%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO009-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 5.62s 1.19s
% Output : CNFRefutation 5.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of clauses : 54 ( 54 unt; 0 nHn; 7 RR)
% Number of literals : 54 ( 53 equ; 6 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 : 70 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t4,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t28,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t5,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t10,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t6,axiom,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t12,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t6]) ).
cnf(t3,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t17,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t19,plain,
multiply(X1,add(X2,inverse(X1))) = add(multiply(X1,X2),additive_identity),
inference(cp,[status(thm)],[t12,t17]) ).
cnf(t0,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t9,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t171,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(step,[status(thm)],[t19,t9]) ).
cnf(t99,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(orient,[status(thm)],[t171]) ).
cnf(t2,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t33,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(orient,[status(thm)],[t2]) ).
cnf(t101,plain,
multiply(X1,X1) = multiply(X1,multiplicative_identity),
inference(cp,[status(thm)],[t99,t33]) ).
cnf(t1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t8,plain,
multiply(X1,multiplicative_identity) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t172,plain,
multiply(X1,X1) = X1,
inference(step,[status(thm)],[t101,t8]) ).
cnf(t108,plain,
multiply(X1,X1) = X1,
inference(orient,[status(thm)],[t172]) ).
cnf(t110,plain,
multiply(X1,add(X2,X1)) = add(multiply(X1,X2),X1),
inference(cp,[status(thm)],[t12,t108]) ).
cnf(t183,plain,
multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
inference(step,[status(thm)],[t110,t28]) ).
cnf(t13,plain,
multiply(X1,add(multiplicative_identity,X2)) = add(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t12,t8]) ).
cnf(t42,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(multiplicative_identity,X2)),
inference(orient,[status(thm)],[t13]) ).
cnf(t184,plain,
multiply(X1,add(X2,X1)) = multiply(X1,add(multiplicative_identity,X2)),
inference(step,[status(thm)],[t183,t42]) ).
cnf(t135,plain,
multiply(X1,add(X2,X1)) = multiply(X1,add(multiplicative_identity,X2)),
inference(orient,[status(thm)],[t184]) ).
cnf(t47,plain,
multiply(X1,add(multiplicative_identity,X2)) = add(X1,multiply(X2,X1)),
inference(cp,[status(thm)],[t42,t10]) ).
cnf(t65,plain,
add(X1,multiply(X2,X1)) = multiply(X1,add(multiplicative_identity,X2)),
inference(orient,[status(thm)],[t47]) ).
cnf(t69,plain,
multiply(inverse(X1),add(multiplicative_identity,X1)) = add(inverse(X1),additive_identity),
inference(cp,[status(thm)],[t65,t17]) ).
cnf(t165,plain,
multiply(inverse(X1),add(multiplicative_identity,X1)) = inverse(X1),
inference(step,[status(thm)],[t69,t9]) ).
cnf(t76,plain,
multiply(inverse(X1),add(multiplicative_identity,X1)) = inverse(X1),
inference(orient,[status(thm)],[t165]) ).
cnf(t80,plain,
multiply(add(multiplicative_identity,X1),add(multiplicative_identity,inverse(X1))) = add(add(multiplicative_identity,X1),inverse(X1)),
inference(cp,[status(thm)],[t65,t76]) ).
cnf(t7,axiom,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t20,plain,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t7]) ).
cnf(t166,plain,
add(multiplicative_identity,multiply(X1,inverse(X1))) = add(add(multiplicative_identity,X1),inverse(X1)),
inference(step,[status(thm)],[t80,t20]) ).
cnf(t167,plain,
add(multiplicative_identity,additive_identity) = add(add(multiplicative_identity,X1),inverse(X1)),
inference(step,[status(thm)],[t166,t17]) ).
cnf(t168,plain,
multiplicative_identity = add(add(multiplicative_identity,X1),inverse(X1)),
inference(step,[status(thm)],[t167,t9]) ).
cnf(t169,plain,
multiplicative_identity = add(inverse(X1),add(multiplicative_identity,X1)),
inference(step,[status(thm)],[t168,t28]) ).
cnf(t82,plain,
add(inverse(X1),add(multiplicative_identity,X1)) = multiplicative_identity,
inference(orient,[status(thm)],[t169]) ).
cnf(t140,plain,
multiply(add(multiplicative_identity,X1),add(multiplicative_identity,inverse(X1))) = multiply(add(multiplicative_identity,X1),multiplicative_identity),
inference(cp,[status(thm)],[t135,t82]) ).
cnf(t185,plain,
add(multiplicative_identity,multiply(X1,inverse(X1))) = multiply(add(multiplicative_identity,X1),multiplicative_identity),
inference(step,[status(thm)],[t140,t20]) ).
cnf(t186,plain,
add(multiplicative_identity,additive_identity) = multiply(add(multiplicative_identity,X1),multiplicative_identity),
inference(step,[status(thm)],[t185,t17]) ).
cnf(t187,plain,
multiplicative_identity = multiply(add(multiplicative_identity,X1),multiplicative_identity),
inference(step,[status(thm)],[t186,t9]) ).
cnf(t188,plain,
multiplicative_identity = add(multiplicative_identity,X1),
inference(step,[status(thm)],[t187,t8]) ).
cnf(t155,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(orient,[status(thm)],[t188]) ).
cnf(t11,plain,
multiply(multiplicative_identity,X1) = X1,
inference(cp,[status(thm)],[t10,t8]) ).
cnf(t36,plain,
multiply(multiplicative_identity,X1) = X1,
inference(orient,[status(thm)],[t11]) ).
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,t28]) ).
cnf(g0_1,plain,
multiply(a,add(a,b)) != multiply(a,add(multiplicative_identity,b)),
inference(rw,[status(thm)],[g0_0]) ).
cnf(g0_2,plain,
multiply(a,add(a,b)) != multiply(add(multiplicative_identity,b),a),
inference(rw,[status(thm)],[g0_1,t10]) ).
cnf(g0_3,plain,
multiply(a,add(a,b)) != multiply(multiplicative_identity,a),
inference(rw,[status(thm)],[g0_2,t155]) ).
cnf(g0_4,plain,
multiply(a,add(a,b)) != a,
inference(rw,[status(thm)],[g0_3,t36]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO009-4 : 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 : n007.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 06:28:23 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.62/1.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.62/1.19 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------