%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO004-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 12:59:32 PM UTC 2026
% Result : Unsatisfiable 5.25s 1.13s
% Output : CNFRefutation 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of clauses : 57 ( 57 unt; 0 nHn; 8 RR)
% Number of literals : 57 ( 56 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 : 68 ( 0 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(t12,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(orient,[status(thm)],[t6]) ).
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(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(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(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(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(t138,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)],[t138]) ).
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(t139,plain,
multiply(X1,X1) = X1,
inference(step,[status(thm)],[t101,t8]) ).
cnf(t108,plain,
multiply(X1,X1) = X1,
inference(orient,[status(thm)],[t139]) ).
cnf(t111,plain,
multiply(X1,add(multiplicative_identity,X1)) = add(X1,X1),
inference(cp,[status(thm)],[t65,t108]) ).
cnf(t117,plain,
multiply(X1,add(multiplicative_identity,X1)) = add(X1,X1),
inference(orient,[status(thm)],[t111]) ).
cnf(t119,plain,
add(multiply(X1,multiplicative_identity),multiply(X1,multiplicative_identity)) = multiply(multiply(X1,multiplicative_identity),multiply(multiplicative_identity,add(multiplicative_identity,X1))),
inference(cp,[status(thm)],[t117,t65]) ).
cnf(t141,plain,
multiply(X1,add(multiplicative_identity,multiplicative_identity)) = multiply(multiply(X1,multiplicative_identity),multiply(multiplicative_identity,add(multiplicative_identity,X1))),
inference(step,[status(thm)],[t119,t12]) ).
cnf(t69,plain,
multiply(inverse(X1),add(multiplicative_identity,X1)) = add(inverse(X1),additive_identity),
inference(cp,[status(thm)],[t65,t17]) ).
cnf(t132,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)],[t132]) ).
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(t133,plain,
add(multiplicative_identity,multiply(X1,inverse(X1))) = add(add(multiplicative_identity,X1),inverse(X1)),
inference(step,[status(thm)],[t80,t20]) ).
cnf(t134,plain,
add(multiplicative_identity,additive_identity) = add(add(multiplicative_identity,X1),inverse(X1)),
inference(step,[status(thm)],[t133,t17]) ).
cnf(t135,plain,
multiplicative_identity = add(add(multiplicative_identity,X1),inverse(X1)),
inference(step,[status(thm)],[t134,t9]) ).
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(t136,plain,
multiplicative_identity = add(inverse(X1),add(multiplicative_identity,X1)),
inference(step,[status(thm)],[t135,t28]) ).
cnf(t82,plain,
add(inverse(X1),add(multiplicative_identity,X1)) = multiplicative_identity,
inference(orient,[status(thm)],[t136]) ).
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(t37,plain,
inverse(multiplicative_identity) = additive_identity,
inference(cp,[status(thm)],[t36,t17]) ).
cnf(t38,plain,
inverse(multiplicative_identity) = additive_identity,
inference(orient,[status(thm)],[t37]) ).
cnf(t83,plain,
multiplicative_identity = add(additive_identity,add(multiplicative_identity,multiplicative_identity)),
inference(cp,[status(thm)],[t82,t38]) ).
cnf(t29,plain,
add(additive_identity,X1) = X1,
inference(cp,[status(thm)],[t28,t9]) ).
cnf(t39,plain,
add(additive_identity,X1) = X1,
inference(orient,[status(thm)],[t29]) ).
cnf(t137,plain,
multiplicative_identity = add(multiplicative_identity,multiplicative_identity),
inference(step,[status(thm)],[t83,t39]) ).
cnf(t90,plain,
add(multiplicative_identity,multiplicative_identity) = multiplicative_identity,
inference(orient,[status(thm)],[t137]) ).
cnf(t142,plain,
multiply(X1,multiplicative_identity) = multiply(multiply(X1,multiplicative_identity),multiply(multiplicative_identity,add(multiplicative_identity,X1))),
inference(step,[status(thm)],[t141,t90]) ).
cnf(t143,plain,
X1 = multiply(multiply(X1,multiplicative_identity),multiply(multiplicative_identity,add(multiplicative_identity,X1))),
inference(step,[status(thm)],[t142,t8]) ).
cnf(t144,plain,
X1 = multiply(X1,multiply(multiplicative_identity,add(multiplicative_identity,X1))),
inference(step,[status(thm)],[t143,t8]) ).
cnf(t145,plain,
X1 = multiply(X1,add(multiplicative_identity,X1)),
inference(step,[status(thm)],[t144,t36]) ).
cnf(t146,plain,
X1 = add(X1,X1),
inference(step,[status(thm)],[t145,t117]) ).
cnf(t125,plain,
add(X1,X1) = X1,
inference(orient,[status(thm)],[t146]) ).
cnf(goal_0,negated_conjecture,
add(a,a) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
a != a,
inference(rw,[status(thm)],[goal_0,t125]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO004-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 06:26:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.25/1.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.25/1.13 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------