%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL186-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 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 : Mon Sep 7 11:11:26 AM UTC 2026
% Result : Unsatisfiable 4.85s 2.81s
% Output : CNFRefutation 4.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 36 ( 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ ifeq > or > #nlpp > theorem > not > axiom > true > q > p
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(axiom,type,
axiom: $i > $i ).
tff(or,type,
or: ( $i * $i ) > $i ).
tff(not,type,
not: $i > $i ).
tff(theorem,type,
theorem: $i > $i ).
tff(q,type,
q: $i ).
tff(true,type,
true: $i ).
tff(p,type,
p: $i ).
tff(ifeq,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(f_30,axiom,
! [A,B] : ( axiom(or(not(or(A,B)),or(B,A))) = true ),
file(unknown,unknown) ).
tff(f_36,axiom,
! [X] : ( ifeq(axiom(X),true,theorem(X),true) = true ),
file(unknown,unknown) ).
tff(f_24,axiom,
! [A,B,C] : ( ifeq(A,A,B,C) = B ),
file(unknown,unknown) ).
tff(f_28,axiom,
! [A,B] : ( axiom(or(not(A),or(B,A))) = true ),
file(unknown,unknown) ).
tff(f_40,axiom,
! [Y,Z,X] : ( ifeq(theorem(or(not(Y),Z)),true,ifeq(axiom(or(not(X),Y)),true,theorem(or(not(X),Z)),true),true) = true ),
file(unknown,unknown) ).
tff(f_42,axiom,
theorem(or(not(not(p)),or(not(p),q))) != true,
file(unknown,unknown) ).
tff(c_57,plain,
! [A_28,B_29] : ( axiom(or(not(or(A_28,B_29)),or(B_29,A_28))) = true ),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_14,plain,
! [X_15] : ( ifeq(axiom(X_15),true,theorem(X_15),true) = true ),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_131,plain,
! [A_39,B_40] : ( ifeq(true,true,theorem(or(not(or(A_39,B_40)),or(B_40,A_39))),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_57,c_14]) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( ifeq(A_1,A_1,B_2,C_3) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_136,plain,
! [A_39,B_40] : ( theorem(or(not(or(A_39,B_40)),or(B_40,A_39))) = true ),
inference(superposition,[status(thm),theory(equality)],[c_131,c_2]) ).
tff(c_6,plain,
! [A_5,B_6] : ( axiom(or(not(A_5),or(B_6,A_5))) = true ),
inference(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_246,plain,
! [Y_50,Z_51,X_52] : ( ifeq(theorem(or(not(Y_50),Z_51)),true,ifeq(axiom(or(not(X_52),Y_50)),true,theorem(or(not(X_52),Z_51)),true),true) = true ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_280,plain,
! [B_6,A_5,Z_51] : ( ifeq(theorem(or(not(or(B_6,A_5)),Z_51)),true,ifeq(true,true,theorem(or(not(A_5),Z_51)),true),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_246]) ).
tff(c_1181,plain,
! [B_94,A_95,Z_96] : ( ifeq(theorem(or(not(or(B_94,A_95)),Z_96)),true,theorem(or(not(A_95),Z_96)),true) = true ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_280]) ).
tff(c_1384,plain,
! [B_101,A_102] : ( ifeq(true,true,theorem(or(not(B_101),or(B_101,A_102))),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_136,c_1181]) ).
tff(c_1389,plain,
! [B_101,A_102] : ( theorem(or(not(B_101),or(B_101,A_102))) = true ),
inference(superposition,[status(thm),theory(equality)],[c_1384,c_2]) ).
tff(c_20,plain,
theorem(or(not(not(p)),or(not(p),q))) != true,
inference(cnfTransformation,[status(thm)],[f_42]) ).
tff(c_1417,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1389,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL186-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 5 11:51:20 UTC 2026
% 0.11/0.36 % CPUTime :
% 4.85/2.81 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.85/2.82
% 4.85/2.82 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------