%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO012-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 12:59:35 PM UTC 2026
% Result : Unsatisfiable 6.19s 1.17s
% Output : CNFRefutation 6.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 11
% Syntax : Number of clauses : 59 ( 59 unt; 0 nHn; 3 RR)
% Number of literals : 59 ( 58 equ; 2 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 : 87 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t10,axiom,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t39,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(t53,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t6]) ).
cnf(t55,plain,
multiply(X1,add(inverse(X1),X2)) = add(additive_identity,multiply(X1,X2)),
inference(cp,[status(thm)],[t39,t53]) ).
cnf(t1,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t15,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t339,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(step,[status(thm)],[t55,t15]) ).
cnf(t280,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t339]) ).
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(t288,plain,
multiply(X1,inverse(inverse(X1))) = multiply(X1,multiplicative_identity),
inference(cp,[status(thm)],[t280,t24]) ).
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(t27,plain,
add(X1,multiply(X2,inverse(X1))) = multiply(add(X1,X2),multiplicative_identity),
inference(cp,[status(thm)],[t19,t24]) ).
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(t330,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(step,[status(thm)],[t27,t16]) ).
cnf(t183,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(orient,[status(thm)],[t330]) ).
cnf(t41,plain,
multiply(X1,add(multiplicative_identity,X2)) = add(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t39,t16]) ).
cnf(t76,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(multiplicative_identity,X2)),
inference(orient,[status(thm)],[t41]) ).
cnf(t26,plain,
add(X1,multiply(inverse(X1),X2)) = multiply(multiplicative_identity,add(X1,X2)),
inference(cp,[status(thm)],[t19,t24]) ).
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(t315,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(step,[status(thm)],[t26,t17]) ).
cnf(t150,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(orient,[status(thm)],[t315]) ).
cnf(t156,plain,
add(X1,multiplicative_identity) = add(X1,inverse(X1)),
inference(cp,[status(thm)],[t150,t16]) ).
cnf(t316,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(step,[status(thm)],[t156,t24]) ).
cnf(t166,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(orient,[status(thm)],[t316]) ).
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(t167,plain,
multiplicative_identity = add(multiplicative_identity,X1),
inference(cp,[status(thm)],[t166,t18]) ).
cnf(t169,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(orient,[status(thm)],[t167]) ).
cnf(t319,plain,
add(X1,multiply(X1,X2)) = multiply(X1,multiplicative_identity),
inference(step,[status(thm)],[t76,t169]) ).
cnf(t320,plain,
add(X1,multiply(X1,X2)) = X1,
inference(step,[status(thm)],[t319,t16]) ).
cnf(t170,plain,
add(X1,multiply(X1,X2)) = X1,
inference(orient,[status(thm)],[t320]) ).
cnf(t184,plain,
add(X1,X1) = X1,
inference(cp,[status(thm)],[t183,t170]) ).
cnf(t191,plain,
add(X1,X1) = X1,
inference(orient,[status(thm)],[t184]) ).
cnf(t192,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(X1,X2)),
inference(cp,[status(thm)],[t19,t191]) ).
cnf(t331,plain,
X1 = multiply(X1,add(X1,X2)),
inference(step,[status(thm)],[t192,t170]) ).
cnf(t196,plain,
multiply(X1,add(X1,X2)) = X1,
inference(orient,[status(thm)],[t331]) ).
cnf(t204,plain,
X1 = multiply(X1,add(X2,X1)),
inference(cp,[status(thm)],[t196,t18]) ).
cnf(t215,plain,
multiply(X1,add(X2,X1)) = X1,
inference(orient,[status(thm)],[t204]) ).
cnf(t157,plain,
add(X1,inverse(inverse(X1))) = add(X1,additive_identity),
inference(cp,[status(thm)],[t150,t53]) ).
cnf(t0,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t14,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t329,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(step,[status(thm)],[t157,t14]) ).
cnf(t178,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(orient,[status(thm)],[t329]) ).
cnf(t220,plain,
inverse(inverse(X1)) = multiply(inverse(inverse(X1)),X1),
inference(cp,[status(thm)],[t215,t178]) ).
cnf(t9,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t36,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t335,plain,
inverse(inverse(X1)) = multiply(X1,inverse(inverse(X1))),
inference(step,[status(thm)],[t220,t36]) ).
cnf(t249,plain,
multiply(X1,inverse(inverse(X1))) = inverse(inverse(X1)),
inference(orient,[status(thm)],[t335]) ).
cnf(t340,plain,
inverse(inverse(X1)) = multiply(X1,multiplicative_identity),
inference(step,[status(thm)],[t288,t249]) ).
cnf(t341,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t340,t16]) ).
cnf(t298,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t341]) ).
cnf(goal_0,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
x != x,
inference(rw,[status(thm)],[goal_0,t298]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO012-2 : 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 : n002.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 06:33:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.19/1.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.19/1.17 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------