%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 02:01:06 PM UTC 2026
% Result : Unsatisfiable 2.17s 0.80s
% Output : CNFRefutation 2.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of clauses : 53 ( 53 unt; 0 nHn; 6 RR)
% Number of literals : 53 ( 52 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t10,axiom,
xor(truth,and_star(X1,xor(truth,X2))) = implies(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t28,plain,
xor(truth,and_star(X1,xor(truth,X2))) = implies(X1,X2),
inference(orient,[status(thm)],[t10]) ).
cnf(t5,axiom,
xor(X1,truth) = not(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t24,plain,
xor(X1,truth) = not(X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t8,axiom,
xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t15,plain,
xor(X1,X2) = xor(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t26,plain,
not(X1) = xor(truth,X1),
inference(cp,[status(thm)],[t24,t15]) ).
cnf(t77,plain,
xor(truth,X1) = not(X1),
inference(orient,[status(thm)],[t26]) ).
cnf(t200,plain,
not(and_star(X1,xor(truth,X2))) = implies(X1,X2),
inference(step,[status(thm)],[t28,t77]) ).
cnf(t201,plain,
not(and_star(X1,not(X2))) = implies(X1,X2),
inference(step,[status(thm)],[t200,t77]) ).
cnf(t80,plain,
not(and_star(X1,not(X2))) = implies(X1,X2),
inference(rw,[status(thm)],[t201]) ).
cnf(t84,plain,
not(and_star(X1,not(X2))) = implies(X1,X2),
inference(orient,[status(thm)],[t80]) ).
cnf(t6,axiom,
and_star(X1,X2) = and_star(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t34,plain,
and_star(X1,X2) = and_star(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t87,plain,
implies(X1,X2) = not(and_star(not(X2),X1)),
inference(cp,[status(thm)],[t84,t34]) ).
cnf(t102,plain,
not(and_star(not(X1),X2)) = implies(X2,X1),
inference(orient,[status(thm)],[t87]) ).
cnf(t2,axiom,
and_star(X1,truth) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t14,plain,
and_star(X1,truth) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t35,plain,
and_star(truth,X1) = X1,
inference(cp,[status(thm)],[t34,t14]) ).
cnf(t69,plain,
and_star(truth,X1) = X1,
inference(orient,[status(thm)],[t35]) ).
cnf(t85,plain,
implies(truth,X1) = not(not(X1)),
inference(cp,[status(thm)],[t84,t69]) ).
cnf(t94,plain,
not(not(X1)) = implies(truth,X1),
inference(orient,[status(thm)],[t85]) ).
cnf(t98,plain,
implies(X1,not(X2)) = not(and_star(X1,implies(truth,X2))),
inference(cp,[status(thm)],[t84,t94]) ).
cnf(t11,axiom,
xor(xor(X1,truth),X2) = xor(X1,xor(truth,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t18,plain,
xor(xor(X1,truth),X2) = xor(X1,xor(truth,X2)),
inference(orient,[status(thm)],[t11]) ).
cnf(t189,plain,
xor(not(X1),X2) = xor(X1,xor(truth,X2)),
inference(step,[status(thm)],[t18,t24]) ).
cnf(t27,plain,
xor(not(X1),X2) = xor(X1,xor(truth,X2)),
inference(rw,[status(thm)],[t189]) ).
cnf(t208,plain,
xor(not(X1),X2) = xor(X1,not(X2)),
inference(step,[status(thm)],[t27,t77]) ).
cnf(t136,plain,
xor(not(X1),X2) = xor(X1,not(X2)),
inference(orient,[status(thm)],[t208]) ).
cnf(t138,plain,
xor(X1,not(truth)) = not(not(X1)),
inference(cp,[status(thm)],[t136,t24]) ).
cnf(t0,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t65,plain,
not(truth) = falsehood,
inference(orient,[status(thm)],[t0]) ).
cnf(t209,plain,
xor(X1,falsehood) = not(not(X1)),
inference(step,[status(thm)],[t138,t65]) ).
cnf(t4,axiom,
xor(X1,falsehood) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t13,plain,
xor(X1,falsehood) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t210,plain,
X1 = not(not(X1)),
inference(step,[status(thm)],[t209,t13]) ).
cnf(t211,plain,
X1 = implies(truth,X1),
inference(step,[status(thm)],[t210,t94]) ).
cnf(t145,plain,
implies(truth,X1) = X1,
inference(orient,[status(thm)],[t211]) ).
cnf(t219,plain,
implies(X1,not(X2)) = not(and_star(X1,X2)),
inference(step,[status(thm)],[t98,t145]) ).
cnf(t169,plain,
not(and_star(X1,X2)) = implies(X1,not(X2)),
inference(orient,[status(thm)],[t219]) ).
cnf(t220,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(step,[status(thm)],[t102,t169]) ).
cnf(t178,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(rw,[status(thm)],[t220]) ).
cnf(t180,plain,
implies(not(X1),not(X2)) = implies(X2,X1),
inference(orient,[status(thm)],[t178]) ).
cnf(t7,axiom,
and_star(xor(truth,X1),X1) = falsehood,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t194,plain,
and_star(X1,xor(truth,X1)) = falsehood,
inference(step,[status(thm)],[t7,t34]) ).
cnf(t57,plain,
and_star(X1,xor(truth,X1)) = falsehood,
inference(orient,[status(thm)],[t194]) ).
cnf(t63,plain,
implies(X1,X1) = xor(truth,falsehood),
inference(cp,[status(thm)],[t28,t57]) ).
cnf(t195,plain,
implies(X1,X1) = truth,
inference(step,[status(thm)],[t63,t13]) ).
cnf(t75,plain,
implies(X1,X1) = truth,
inference(orient,[status(thm)],[t195]) ).
cnf(goal_0,negated_conjecture,
implies(implies(not(x),not(y)),implies(y,x)) != truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
implies(implies(y,x),implies(y,x)) != truth,
inference(rw,[status(thm)],[goal_0,t180]) ).
cnf(g0_1,plain,
truth != truth,
inference(rw,[status(thm)],[g0_0,t75]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n014.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 : Wed Sep 23 22:07:33 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.17/0.80 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.17/0.80 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------