%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO007-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 12:59:33 PM UTC 2026
% Result : Unsatisfiable 5.52s 1.30s
% Output : CNFRefutation 5.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 9
% Syntax : Number of clauses : 76 ( 76 unt; 0 nHn; 4 RR)
% Number of literals : 76 ( 75 equ; 3 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 : 159 ( 22 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(t10,axiom,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t48,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
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(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(t11711,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(step,[status(thm)],[t27,t16]) ).
cnf(t185,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(orient,[status(thm)],[t11711]) ).
cnf(t51,plain,
multiply(X1,add(multiplicative_identity,X2)) = add(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t48,t16]) ).
cnf(t117,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(multiplicative_identity,X2)),
inference(orient,[status(thm)],[t51]) ).
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(t11696,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)],[t11696]) ).
cnf(t158,plain,
add(X1,multiplicative_identity) = add(X1,inverse(X1)),
inference(cp,[status(thm)],[t152,t16]) ).
cnf(t11697,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)],[t11697]) ).
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(t169,plain,
multiplicative_identity = add(multiplicative_identity,X1),
inference(cp,[status(thm)],[t168,t18]) ).
cnf(t171,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(orient,[status(thm)],[t169]) ).
cnf(t11704,plain,
add(X1,multiply(X1,X2)) = multiply(X1,multiplicative_identity),
inference(step,[status(thm)],[t117,t171]) ).
cnf(t11705,plain,
add(X1,multiply(X1,X2)) = X1,
inference(step,[status(thm)],[t11704,t16]) ).
cnf(t174,plain,
add(X1,multiply(X1,X2)) = X1,
inference(orient,[status(thm)],[t11705]) ).
cnf(t186,plain,
add(X1,X1) = X1,
inference(cp,[status(thm)],[t185,t174]) ).
cnf(t193,plain,
add(X1,X1) = X1,
inference(orient,[status(thm)],[t186]) ).
cnf(t194,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(X1,X2)),
inference(cp,[status(thm)],[t19,t193]) ).
cnf(t11712,plain,
X1 = multiply(X1,add(X1,X2)),
inference(step,[status(thm)],[t194,t174]) ).
cnf(t198,plain,
multiply(X1,add(X1,X2)) = X1,
inference(orient,[status(thm)],[t11712]) ).
cnf(t206,plain,
X1 = multiply(X1,add(X2,X1)),
inference(cp,[status(thm)],[t198,t18]) ).
cnf(t217,plain,
multiply(X1,add(X2,X1)) = X1,
inference(orient,[status(thm)],[t206]) ).
cnf(t221,plain,
multiply(X1,X2) = multiply(multiply(X1,X2),X1),
inference(cp,[status(thm)],[t217,t174]) ).
cnf(t11715,plain,
multiply(X1,X2) = multiply(X1,multiply(X1,X2)),
inference(step,[status(thm)],[t221,t61]) ).
cnf(t245,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t11715]) ).
cnf(t247,plain,
multiply(X1,add(multiply(X1,X2),X3)) = add(multiply(X1,X2),multiply(X1,X3)),
inference(cp,[status(thm)],[t48,t245]) ).
cnf(t11806,plain,
multiply(X1,add(multiply(X1,X2),X3)) = multiply(X1,add(X2,X3)),
inference(step,[status(thm)],[t247,t48]) ).
cnf(t5947,plain,
multiply(X1,add(multiply(X1,X2),X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t11806]) ).
cnf(t64,plain,
multiply(X1,add(X2,X3)) = add(multiply(X2,X1),multiply(X1,X3)),
inference(cp,[status(thm)],[t48,t61]) ).
cnf(t4678,plain,
add(multiply(X1,X2),multiply(X2,X3)) = multiply(X2,add(X1,X3)),
inference(orient,[status(thm)],[t64]) ).
cnf(t5951,plain,
multiply(X1,add(X2,multiply(X2,X3))) = multiply(X1,multiply(X2,add(X1,X3))),
inference(cp,[status(thm)],[t5947,t4678]) ).
cnf(t11807,plain,
multiply(X1,X2) = multiply(X1,multiply(X2,add(X1,X3))),
inference(step,[status(thm)],[t5951,t174]) ).
cnf(t6094,plain,
multiply(X1,multiply(X2,add(X1,X3))) = multiply(X1,X2),
inference(orient,[status(thm)],[t11807]) ).
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(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(t11700,plain,
add(X1,multiply(X2,X1)) = multiply(multiplicative_identity,X1),
inference(step,[status(thm)],[t76,t171]) ).
cnf(t11701,plain,
add(X1,multiply(X2,X1)) = X1,
inference(step,[status(thm)],[t11700,t17]) ).
cnf(t172,plain,
add(X1,multiply(X2,X1)) = X1,
inference(orient,[status(thm)],[t11701]) ).
cnf(t225,plain,
add(X1,X2) = add(add(X1,X2),X2),
inference(cp,[status(thm)],[t172,t217]) ).
cnf(t11717,plain,
add(X1,X2) = add(X2,add(X1,X2)),
inference(step,[status(thm)],[t225,t18]) ).
cnf(t257,plain,
add(X1,add(X2,X1)) = add(X2,X1),
inference(orient,[status(thm)],[t11717]) ).
cnf(t6118,plain,
multiply(X1,X2) = multiply(X1,multiply(X2,add(X3,X1))),
inference(cp,[status(thm)],[t6094,t257]) ).
cnf(t6293,plain,
multiply(X1,multiply(X2,add(X3,X1))) = multiply(X1,X2),
inference(orient,[status(thm)],[t6118]) ).
cnf(t6327,plain,
multiply(multiply(X1,X2),X3) = multiply(multiply(X1,X2),multiply(X3,X1)),
inference(cp,[status(thm)],[t6293,t174]) ).
cnf(t9510,plain,
multiply(multiply(X1,X2),multiply(X3,X1)) = multiply(multiply(X1,X2),X3),
inference(orient,[status(thm)],[t6327]) ).
cnf(t9520,plain,
multiply(multiply(X1,X2),X3) = multiply(multiply(X3,X1),multiply(X1,X2)),
inference(cp,[status(thm)],[t9510,t61]) ).
cnf(t5952,plain,
multiply(X1,add(X2,multiply(X3,X2))) = multiply(X1,multiply(add(X1,X3),X2)),
inference(cp,[status(thm)],[t5947,t36]) ).
cnf(t11808,plain,
multiply(X1,X2) = multiply(X1,multiply(add(X1,X3),X2)),
inference(step,[status(thm)],[t5952,t172]) ).
cnf(t6192,plain,
multiply(X1,multiply(add(X1,X2),X3)) = multiply(X1,X3),
inference(orient,[status(thm)],[t11808]) ).
cnf(t6227,plain,
multiply(X1,X2) = multiply(X1,multiply(add(X3,X1),X2)),
inference(cp,[status(thm)],[t6192,t257]) ).
cnf(t6399,plain,
multiply(X1,multiply(add(X2,X1),X3)) = multiply(X1,X3),
inference(orient,[status(thm)],[t6227]) ).
cnf(t6450,plain,
multiply(multiply(X1,X2),X3) = multiply(multiply(X1,X2),multiply(X2,X3)),
inference(cp,[status(thm)],[t6399,t172]) ).
cnf(t9685,plain,
multiply(multiply(X1,X2),multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
inference(orient,[status(thm)],[t6450]) ).
cnf(t11845,plain,
multiply(multiply(X1,X2),X3) = multiply(multiply(X3,X1),X2),
inference(step,[status(thm)],[t9520,t9685]) ).
cnf(t11260,plain,
multiply(multiply(X1,X2),X3) = multiply(multiply(X3,X1),X2),
inference(orient,[status(thm)],[t11845]) ).
cnf(goal_0,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
multiply(multiply(b,c),a) != multiply(a,multiply(b,c)),
inference(rw,[status(thm)],[goal_0,t61]) ).
cnf(g0_1,plain,
multiply(multiply(b,c),a) != multiply(multiply(b,c),a),
inference(rw,[status(thm)],[g0_0,t11260]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO007-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n004.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 06:27:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.52/1.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.52/1.30 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------