%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL145-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 01:09:26 PM UTC 2026
% Result : Unsatisfiable 29.38s 4.14s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL145-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 00:10:01 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.37 % Drodi V4.1.1
% 29.38/4.14 % Refutation found
% 29.38/4.14 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 29.38/4.14 % SZS output start CNFRefutation for theBenchmark
% 29.38/4.14 fof(f1,axiom,(
% 29.38/4.14 (![X]: (implies(truth,X) = X ))),
% 29.38/4.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 29.38/4.14 fof(f2,axiom,(
% 29.38/4.14 (![X,Y,Z]: (implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ))),
% 29.38/4.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 29.38/4.14 fof(f3,axiom,(
% 29.38/4.14 (![X,Y]: (implies(implies(X,Y),Y) = implies(implies(Y,X),X) ))),
% 29.38/4.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 29.38/4.14 fof(f4,axiom,(
% 29.38/4.14 (![X,Y]: (implies(implies(not(X),not(Y)),implies(Y,X)) = truth ))),
% 29.38/4.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 29.38/4.14 fof(f5,axiom,(
% 29.38/4.14 (![X,Y]: (big_V(X,Y) = implies(implies(X,Y),Y) ))),
% 29.38/4.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 29.38/4.14 fof(f6,axiom,(
% 29.38/4.14 (![X,Y]: (big_hat(X,Y) = not(big_V(not(X),not(Y))) ))),
% 29.38/4.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 29.38/4.14 fof(f9,negated_conjecture,(
% 29.38/4.14 not(big_V(x,y)) != big_hat(not(x),not(y)) ),
% 29.38/4.14 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 29.38/4.14 fof(f10,plain,(
% 29.38/4.14 ![X0]: (implies(truth,X0)=X0)),
% 29.38/4.14 inference(cnf_transformation,[status(thm)],[f1])).
% 29.38/4.14 fof(f11,plain,(
% 29.38/4.14 ![X0,X1,X2]: (implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))=truth)),
% 29.38/4.14 inference(cnf_transformation,[status(thm)],[f2])).
% 29.38/4.14 fof(f12,plain,(
% 29.38/4.14 ![X0,X1]: (implies(implies(X0,X1),X1)=implies(implies(X1,X0),X0))),
% 29.38/4.14 inference(cnf_transformation,[status(thm)],[f3])).
% 29.38/4.14 fof(f13,plain,(
% 29.38/4.14 ![X0,X1]: (implies(implies(not(X0),not(X1)),implies(X1,X0))=truth)),
% 29.38/4.14 inference(cnf_transformation,[status(thm)],[f4])).
% 29.38/4.14 fof(f14,plain,(
% 29.38/4.14 ![X0,X1]: (big_V(X0,X1)=implies(implies(X0,X1),X1))),
% 29.38/4.14 inference(cnf_transformation,[status(thm)],[f5])).
% 29.38/4.14 fof(f15,plain,(
% 29.38/4.14 ![X0,X1]: (big_hat(X0,X1)=not(big_V(not(X0),not(X1))))),
% 29.38/4.14 inference(cnf_transformation,[status(thm)],[f6])).
% 29.38/4.14 fof(f18,plain,(
% 29.38/4.14 ~not(big_V(x,y))=big_hat(not(x),not(y))),
% 29.38/4.14 inference(cnf_transformation,[status(thm)],[f9])).
% 29.38/4.14 fof(f19,plain,(
% 29.38/4.14 ![X0,X1]: (implies(implies(X0,X1),X1)=big_V(X1,X0))),
% 29.38/4.14 inference(backward_demodulation,[status(thm)],[f14,f12])).
% 29.38/4.14 fof(f21,plain,(
% 29.38/4.14 ![X0]: (big_V(truth,X0)=implies(X0,X0))),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f10,f14])).
% 29.38/4.14 fof(f26,plain,(
% 29.38/4.14 ![X0,X1]: (big_V(X0,X1)=big_V(X1,X0))),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f14,f19])).
% 29.38/4.14 fof(f29,plain,(
% 29.38/4.14 ![X0]: (implies(X0,X0)=big_V(X0,truth))),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f10,f19])).
% 29.38/4.14 fof(f39,plain,(
% 29.38/4.14 ![X0,X1]: (implies(X0,implies(implies(X0,X1),implies(truth,X1)))=truth)),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f10,f11])).
% 29.38/4.14 fof(f46,plain,(
% 29.38/4.14 ![X0,X1]: (implies(implies(X0,truth),implies(X1,implies(X0,X1)))=truth)),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f10,f11])).
% 29.38/4.14 fof(f56,plain,(
% 29.38/4.14 ![X0,X1]: (implies(X0,implies(implies(X0,X1),X1))=truth)),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f10,f39])).
% 29.38/4.14 fof(f57,plain,(
% 29.38/4.14 ![X0,X1]: (implies(X0,big_V(X1,X0))=truth)),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f19,f56])).
% 29.38/4.14 fof(f85,plain,(
% 29.38/4.14 ![X0]: (big_V(X0,truth)=truth)),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f10,f57])).
% 29.38/4.14 fof(f96,plain,(
% 29.38/4.14 ![X0]: (implies(X0,X0)=truth)),
% 29.38/4.14 inference(backward_demodulation,[status(thm)],[f85,f29])).
% 29.38/4.14 fof(f104,plain,(
% 29.38/4.14 ![X0]: (big_V(truth,X0)=truth)),
% 29.38/4.14 inference(backward_demodulation,[status(thm)],[f96,f21])).
% 29.38/4.14 fof(f121,plain,(
% 29.38/4.14 ![X0]: (implies(truth,X0)=big_V(X0,X0))),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f96,f19])).
% 29.38/4.14 fof(f126,plain,(
% 29.38/4.14 ![X0]: (X0=big_V(X0,X0))),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f10,f121])).
% 29.38/4.14 fof(f139,plain,(
% 29.38/4.14 ![X0,X1,X2]: (implies(implies(X0,implies(not(X1),not(X2))),implies(truth,implies(X0,implies(X2,X1))))=truth)),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f13,f11])).
% 29.38/4.14 fof(f145,plain,(
% 29.38/4.14 ![X0,X1,X2]: (implies(implies(X0,implies(not(X1),not(X2))),implies(X0,implies(X2,X1)))=truth)),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f10,f139])).
% 29.38/4.14 fof(f162,plain,(
% 29.38/4.14 ![X0]: (implies(X0,truth)=truth)),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f104,f57])).
% 29.38/4.14 fof(f174,plain,(
% 29.38/4.14 ![X0,X1]: (implies(truth,implies(X0,implies(X1,X0)))=truth)),
% 29.38/4.14 inference(backward_demodulation,[status(thm)],[f162,f46])).
% 29.38/4.14 fof(f175,plain,(
% 29.38/4.14 ![X0,X1]: (implies(X0,implies(X1,X0))=truth)),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f10,f174])).
% 29.38/4.14 fof(f235,plain,(
% 29.38/4.14 ![X0,X1,X2]: (implies(truth,implies(implies(implies(X0,X1),X2),implies(X1,X2)))=truth)),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f175,f11])).
% 29.38/4.14 fof(f240,plain,(
% 29.38/4.14 ![X0,X1,X2]: (implies(implies(implies(X0,X1),X2),implies(X1,X2))=truth)),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f10,f235])).
% 29.38/4.14 fof(f245,plain,(
% 29.38/4.14 ![X0]: (big_hat(X0,X0)=not(not(X0)))),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f126,f15])).
% 29.38/4.14 fof(f246,plain,(
% 29.38/4.14 ![X0,X1]: (big_hat(X0,X1)=not(big_V(not(X1),not(X0))))),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f26,f15])).
% 29.38/4.14 fof(f1813,plain,(
% 29.38/4.14 ![X0,X1]: (implies(truth,implies(not(X0),implies(X0,X1)))=truth)),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f13,f240])).
% 29.38/4.14 fof(f1899,plain,(
% 29.38/4.14 ![X0,X1]: (implies(not(X0),implies(X0,X1))=truth)),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f10,f1813])).
% 29.38/4.14 fof(f2174,plain,(
% 29.38/4.14 ![X0,X1]: (implies(big_hat(X0,X0),implies(not(X0),X1))=truth)),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f245,f1899])).
% 29.38/4.14 fof(f2266,plain,(
% 29.38/4.14 ![X0,X1]: (implies(big_hat(not(X0),not(X0)),implies(big_hat(X0,X0),X1))=truth)),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f245,f2174])).
% 29.38/4.14 fof(f2297,plain,(
% 29.38/4.14 ![X0,X1]: (big_V(big_hat(X0,X0),implies(not(X0),X1))=implies(truth,implies(not(X0),X1)))),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f2174,f14])).
% 29.38/4.14 fof(f2324,plain,(
% 29.38/4.14 ![X0,X1]: (big_V(big_hat(X0,X0),implies(not(X0),X1))=implies(not(X0),X1))),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f10,f2297])).
% 29.38/4.14 fof(f15405,plain,(
% 29.38/4.14 ![X0,X1]: (big_V(big_hat(not(X0),not(X0)),implies(big_hat(X0,X0),X1))=implies(not(not(X0)),X1))),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f245,f2324])).
% 29.38/4.14 fof(f18831,plain,(
% 29.38/4.14 ![X0,X1]: (big_V(big_hat(not(X0),not(X0)),implies(big_hat(X0,X0),X1))=implies(truth,implies(big_hat(X0,X0),X1)))),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f2266,f14])).
% 29.38/4.14 fof(f18925,plain,(
% 29.38/4.14 ![X0,X1]: (implies(not(not(X0)),X1)=implies(truth,implies(big_hat(X0,X0),X1)))),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f15405,f18831])).
% 29.38/4.14 fof(f18926,plain,(
% 29.38/4.14 ![X0,X1]: (implies(not(not(X0)),X1)=implies(big_hat(X0,X0),X1))),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f10,f18925])).
% 29.38/4.14 fof(f20646,plain,(
% 29.38/4.14 ![X0,X1]: (implies(truth,implies(big_hat(X0,X0),implies(X1,X0)))=truth)),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f2174,f145])).
% 29.38/4.14 fof(f20894,plain,(
% 29.38/4.14 ![X0,X1]: (implies(big_hat(X0,X0),implies(X1,X0))=truth)),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f10,f20646])).
% 29.38/4.14 fof(f21157,plain,(
% 29.38/4.14 ![X0]: (implies(big_hat(X0,X0),X0)=truth)),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f10,f20894])).
% 29.38/4.14 fof(f21341,plain,(
% 29.38/4.14 ![X0]: (implies(not(not(X0)),X0)=truth)),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f18926,f21157])).
% 29.38/4.14 fof(f21433,plain,(
% 29.38/4.14 ![X0]: (big_V(big_hat(X0,X0),X0)=implies(truth,X0))),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f21157,f14])).
% 29.38/4.14 fof(f21524,plain,(
% 29.38/4.14 ![X0]: (big_V(big_hat(X0,X0),X0)=X0)),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f10,f21433])).
% 29.38/4.14 fof(f21686,plain,(
% 29.38/4.14 ![X0]: (big_V(not(not(X0)),X0)=X0)),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f245,f21524])).
% 29.38/4.14 fof(f22680,plain,(
% 29.38/4.14 ![X0]: (implies(truth,implies(X0,not(not(X0))))=truth)),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f21341,f13])).
% 29.38/4.14 fof(f22783,plain,(
% 29.38/4.14 ![X0]: (implies(X0,not(not(X0)))=truth)),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f10,f22680])).
% 29.38/4.14 fof(f22996,plain,(
% 29.38/4.14 ![X0]: (implies(truth,not(not(X0)))=big_V(not(not(X0)),X0))),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f22783,f19])).
% 29.38/4.14 fof(f23197,plain,(
% 29.38/4.14 ![X0]: (not(not(X0))=big_V(not(not(X0)),X0))),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f10,f22996])).
% 29.38/4.14 fof(f23385,plain,(
% 29.38/4.14 ![X0]: (not(not(X0))=X0)),
% 29.38/4.14 inference(forward_demodulation,[status(thm)],[f21686,f23197])).
% 29.38/4.14 fof(f23902,plain,(
% 29.38/4.14 ![X0,X1]: (big_hat(not(X0),X1)=not(big_V(not(X1),X0)))),
% 29.38/4.14 inference(paramodulation,[status(thm)],[f23385,f246])).
% 29.38/4.14 fof(f25559,plain,(
% 29.38/4.14 ![X0,X1]: (big_hat(not(X0),not(X1))=not(big_V(X1,X0)))),
% 29.38/4.19 inference(paramodulation,[status(thm)],[f23385,f23902])).
% 29.38/4.19 fof(f25608,plain,(
% 29.38/4.19 ~not(big_V(x,y))=not(big_V(y,x))),
% 29.38/4.19 inference(backward_demodulation,[status(thm)],[f25559,f18])).
% 29.38/4.19 fof(f25862,plain,(
% 29.38/4.19 ~not(big_V(x,y))=not(big_V(x,y))),
% 29.38/4.19 inference(paramodulation,[status(thm)],[f26,f25608])).
% 29.38/4.19 fof(f25864,plain,(
% 29.38/4.19 $false),
% 29.38/4.19 inference(trivial_equality_resolution,[status(thm)],[f25862])).
% 29.38/4.19 % SZS output end CNFRefutation for theBenchmark.p
% 2.99/4.21 % Elapsed time: 3.840140 seconds
% 2.99/4.21 % CPU time: 30.202463 seconds
% 2.99/4.21 % Total memory used: 443.351 MB
% 2.99/4.21 % Net memory used: 431.623 MB
%------------------------------------------------------------------------------