%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO013-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 12:59:36 PM UTC 2026
% Result : Unsatisfiable 5.75s 1.18s
% Output : CNFRefutation 5.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of clauses : 56 ( 56 unt; 0 nHn; 26 RR)
% Number of literals : 56 ( 55 equ; 9 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 : 44 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t9,axiom,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t14,plain,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t1,axiom,
add(a,b) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t6,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t12,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t134,plain,
add(b,a) = multiplicative_identity,
inference(step,[status(thm)],[t1,t12]) ).
cnf(t22,plain,
add(b,a) = multiplicative_identity,
inference(orient,[status(thm)],[t134]) ).
cnf(t24,plain,
add(b,multiply(X1,a)) = multiply(add(b,X1),multiplicative_identity),
inference(cp,[status(thm)],[t14,t22]) ).
cnf(t2,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t11,plain,
multiply(X1,multiplicative_identity) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t136,plain,
add(b,multiply(X1,a)) = add(b,X1),
inference(step,[status(thm)],[t24,t11]) ).
cnf(t50,plain,
add(b,multiply(X1,a)) = add(b,X1),
inference(orient,[status(thm)],[t136]) ).
cnf(t7,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t25,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t53,plain,
add(b,X1) = add(b,multiply(a,X1)),
inference(cp,[status(thm)],[t50,t25]) ).
cnf(t72,plain,
add(b,multiply(a,X1)) = add(b,X1),
inference(orient,[status(thm)],[t53]) ).
cnf(t5,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t38,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t74,plain,
add(b,inverse(a)) = add(b,additive_identity),
inference(cp,[status(thm)],[t72,t38]) ).
cnf(t0,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t10,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t143,plain,
add(b,inverse(a)) = b,
inference(step,[status(thm)],[t74,t10]) ).
cnf(t77,plain,
add(b,inverse(a)) = b,
inference(orient,[status(thm)],[t143]) ).
cnf(t8,axiom,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t28,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t8]) ).
cnf(t3,axiom,
multiply(a,b) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t135,plain,
multiply(b,a) = additive_identity,
inference(step,[status(thm)],[t3,t25]) ).
cnf(t41,plain,
multiply(b,a) = additive_identity,
inference(orient,[status(thm)],[t135]) ).
cnf(t43,plain,
multiply(b,add(X1,a)) = add(multiply(b,X1),additive_identity),
inference(cp,[status(thm)],[t28,t41]) ).
cnf(t140,plain,
multiply(b,add(X1,a)) = multiply(b,X1),
inference(step,[status(thm)],[t43,t10]) ).
cnf(t62,plain,
multiply(b,add(X1,a)) = multiply(b,X1),
inference(orient,[status(thm)],[t140]) ).
cnf(t65,plain,
multiply(b,X1) = multiply(b,add(a,X1)),
inference(cp,[status(thm)],[t62,t12]) ).
cnf(t98,plain,
multiply(b,add(a,X1)) = multiply(b,X1),
inference(orient,[status(thm)],[t65]) ).
cnf(t4,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t19,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(orient,[status(thm)],[t4]) ).
cnf(t99,plain,
multiply(b,inverse(a)) = multiply(b,multiplicative_identity),
inference(cp,[status(thm)],[t98,t19]) ).
cnf(t149,plain,
multiply(b,inverse(a)) = b,
inference(step,[status(thm)],[t99,t11]) ).
cnf(t103,plain,
multiply(b,inverse(a)) = b,
inference(orient,[status(thm)],[t149]) ).
cnf(t30,plain,
multiply(X1,add(multiplicative_identity,X2)) = add(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t28,t11]) ).
cnf(t124,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(multiplicative_identity,X2)),
inference(orient,[status(thm)],[t30]) ).
cnf(t26,plain,
multiply(multiplicative_identity,X1) = X1,
inference(cp,[status(thm)],[t25,t11]) ).
cnf(t47,plain,
multiply(multiplicative_identity,X1) = X1,
inference(orient,[status(thm)],[t26]) ).
cnf(t51,plain,
add(b,multiplicative_identity) = add(b,a),
inference(cp,[status(thm)],[t50,t47]) ).
cnf(t137,plain,
add(multiplicative_identity,b) = add(b,a),
inference(step,[status(thm)],[t51,t12]) ).
cnf(t138,plain,
add(multiplicative_identity,b) = multiplicative_identity,
inference(step,[status(thm)],[t137,t22]) ).
cnf(t56,plain,
add(multiplicative_identity,b) = multiplicative_identity,
inference(orient,[status(thm)],[t138]) ).
cnf(goal_0,negated_conjecture,
inverse(a) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
add(b,inverse(a)) != b,
inference(rw,[status(thm)],[goal_0,t77]) ).
cnf(g0_1,plain,
add(inverse(a),b) != b,
inference(rw,[status(thm)],[g0_0,t12]) ).
cnf(g0_2,plain,
add(inverse(a),multiply(b,inverse(a))) != b,
inference(rw,[status(thm)],[g0_1,t103]) ).
cnf(g0_3,plain,
add(inverse(a),multiply(inverse(a),b)) != b,
inference(rw,[status(thm)],[g0_2,t25]) ).
cnf(g0_4,plain,
multiply(inverse(a),add(multiplicative_identity,b)) != b,
inference(rw,[status(thm)],[g0_3,t124]) ).
cnf(g0_5,plain,
multiply(add(multiplicative_identity,b),inverse(a)) != b,
inference(rw,[status(thm)],[g0_4,t25]) ).
cnf(g0_6,plain,
multiply(multiplicative_identity,inverse(a)) != b,
inference(rw,[status(thm)],[g0_5,t56]) ).
cnf(g0_7,plain,
inverse(a) != b,
inference(rw,[status(thm)],[g0_6,t47]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO013-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 06:32:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.75/1.18 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.75/1.18 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------