%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL145-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 : Thu Sep 24 01:06:55 PM UTC 2026
% Result : Unsatisfiable 12.56s 2.05s
% Output : CNFRefutation 12.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 7
% Syntax : Number of formulae : 83 ( 83 unt; 0 def)
% Number of atoms : 83 ( 82 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 153 ( 153 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : implies(truth,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : big_V(X,Y) = implies(implies(X,Y),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : big_hat(X,Y) = not(big_V(not(X),not(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
not(big_V(x,y)) != big_hat(not(x),not(y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0] : implies(truth,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1] : big_V(X0,X1) = implies(implies(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1] : big_hat(X0,X1) = not(big_V(not(X0),not(X1))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f18,plain,
not(big_V(x,y)) != big_hat(not(x),not(y)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f19,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = big_V(X1,X0),
inference(backward_demodulation,[status(thm)],[f14,f12]) ).
fof(f20,plain,
! [X0,X1] : big_V(X0,X1) = big_V(X1,X0),
inference(forward_demodulation,[status(thm)],[f14,f19]) ).
fof(f35,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),implies(truth,X1))) = truth,
inference(paramodulation,[status(thm)],[f10,f11]) ).
fof(f40,plain,
! [X0,X1,X2] : implies(implies(X0,implies(X1,X2)),implies(big_V(X1,X2),implies(X0,X2))) = truth,
inference(paramodulation,[status(thm)],[f14,f11]) ).
fof(f41,plain,
! [X0,X1] : implies(implies(X0,truth),implies(X1,implies(X0,X1))) = truth,
inference(paramodulation,[status(thm)],[f10,f11]) ).
fof(f47,plain,
! [X0,X1,X2] : big_V(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = implies(truth,implies(implies(X1,X2),implies(X0,X2))),
inference(paramodulation,[status(thm)],[f11,f14]) ).
fof(f49,plain,
! [X0,X1] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f10,f35]) ).
fof(f50,plain,
! [X0,X1] : implies(X0,big_V(X0,X1)) = truth,
inference(forward_demodulation,[status(thm)],[f14,f49]) ).
fof(f57,plain,
! [X0,X1,X2] : big_V(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = implies(implies(X1,X2),implies(X0,X2)),
inference(forward_demodulation,[status(thm)],[f10,f47]) ).
fof(f58,plain,
! [X0] : big_V(truth,X0) = truth,
inference(paramodulation,[status(thm)],[f10,f50]) ).
fof(f60,plain,
! [X0,X1] : implies(X0,big_V(X1,X0)) = truth,
inference(paramodulation,[status(thm)],[f20,f50]) ).
fof(f64,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(truth,implies(X0,big_V(X1,X2)))) = truth,
inference(paramodulation,[status(thm)],[f50,f11]) ).
fof(f65,plain,
! [X0,X1,X2] : implies(truth,implies(implies(big_V(X0,X1),X2),implies(X0,X2))) = truth,
inference(paramodulation,[status(thm)],[f50,f11]) ).
fof(f72,plain,
! [X0,X1,X2] : implies(implies(X0,X1),implies(X0,big_V(X1,X2))) = truth,
inference(forward_demodulation,[status(thm)],[f10,f64]) ).
fof(f73,plain,
! [X0,X1,X2] : implies(implies(big_V(X0,X1),X2),implies(X0,X2)) = truth,
inference(forward_demodulation,[status(thm)],[f10,f65]) ).
fof(f79,plain,
! [X0] : big_V(X0,truth) = truth,
inference(paramodulation,[status(thm)],[f20,f58]) ).
fof(f88,plain,
! [X0] : implies(X0,truth) = truth,
inference(paramodulation,[status(thm)],[f79,f50]) ).
fof(f95,plain,
! [X0,X1] : implies(truth,implies(X0,implies(X1,X0))) = truth,
inference(backward_demodulation,[status(thm)],[f88,f41]) ).
fof(f96,plain,
! [X0,X1] : implies(X0,implies(X1,X0)) = truth,
inference(forward_demodulation,[status(thm)],[f10,f95]) ).
fof(f123,plain,
! [X0,X1] : big_V(X0,big_V(X1,X0)) = implies(truth,big_V(X1,X0)),
inference(paramodulation,[status(thm)],[f60,f14]) ).
fof(f127,plain,
! [X0,X1] : big_V(X0,big_V(X1,X0)) = big_V(X1,X0),
inference(forward_demodulation,[status(thm)],[f10,f123]) ).
fof(f131,plain,
! [X0] : implies(implies(not(X0),not(truth)),X0) = truth,
inference(paramodulation,[status(thm)],[f10,f13]) ).
fof(f139,plain,
! [X0,X1] : big_V(implies(not(X0),not(X1)),implies(X1,X0)) = implies(truth,implies(X1,X0)),
inference(paramodulation,[status(thm)],[f13,f14]) ).
fof(f143,plain,
! [X0,X1] : big_V(implies(X0,X1),implies(not(X1),not(X0))) = implies(truth,implies(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f139]) ).
fof(f144,plain,
! [X0,X1] : big_V(implies(X0,X1),implies(not(X1),not(X0))) = implies(X0,X1),
inference(forward_demodulation,[status(thm)],[f10,f143]) ).
fof(f160,plain,
! [X0,X1,X2] : implies(truth,implies(implies(implies(X0,X1),X2),implies(X1,X2))) = truth,
inference(paramodulation,[status(thm)],[f96,f11]) ).
fof(f164,plain,
! [X0,X1,X2] : implies(implies(implies(X0,X1),X2),implies(X1,X2)) = truth,
inference(forward_demodulation,[status(thm)],[f10,f160]) ).
fof(f283,plain,
! [X0] : big_V(implies(not(X0),not(truth)),X0) = implies(truth,X0),
inference(paramodulation,[status(thm)],[f131,f14]) ).
fof(f292,plain,
! [X0] : big_V(X0,implies(not(X0),not(truth))) = implies(truth,X0),
inference(forward_demodulation,[status(thm)],[f20,f283]) ).
fof(f293,plain,
! [X0] : big_V(X0,implies(not(X0),not(truth))) = X0,
inference(forward_demodulation,[status(thm)],[f10,f292]) ).
fof(f320,plain,
! [X0,X1,X2] : implies(truth,implies(X0,big_V(implies(X1,X0),X2))) = truth,
inference(paramodulation,[status(thm)],[f96,f72]) ).
fof(f353,plain,
! [X0,X1,X2] : implies(X0,big_V(implies(X1,X0),X2)) = truth,
inference(forward_demodulation,[status(thm)],[f10,f320]) ).
fof(f371,plain,
! [X0,X1,X2] : implies(X0,big_V(X1,implies(X2,X0))) = truth,
inference(paramodulation,[status(thm)],[f127,f353]) ).
fof(f573,plain,
! [X0] : implies(not(truth),X0) = truth,
inference(paramodulation,[status(thm)],[f293,f371]) ).
fof(f669,plain,
! [X0] : big_V(not(truth),X0) = implies(truth,X0),
inference(paramodulation,[status(thm)],[f573,f14]) ).
fof(f682,plain,
! [X0] : big_V(not(truth),X0) = X0,
inference(forward_demodulation,[status(thm)],[f10,f669]) ).
fof(f896,plain,
! [X0] : big_V(X0,not(truth)) = X0,
inference(paramodulation,[status(thm)],[f20,f682]) ).
fof(f2791,plain,
! [X0,X1] : implies(truth,implies(not(X0),implies(X0,X1))) = truth,
inference(paramodulation,[status(thm)],[f13,f164]) ).
fof(f2916,plain,
! [X0,X1] : implies(not(X0),implies(X0,X1)) = truth,
inference(forward_demodulation,[status(thm)],[f10,f2791]) ).
fof(f3058,plain,
! [X0,X1] : implies(truth,implies(big_V(X0,X1),implies(not(X0),X1))) = truth,
inference(paramodulation,[status(thm)],[f2916,f40]) ).
fof(f3091,plain,
! [X0,X1] : implies(big_V(X0,X1),implies(not(X0),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f10,f3058]) ).
fof(f3378,plain,
! [X0,X1] : implies(truth,implies(X0,implies(not(X0),X1))) = truth,
inference(paramodulation,[status(thm)],[f3091,f73]) ).
fof(f3421,plain,
! [X0,X1] : implies(X0,implies(not(X0),X1)) = truth,
inference(forward_demodulation,[status(thm)],[f10,f3378]) ).
fof(f3540,plain,
! [X0,X1] : big_V(X0,implies(not(X0),X1)) = implies(truth,implies(not(X0),X1)),
inference(paramodulation,[status(thm)],[f3421,f14]) ).
fof(f3583,plain,
! [X0] : implies(not(X0),not(truth)) = X0,
inference(backward_demodulation,[status(thm)],[f3586,f293]) ).
fof(f3586,plain,
! [X0,X1] : big_V(X0,implies(not(X0),X1)) = implies(not(X0),X1),
inference(forward_demodulation,[status(thm)],[f10,f3540]) ).
fof(f4003,plain,
! [X0,X1] : implies(big_hat(X0,X1),not(truth)) = big_V(not(X0),not(X1)),
inference(paramodulation,[status(thm)],[f15,f3583]) ).
fof(f4041,plain,
! [X0] : big_V(not(X0),not(truth)) = implies(X0,not(truth)),
inference(paramodulation,[status(thm)],[f3583,f14]) ).
fof(f4079,plain,
! [X0,X1] : not(big_hat(X0,X1)) = big_V(not(X0),not(X1)),
inference(backward_demodulation,[status(thm)],[f4102,f4003]) ).
fof(f4102,plain,
! [X0] : not(X0) = implies(X0,not(truth)),
inference(forward_demodulation,[status(thm)],[f896,f4041]) ).
fof(f4216,plain,
! [X0] : not(implies(X0,not(truth))) = big_V(X0,not(truth)),
inference(paramodulation,[status(thm)],[f14,f4102]) ).
fof(f4266,plain,
! [X0] : not(not(X0)) = big_V(X0,not(truth)),
inference(forward_demodulation,[status(thm)],[f4102,f4216]) ).
fof(f4268,plain,
! [X0] : not(not(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f896,f4266]) ).
fof(f4384,plain,
! [X0,X1] : big_V(implies(X0,X1),implies(not(X1),implies(X0,not(truth)))) = implies(implies(X1,not(truth)),implies(X0,not(truth))),
inference(paramodulation,[status(thm)],[f4102,f57]) ).
fof(f4571,plain,
! [X0,X1] : big_V(implies(X0,X1),implies(not(X1),not(X0))) = implies(implies(X1,not(truth)),implies(X0,not(truth))),
inference(forward_demodulation,[status(thm)],[f4102,f4384]) ).
fof(f4572,plain,
! [X0,X1] : implies(X0,X1) = implies(implies(X1,not(truth)),implies(X0,not(truth))),
inference(forward_demodulation,[status(thm)],[f144,f4571]) ).
fof(f4573,plain,
! [X0,X1] : implies(X0,X1) = implies(not(X1),implies(X0,not(truth))),
inference(forward_demodulation,[status(thm)],[f4102,f4572]) ).
fof(f4597,plain,
! [X0,X1] : implies(X0,X1) = implies(not(X1),not(X0)),
inference(forward_demodulation,[status(thm)],[f4102,f4573]) ).
fof(f4824,plain,
! [X0,X1] : implies(X0,not(X1)) = implies(X1,not(X0)),
inference(paramodulation,[status(thm)],[f4268,f4597]) ).
fof(f4865,plain,
! [X0,X1] : big_V(not(X0),not(X1)) = implies(implies(X1,X0),not(X1)),
inference(paramodulation,[status(thm)],[f4597,f14]) ).
fof(f4887,plain,
! [X0,X1] : not(big_hat(X0,X1)) = implies(implies(X1,X0),not(X1)),
inference(forward_demodulation,[status(thm)],[f4079,f4865]) ).
fof(f4888,plain,
! [X0,X1] : not(big_hat(X0,X1)) = implies(X1,not(implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f4824,f4887]) ).
fof(f4958,plain,
! [X0,X1] : big_V(X0,not(X1)) = implies(implies(X1,not(X0)),not(X1)),
inference(paramodulation,[status(thm)],[f4824,f14]) ).
fof(f5019,plain,
! [X0,X1] : big_V(X0,not(X1)) = implies(X1,not(implies(X1,not(X0)))),
inference(forward_demodulation,[status(thm)],[f4824,f4958]) ).
fof(f5020,plain,
! [X0,X1] : big_V(X0,not(X1)) = not(big_hat(not(X0),X1)),
inference(forward_demodulation,[status(thm)],[f4888,f5019]) ).
fof(f17389,plain,
! [X0,X1] : not(big_V(X0,not(X1))) = big_hat(not(X0),X1),
inference(paramodulation,[status(thm)],[f5020,f4268]) ).
fof(f23616,plain,
! [X0,X1] : not(big_V(X0,X1)) = big_hat(not(X0),not(X1)),
inference(paramodulation,[status(thm)],[f4268,f17389]) ).
fof(f23661,plain,
not(big_V(x,y)) != not(big_V(x,y)),
inference(backward_demodulation,[status(thm)],[f23616,f18]) ).
fof(f23662,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f23661]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL145-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 00:06:50 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 12.56/2.05 % Refutation found
% 12.56/2.05 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 12.56/2.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.54/2.11 % Elapsed time: 1.727506 seconds
% 0.54/2.11 % CPU time: 13.379444 seconds
% 0.54/2.11 % Total memory used: 283.018 MB
% 0.54/2.11 % Net memory used: 273.789 MB
%------------------------------------------------------------------------------