%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO012-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 4.96s 1.20s
% Output : CNFRefutation 4.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of clauses : 65 ( 65 unt; 0 nHn; 3 RR)
% Number of literals : 65 ( 64 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 : 97 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t6,axiom,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t23,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(t33,plain,
multiply(X1,inverse(X1)) = additive_identity,
inference(orient,[status(thm)],[t3]) ).
cnf(t35,plain,
multiply(X1,add(X2,inverse(X1))) = add(multiply(X1,X2),additive_identity),
inference(cp,[status(thm)],[t23,t33]) ).
cnf(t0,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t8,plain,
add(X1,additive_identity) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t254,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(step,[status(thm)],[t35,t8]) ).
cnf(t167,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(orient,[status(thm)],[t254]) ).
cnf(t4,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t10,plain,
add(X1,X2) = add(X2,X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t169,plain,
multiply(X1,X2) = multiply(X1,add(inverse(X1),X2)),
inference(cp,[status(thm)],[t167,t10]) ).
cnf(t202,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t169]) ).
cnf(t2,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t17,plain,
add(X1,inverse(X1)) = multiplicative_identity,
inference(orient,[status(thm)],[t2]) ).
cnf(t209,plain,
multiply(X1,inverse(inverse(X1))) = multiply(X1,multiplicative_identity),
inference(cp,[status(thm)],[t202,t17]) ).
cnf(t7,axiom,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t12,plain,
multiply(add(X1,X2),add(X1,X3)) = add(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t7]) ).
cnf(t19,plain,
add(X1,multiply(X2,inverse(X1))) = multiply(add(X1,X2),multiplicative_identity),
inference(cp,[status(thm)],[t12,t17]) ).
cnf(t1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t9,plain,
multiply(X1,multiplicative_identity) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t233,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(step,[status(thm)],[t19,t9]) ).
cnf(t99,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(orient,[status(thm)],[t233]) ).
cnf(t25,plain,
multiply(X1,add(multiplicative_identity,X2)) = add(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t23,t9]) ).
cnf(t42,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(multiplicative_identity,X2)),
inference(orient,[status(thm)],[t25]) ).
cnf(t100,plain,
add(X1,X1) = multiply(X1,add(multiplicative_identity,inverse(X1))),
inference(cp,[status(thm)],[t99,t42]) ).
cnf(t45,plain,
multiply(X1,add(multiplicative_identity,inverse(X1))) = add(X1,additive_identity),
inference(cp,[status(thm)],[t42,t33]) ).
cnf(t226,plain,
multiply(X1,add(multiplicative_identity,inverse(X1))) = X1,
inference(step,[status(thm)],[t45,t8]) ).
cnf(t60,plain,
multiply(X1,add(multiplicative_identity,inverse(X1))) = X1,
inference(orient,[status(thm)],[t226]) ).
cnf(t234,plain,
add(X1,X1) = X1,
inference(step,[status(thm)],[t100,t60]) ).
cnf(t111,plain,
add(X1,X1) = X1,
inference(orient,[status(thm)],[t234]) ).
cnf(t113,plain,
add(X1,multiply(X2,X1)) = multiply(add(X1,X2),X1),
inference(cp,[status(thm)],[t12,t111]) ).
cnf(t5,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t20,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t47,plain,
multiply(X1,add(multiplicative_identity,X2)) = add(X1,multiply(X2,X1)),
inference(cp,[status(thm)],[t42,t20]) ).
cnf(t65,plain,
add(X1,multiply(X2,X1)) = multiply(X1,add(multiplicative_identity,X2)),
inference(orient,[status(thm)],[t47]) ).
cnf(t21,plain,
multiply(multiplicative_identity,X1) = X1,
inference(cp,[status(thm)],[t20,t9]) ).
cnf(t39,plain,
multiply(multiplicative_identity,X1) = X1,
inference(orient,[status(thm)],[t21]) ).
cnf(t103,plain,
add(X1,multiplicative_identity) = add(X1,inverse(X1)),
inference(cp,[status(thm)],[t99,t39]) ).
cnf(t235,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(step,[status(thm)],[t103,t17]) ).
cnf(t114,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(orient,[status(thm)],[t235]) ).
cnf(t115,plain,
multiplicative_identity = add(multiplicative_identity,X1),
inference(cp,[status(thm)],[t114,t10]) ).
cnf(t117,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(orient,[status(thm)],[t115]) ).
cnf(t242,plain,
add(X1,multiply(X2,X1)) = multiply(X1,multiplicative_identity),
inference(step,[status(thm)],[t65,t117]) ).
cnf(t243,plain,
add(X1,multiply(X2,X1)) = X1,
inference(step,[status(thm)],[t242,t9]) ).
cnf(t120,plain,
add(X1,multiply(X2,X1)) = X1,
inference(orient,[status(thm)],[t243]) ).
cnf(t248,plain,
X1 = multiply(add(X1,X2),X1),
inference(step,[status(thm)],[t113,t120]) ).
cnf(t249,plain,
X1 = multiply(X1,add(X1,X2)),
inference(step,[status(thm)],[t248,t20]) ).
cnf(t126,plain,
multiply(X1,add(X1,X2)) = X1,
inference(orient,[status(thm)],[t249]) ).
cnf(t132,plain,
X1 = multiply(X1,add(X2,X1)),
inference(cp,[status(thm)],[t126,t10]) ).
cnf(t138,plain,
multiply(X1,add(X2,X1)) = X1,
inference(orient,[status(thm)],[t132]) ).
cnf(t104,plain,
add(X1,X2) = add(X1,multiply(inverse(X1),X2)),
inference(cp,[status(thm)],[t99,t20]) ).
cnf(t174,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(orient,[status(thm)],[t104]) ).
cnf(t178,plain,
add(X1,inverse(inverse(X1))) = add(X1,additive_identity),
inference(cp,[status(thm)],[t174,t33]) ).
cnf(t255,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(step,[status(thm)],[t178,t8]) ).
cnf(t183,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(orient,[status(thm)],[t255]) ).
cnf(t187,plain,
inverse(inverse(X1)) = multiply(inverse(inverse(X1)),X1),
inference(cp,[status(thm)],[t138,t183]) ).
cnf(t256,plain,
inverse(inverse(X1)) = multiply(X1,inverse(inverse(X1))),
inference(step,[status(thm)],[t187,t20]) ).
cnf(t188,plain,
multiply(X1,inverse(inverse(X1))) = inverse(inverse(X1)),
inference(orient,[status(thm)],[t256]) ).
cnf(t259,plain,
inverse(inverse(X1)) = multiply(X1,multiplicative_identity),
inference(step,[status(thm)],[t209,t188]) ).
cnf(t260,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t259,t9]) ).
cnf(t216,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t260]) ).
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,t216]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 06:26:32 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.96/1.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.96/1.20 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------