%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : ALG030-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 : Sun Sep 27 06:49:12 AM UTC 2026
% Result : Unsatisfiable 0.22s 5.50s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 56 unt; 0 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 38 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ifeq_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq2(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c_1,plain,
ifeq2(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom]) ).
fof(ifeq_axiom_001,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom_001) ).
cnf(c_2,plain,
ifeq(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom_001]) ).
fof(ax1,axiom,
! [VAR_0,VAR_1] : ifeq(sorti1(VAR_0),true,ifeq(sorti1(VAR_1),true,sorti1(op1(VAR_1,VAR_0)),true),true) = true,
file('theBenchmark.p',ax1) ).
cnf(c_3,plain,
ifeq(sorti1(A),true,ifeq(sorti1(B),true,sorti1(op1(B,A)),true),true) = true,
inference(clausify,[status(thm)],[ax1]) ).
fof(ax3_2,axiom,
op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
file('theBenchmark.p',ax3_2) ).
cnf(c_5,plain,
op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
inference(clausify,[status(thm)],[ax3_2]) ).
fof(ax3_1,axiom,
sorti1(sK1_ax3_V) = true,
file('theBenchmark.p',ax3_1) ).
cnf(c_6,plain,
sorti1(sK1_ax3_V) = true,
inference(clausify,[status(thm)],[ax3_1]) ).
fof(ax3,axiom,
sorti1(sK2_ax3_U) = true,
file('theBenchmark.p',ax3) ).
cnf(c_7,plain,
sorti1(sK2_ax3_U) = true,
inference(clausify,[status(thm)],[ax3]) ).
fof(ax4,axiom,
! [VAR_0,VAR_1] : ifeq2(sorti2(VAR_0),true,ifeq2(sorti2(VAR_1),true,op2(VAR_1,VAR_0),op2(VAR_0,VAR_1)),op2(VAR_0,VAR_1)) = op2(VAR_0,VAR_1),
file('theBenchmark.p',ax4) ).
cnf(c_8,plain,
ifeq2(sorti2(A),true,ifeq2(sorti2(B),true,op2(B,A),op2(A,B)),op2(A,B)) = op2(A,B),
inference(clausify,[status(thm)],[ax4]) ).
fof(co1,axiom,
! [VAR_0] : ifeq(sorti1(VAR_0),true,sorti2(h(VAR_0)),true) = true,
file('theBenchmark.p',co1) ).
cnf(c_9,plain,
ifeq(sorti1(A),true,sorti2(h(A)),true) = true,
inference(clausify,[status(thm)],[co1]) ).
fof(co1_1,axiom,
! [VAR_0,VAR_1] : ifeq2(sorti1(VAR_0),true,ifeq2(sorti1(VAR_1),true,op2(h(VAR_1),h(VAR_0)),h(op1(VAR_1,VAR_0))),h(op1(VAR_1,VAR_0))) = h(op1(VAR_1,VAR_0)),
file('theBenchmark.p',co1_1) ).
cnf(c_10,plain,
ifeq2(sorti1(A),true,ifeq2(sorti1(B),true,op2(h(B),h(A)),h(op1(B,A))),h(op1(B,A))) = h(op1(B,A)),
inference(clausify,[status(thm)],[co1_1]) ).
fof(co1_2,axiom,
! [VAR_0] : ifeq2(sorti1(VAR_0),true,j(h(VAR_0)),VAR_0) = VAR_0,
file('theBenchmark.p',co1_2) ).
cnf(c_11,plain,
ifeq2(sorti1(A),true,j(h(A)),A) = A,
inference(clausify,[status(thm)],[co1_2]) ).
cnf(c_168,plain,
ifeq(true,true,ifeq(sorti1(A),true,sorti1(op1(A,sK1_ax3_V)),true),true) = true,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_15,plain,
ifeq(sorti1(A),true,sorti1(op1(A,sK1_ax3_V)),true) = true,
inference(paramod,[status(thm)],[c_2,c_168]) ).
cnf(c_169,plain,
ifeq(sorti1(A),true,ifeq(true,true,sorti1(op1(sK1_ax3_V,A)),true),true) = true,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_16,plain,
ifeq(sorti1(A),true,sorti1(op1(sK1_ax3_V,A)),true) = true,
inference(paramod,[status(thm)],[c_2,c_169]) ).
cnf(c_170,plain,
ifeq(true,true,sorti2(h(sK1_ax3_V)),true) = true,
inference(paramod,[status(thm)],[c_6,c_9]) ).
cnf(c_19,plain,
sorti2(h(sK1_ax3_V)) = true,
inference(paramod,[status(thm)],[c_2,c_170]) ).
cnf(c_171,plain,
ifeq(true,true,sorti2(h(sK2_ax3_U)),true) = true,
inference(paramod,[status(thm)],[c_7,c_9]) ).
cnf(c_20,plain,
sorti2(h(sK2_ax3_U)) = true,
inference(paramod,[status(thm)],[c_2,c_171]) ).
cnf(c_172,plain,
ifeq2(true,true,ifeq2(sorti1(A),true,op2(h(A),h(sK1_ax3_V)),h(op1(A,sK1_ax3_V))),h(op1(A,sK1_ax3_V))) = h(op1(A,sK1_ax3_V)),
inference(paramod,[status(thm)],[c_6,c_10]) ).
cnf(c_21,plain,
ifeq2(sorti1(A),true,op2(h(A),h(sK1_ax3_V)),h(op1(A,sK1_ax3_V))) = h(op1(A,sK1_ax3_V)),
inference(paramod,[status(thm)],[c_1,c_172]) ).
cnf(c_173,plain,
ifeq2(sorti1(A),true,ifeq2(true,true,op2(h(sK1_ax3_V),h(A)),h(op1(sK1_ax3_V,A))),h(op1(sK1_ax3_V,A))) = h(op1(sK1_ax3_V,A)),
inference(paramod,[status(thm)],[c_6,c_10]) ).
cnf(c_22,plain,
ifeq2(sorti1(A),true,op2(h(sK1_ax3_V),h(A)),h(op1(sK1_ax3_V,A))) = h(op1(sK1_ax3_V,A)),
inference(paramod,[status(thm)],[c_1,c_173]) ).
cnf(c_174,plain,
ifeq(true,true,sorti1(op1(sK2_ax3_U,sK1_ax3_V)),true) = true,
inference(paramod,[status(thm)],[c_7,c_15]) ).
cnf(c_28,plain,
sorti1(op1(sK2_ax3_U,sK1_ax3_V)) = true,
inference(paramod,[status(thm)],[c_2,c_174]) ).
cnf(c_175,plain,
ifeq(true,true,sorti1(op1(sK1_ax3_V,sK2_ax3_U)),true) = true,
inference(paramod,[status(thm)],[c_7,c_16]) ).
cnf(c_29,plain,
sorti1(op1(sK1_ax3_V,sK2_ax3_U)) = true,
inference(paramod,[status(thm)],[c_2,c_175]) ).
cnf(c_176,plain,
ifeq2(true,true,ifeq2(sorti2(A),true,op2(A,h(sK1_ax3_V)),op2(h(sK1_ax3_V),A)),op2(h(sK1_ax3_V),A)) = op2(h(sK1_ax3_V),A),
inference(paramod,[status(thm)],[c_19,c_8]) ).
cnf(c_33,plain,
ifeq2(sorti2(A),true,op2(A,h(sK1_ax3_V)),op2(h(sK1_ax3_V),A)) = op2(h(sK1_ax3_V),A),
inference(paramod,[status(thm)],[c_1,c_176]) ).
cnf(c_177,plain,
ifeq2(true,true,j(h(op1(sK2_ax3_U,sK1_ax3_V))),op1(sK2_ax3_U,sK1_ax3_V)) = op1(sK2_ax3_U,sK1_ax3_V),
inference(paramod,[status(thm)],[c_28,c_11]) ).
cnf(c_57,plain,
j(h(op1(sK2_ax3_U,sK1_ax3_V))) = op1(sK2_ax3_U,sK1_ax3_V),
inference(paramod,[status(thm)],[c_1,c_177]) ).
cnf(c_178,plain,
ifeq2(true,true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))) = h(op1(sK2_ax3_U,sK1_ax3_V)),
inference(paramod,[status(thm)],[c_7,c_21]) ).
cnf(c_179,plain,
op2(h(sK2_ax3_U),h(sK1_ax3_V)) = h(op1(sK2_ax3_U,sK1_ax3_V)),
inference(paramod,[status(thm)],[c_1,c_178]) ).
cnf(c_64,plain,
h(op1(sK2_ax3_U,sK1_ax3_V)) = op2(h(sK2_ax3_U),h(sK1_ax3_V)),
inference(copy,[status(thm)],[c_179]) ).
cnf(c_71,plain,
j(op2(h(sK2_ax3_U),h(sK1_ax3_V))) = op1(sK2_ax3_U,sK1_ax3_V),
inference(paramod,[status(thm)],[c_64,c_57]) ).
cnf(c_180,plain,
ifeq2(true,true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))) = h(op1(sK1_ax3_V,sK2_ax3_U)),
inference(paramod,[status(thm)],[c_7,c_22]) ).
cnf(c_181,plain,
op2(h(sK1_ax3_V),h(sK2_ax3_U)) = h(op1(sK1_ax3_V,sK2_ax3_U)),
inference(paramod,[status(thm)],[c_1,c_180]) ).
cnf(c_75,plain,
h(op1(sK1_ax3_V,sK2_ax3_U)) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(copy,[status(thm)],[c_181]) ).
cnf(c_182,plain,
ifeq2(true,true,j(h(op1(sK1_ax3_V,sK2_ax3_U))),op1(sK1_ax3_V,sK2_ax3_U)) = op1(sK1_ax3_V,sK2_ax3_U),
inference(paramod,[status(thm)],[c_29,c_11]) ).
cnf(c_183,plain,
ifeq2(true,true,j(op2(h(sK1_ax3_V),h(sK2_ax3_U))),op1(sK1_ax3_V,sK2_ax3_U)) = op1(sK1_ax3_V,sK2_ax3_U),
inference(paramod,[status(thm)],[c_75,c_182]) ).
cnf(c_83,plain,
j(op2(h(sK1_ax3_V),h(sK2_ax3_U))) = op1(sK1_ax3_V,sK2_ax3_U),
inference(paramod,[status(thm)],[c_1,c_183]) ).
cnf(c_184,plain,
ifeq2(true,true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),op2(h(sK1_ax3_V),h(sK2_ax3_U))) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(paramod,[status(thm)],[c_20,c_33]) ).
cnf(c_155,plain,
op2(h(sK2_ax3_U),h(sK1_ax3_V)) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(paramod,[status(thm)],[c_1,c_184]) ).
cnf(c_185,plain,
j(op2(h(sK1_ax3_V),h(sK2_ax3_U))) = op1(sK2_ax3_U,sK1_ax3_V),
inference(paramod,[status(thm)],[c_155,c_71]) ).
cnf(c_186,plain,
op1(sK1_ax3_V,sK2_ax3_U) = op1(sK2_ax3_U,sK1_ax3_V),
inference(paramod,[status(thm)],[c_83,c_185]) ).
cnf(c_166,plain,
op1(sK2_ax3_U,sK1_ax3_V) = op1(sK1_ax3_V,sK2_ax3_U),
inference(copy,[status(thm)],[c_186]) ).
cnf(c_167,plain,
$false,
inference(resolve,[status(thm)],[c_166,c_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG030-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.44 % Computer : n016.cluster.edu
% 0.18/5.44 % Model : x86_64 x86_64
% 0.18/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.44 % Memory : 8046.5625MB
% 0.18/5.44 % OS : Linux 6.8.0-71-generic
% 0.18/5.44 % CPULimit : 300
% 0.18/5.44 % WCLimit : 300
% 0.18/5.44 % DateTime : Sat Sep 26 21:04:40 UTC 2026
% 0.18/5.44 % CPUTime :
% 0.18/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.45 % Process 1715937 was started by sandbox2 on n016,
% 0.18/5.45 % Sat Sep 26 21:04:40 2026
% 0.18/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/5.45
% 0.18/5.45 % From the command line: assign(max_seconds, 300).
% 0.22/5.50
% 0.22/5.50 % SZS status Unsatisfiable for theBenchmark
% 0.22/5.50
% 0.22/5.50 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.22/5.50 % Length of proof is 27.
% 0.22/5.50 % Level of proof is 6.
% 0.22/5.50 % Maximum clause weight is 51.000.
% 0.22/5.50 % Given clauses 43.
% 0.22/5.50
% 0.22/5.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------