,inverse(X1))) = multiply(add(multiplicative_identity,inverse(X1)),multiplicative_identity),
inference(cp,[status(thm)],[t238,t125]) ).
cnf(t304,plain,
add(multiplicative_identity,multiply(X1,inverse(X1))) = multiply(add(multiplicative_identity,inverse(X1)),multiplicative_identity),
inference(step,[status(thm)],[t243,t48]) ).
cnf(t305,plain,
add(multiplicative_identity,additive_identity) = multiply(add(multiplicative_identity,inverse(X1)),multiplicative_identity),
inference(step,[status(thm)],[t304,t24]) ).
cnf(t306,plain,
multiplicative_identity = multiply(add(multiplicative_identity,inverse(X1)),multiplicative_identity),
inference(step,[status(thm)],[t305,t16]) ).
cnf(t307,plain,
multiplicative_identity = add(multiplicative_identity,inverse(X1)),
inference(step,[status(thm)],[t306,t14]) ).
cnf(t267,plain,
add(multiplicative_identity,inverse(X1)) = multiplicative_identity,
inference(orient,[status(thm)],[t307]) ).
cnf(t308,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(step,[status(thm)],[t125,t267]) ).
cnf(t271,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[t308]) ).
cnf(t272,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(orient,[status(thm)],[t271]) ).
cnf(goal_0,negated_conjecture,
multiply(a,add(a,b)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(a,add(a,b)) != multiply(a,add(b,a)),
inference(rw,[status(thm)],[goal_0,t61]) ).
cnf(g0_1,plain,
multiply(a,add(a,b)) != multiply(a,add(multiplicative_identity,b)),
inference(rw,[status(thm)],[g0_0,t214]) ).
cnf(g0_2,plain,
multiply(a,add(a,b)) != multiply(a,add(b,multiplicative_identity)),
inference(rw,[status(thm)],[g0_1,t61]) ).
cnf(g0_3,plain,
multiply(a,add(a,b)) != multiply(add(b,multiplicative_identity),a),
inference(rw,[status(thm)],[g0_2,t18]) ).
cnf(g0_4,plain,
multiply(a,add(a,b)) != multiply(multiplicative_identity,a),
inference(rw,[status(thm)],[g0_3,t272]) ).
cnf(g0_5,plain,
multiply(a,add(a,b)) != a,
inference(rw,[status(thm)],[g0_4,t15]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO009-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n007.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 06:28:37 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.71/1.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.71/1.12 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------