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FindProof---0.1.UNS-Prf.s

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%------------------------------------------------------------------------------
% File     : FindProof---0.1
% Problem  : GEO048-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300

% Computer : n007.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 01:16:48 PM UTC 2026

% Result   : Unsatisfiable 45.16s 6.30s
% Output   : Proof 45.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  126 ( 110 unt;   0 def)
%            Number of atoms       :  150 (  80 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   70 (  46   ~;  24   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-4 aty)
%            Number of functors    :   14 (  14 usr;  11 con; 0-5 aty)
%            Number of variables   :  187 (  18 sgn  46   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
cnf(f8,axiom,
    ( between(X,inner_pasch(U,V,W,X,Y),U)
    | ~ between(Y,X,W)
    | ~ between(U,V,W) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).

fof(f8_nnf,plain,
    ! [U,V,W,Y,X] :
      ( between(X,inner_pasch(U,V,W,X,Y),U)
      | ~ between(Y,X,W)
      | ~ between(U,V,W) ),
    inference(nnf_transformation,[status(thm)],[f8]) ).

fof(f8_sk,plain,
    ! [U,V,W,Y,X] :
      ( between(X,inner_pasch(U,V,W,X,Y),U)
      | ~ between(Y,X,W)
      | ~ between(U,V,W) ),
    inference(skolemisation,[status(esa)],[f8_nnf]) ).

cnf(c8,plain,
    ( between(X4,inner_pasch(X0,X1,X2,X4,X3),X0)
    | ~ between(X3,X4,X2)
    | ~ between(X0,X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f8_sk]) ).

cnf(t27,plain,
    ifeq(between(X1,X2,X3),true,ifeq(between(X4,X5,X3),true,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),true),true) = true,
    inference(equality_encoding,[status(esa)],[c8]) ).

cnf(t45,plain,
    ifeq(between(X1,X2,X3),true,ifeq(between(X4,X5,X3),true,between(X5,inner_pasch(X1,X2,X3,X5,X4),X1),true),true) = true,
    inference(orient,[status(thm)],[t27]) ).

cnf(f7,axiom,
    ( between(V,inner_pasch(U,V,W,X,Y),Y)
    | ~ between(Y,X,W)
    | ~ between(U,V,W) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).

fof(f7_nnf,plain,
    ! [U,V,W,Y,X] :
      ( between(V,inner_pasch(U,V,W,X,Y),Y)
      | ~ between(Y,X,W)
      | ~ between(U,V,W) ),
    inference(nnf_transformation,[status(thm)],[f7]) ).

fof(f7_sk,plain,
    ! [U,V,W,Y,X] :
      ( between(V,inner_pasch(U,V,W,X,Y),Y)
      | ~ between(Y,X,W)
      | ~ between(U,V,W) ),
    inference(skolemisation,[status(esa)],[f7_nnf]) ).

cnf(c7,plain,
    ( between(X1,inner_pasch(X0,X1,X2,X4,X3),X3)
    | ~ between(X3,X4,X2)
    | ~ between(X0,X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f7_sk]) ).

cnf(t26,plain,
    ifeq(between(X1,X2,X3),true,ifeq(between(X4,X5,X3),true,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),true),true) = true,
    inference(equality_encoding,[status(esa)],[c7]) ).

cnf(t54,plain,
    ifeq(between(X1,X2,X3),true,ifeq(between(X4,X5,X3),true,between(X2,inner_pasch(X1,X2,X3,X5,X4),X4),true),true) = true,
    inference(orient,[status(thm)],[t26]) ).

cnf(f6,axiom,
    ( X = Y
    | ~ between(X,Y,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).

fof(f6_nnf,plain,
    ! [X,Y] :
      ( X = Y
      | ~ between(X,Y,X) ),
    inference(nnf_transformation,[status(thm)],[f6]) ).

fof(f6_sk,plain,
    ! [X,Y] :
      ( X = Y
      | ~ between(X,Y,X) ),
    inference(skolemisation,[status(esa)],[f6_nnf]) ).

cnf(c6,plain,
    ( X0 = X1
    | ~ between(X0,X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f6_sk]) ).

cnf(t15,plain,
    ifeq(between(X1,X2,X1),true,X1,X2) = X2,
    inference(equality_encoding,[status(esa)],[c6]) ).

cnf(t36,plain,
    ifeq(between(X1,X2,X1),true,X1,X2) = X2,
    inference(orient,[status(thm)],[t15]) ).

cnf(f18,hypothesis,
    between(u,v,w),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).

fof(f18_nnf,plain,
    between(u,v,w),
    inference(nnf_transformation,[status(thm)],[f18]) ).

cnf(c18,plain,
    between(u,v,w),
    inference(cnf_transformation,[status(esa)],[f18_nnf]) ).

cnf(t8,plain,
    between(u,v,w) = true,
    inference(equality_encoding,[status(esa)],[c18]) ).

cnf(t42,plain,
    between(u,v,w) = true,
    inference(orient,[status(thm)],[t8]) ).

cnf(t52,plain,
    true = ifeq(between(X1,X2,w),true,ifeq(true,true,between(v,inner_pasch(X1,X2,w,v,u),X1),true),true),
    inference(cp,[status(thm)],[t45,t42]) ).

cnf(t12,plain,
    ifeq(X1,X1,X2,X3) = X2,
    introduced(definition) ).

cnf(t35,plain,
    ifeq(X1,X1,X2,X3) = X2,
    inference(orient,[status(thm)],[t12]) ).

cnf(t30505,plain,
    true = ifeq(between(X1,X2,w),true,between(v,inner_pasch(X1,X2,w,v,u),X1),true),
    inference(step,[status(thm)],[t52,t35]) ).

cnf(t910,plain,
    ifeq(between(X1,X2,w),true,between(v,inner_pasch(X1,X2,w,v,u),X1),true) = true,
    inference(orient,[status(thm)],[t30505]) ).

cnf(f3,axiom,
    between(X,Y,extension(X,Y,W,V)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).

fof(f3_nnf,plain,
    ! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
    inference(nnf_transformation,[status(thm)],[f3]) ).

fof(f3_sk,plain,
    ! [X,Y,W,V] : between(X,Y,extension(X,Y,W,V)),
    inference(skolemisation,[status(esa)],[f3_nnf]) ).

cnf(c3,plain,
    between(X0,X1,extension(X0,X1,X2,X3)),
    inference(cnf_transformation,[status(esa)],[f3_sk]) ).

cnf(t14,plain,
    between(X1,X2,extension(X1,X2,X3,X4)) = true,
    inference(equality_encoding,[status(esa)],[c3]) ).

cnf(t41,plain,
    between(X1,X2,extension(X1,X2,X3,X4)) = true,
    inference(orient,[status(thm)],[t14]) ).

cnf(f2,axiom,
    ( X = Y
    | ~ equidistant(X,Y,Z,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).

fof(f2_nnf,plain,
    ! [X,Y,Z] :
      ( X = Y
      | ~ equidistant(X,Y,Z,Z) ),
    inference(nnf_transformation,[status(thm)],[f2]) ).

fof(f2_sk,plain,
    ! [X,Y,Z] :
      ( X = Y
      | ~ equidistant(X,Y,Z,Z) ),
    inference(skolemisation,[status(esa)],[f2_nnf]) ).

cnf(c2,plain,
    ( X0 = X1
    | ~ equidistant(X0,X1,X2,X2) ),
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(t20,plain,
    ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
    inference(equality_encoding,[status(esa)],[c2]) ).

cnf(t37,plain,
    ifeq(equidistant(X1,X2,X3,X3),true,X1,X2) = X2,
    inference(orient,[status(thm)],[t20]) ).

cnf(f4,axiom,
    equidistant(Y,extension(X,Y,W,V),W,V),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).

fof(f4_nnf,plain,
    ! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
    inference(nnf_transformation,[status(thm)],[f4]) ).

fof(f4_sk,plain,
    ! [Y,X,W,V] : equidistant(Y,extension(X,Y,W,V),W,V),
    inference(skolemisation,[status(esa)],[f4_nnf]) ).

cnf(c4,plain,
    equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
    inference(cnf_transformation,[status(esa)],[f4_sk]) ).

cnf(t19,plain,
    equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
    inference(equality_encoding,[status(esa)],[c4]) ).

cnf(t153,plain,
    equidistant(X1,extension(X2,X1,X3,X4),X3,X4) = true,
    inference(orient,[status(thm)],[t19]) ).

cnf(t154,plain,
    extension(X1,X2,X3,X3) = ifeq(true,true,X2,extension(X1,X2,X3,X3)),
    inference(cp,[status(thm)],[t37,t153]) ).

cnf(t30451,plain,
    extension(X1,X2,X3,X3) = X2,
    inference(step,[status(thm)],[t154,t35]) ).

cnf(t284,plain,
    extension(X1,X2,X3,X3) = X2,
    inference(orient,[status(thm)],[t30451]) ).

cnf(t286,plain,
    true = between(X1,X2,X2),
    inference(cp,[status(thm)],[t41,t284]) ).

cnf(t287,plain,
    between(X1,X2,X2) = true,
    inference(orient,[status(thm)],[t286]) ).

cnf(t911,plain,
    true = ifeq(true,true,between(v,inner_pasch(X1,w,w,v,u),X1),true),
    inference(cp,[status(thm)],[t910,t287]) ).

cnf(t30506,plain,
    true = between(v,inner_pasch(X1,w,w,v,u),X1),
    inference(step,[status(thm)],[t911,t35]) ).

cnf(t917,plain,
    between(v,inner_pasch(X1,w,w,v,u),X1) = true,
    inference(orient,[status(thm)],[t30506]) ).

cnf(t918,plain,
    inner_pasch(v,w,w,v,u) = ifeq(true,true,v,inner_pasch(v,w,w,v,u)),
    inference(cp,[status(thm)],[t36,t917]) ).

cnf(t30507,plain,
    inner_pasch(v,w,w,v,u) = v,
    inference(step,[status(thm)],[t918,t35]) ).

cnf(t944,plain,
    inner_pasch(v,w,w,v,u) = v,
    inference(orient,[status(thm)],[t30507]) ).

cnf(t945,plain,
    true = ifeq(between(v,w,w),true,ifeq(between(u,v,w),true,between(w,v,u),true),true),
    inference(cp,[status(thm)],[t54,t944]) ).

cnf(t30508,plain,
    true = ifeq(true,true,ifeq(between(u,v,w),true,between(w,v,u),true),true),
    inference(step,[status(thm)],[t945,t287]) ).

cnf(t30509,plain,
    true = ifeq(between(u,v,w),true,between(w,v,u),true),
    inference(step,[status(thm)],[t30508,t35]) ).

cnf(t30510,plain,
    true = ifeq(true,true,between(w,v,u),true),
    inference(step,[status(thm)],[t30509,t42]) ).

cnf(t30511,plain,
    true = between(w,v,u),
    inference(step,[status(thm)],[t30510,t35]) ).

cnf(t946,plain,
    between(w,v,u) = true,
    inference(orient,[status(thm)],[t30511]) ).

cnf(t948,plain,
    true = ifeq(between(X1,X2,u),true,ifeq(true,true,between(v,inner_pasch(X1,X2,u,v,w),X1),true),true),
    inference(cp,[status(thm)],[t45,t946]) ).

cnf(t31791,plain,
    true = ifeq(between(X1,X2,u),true,between(v,inner_pasch(X1,X2,u,v,w),X1),true),
    inference(step,[status(thm)],[t948,t35]) ).

cnf(t30092,plain,
    ifeq(between(X1,X2,u),true,between(v,inner_pasch(X1,X2,u,v,w),X1),true) = true,
    inference(orient,[status(thm)],[t31791]) ).

cnf(f20,hypothesis,
    between(u,x,u1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_between_u_and_u1) ).

fof(f20_nnf,plain,
    between(u,x,u1),
    inference(nnf_transformation,[status(thm)],[f20]) ).

cnf(c20,plain,
    between(u,x,u1),
    inference(cnf_transformation,[status(esa)],[f20_nnf]) ).

cnf(t9,plain,
    between(u,x,u1) = true,
    inference(equality_encoding,[status(esa)],[c20]) ).

cnf(t43,plain,
    between(u,x,u1) = true,
    inference(orient,[status(thm)],[t9]) ).

cnf(t49,plain,
    true = ifeq(true,true,ifeq(between(X1,X2,u1),true,between(X2,inner_pasch(u,x,u1,X2,X1),u),true),true),
    inference(cp,[status(thm)],[t45,t43]) ).

cnf(t30480,plain,
    true = ifeq(between(X1,X2,u1),true,between(X2,inner_pasch(u,x,u1,X2,X1),u),true),
    inference(step,[status(thm)],[t49,t35]) ).

cnf(t655,plain,
    ifeq(between(X1,X2,u1),true,between(X2,inner_pasch(u,x,u1,X2,X1),u),true) = true,
    inference(orient,[status(thm)],[t30480]) ).

cnf(f19,hypothesis,
    between(u1,v1,w),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_between_u1_and_w) ).

fof(f19_nnf,plain,
    between(u1,v1,w),
    inference(nnf_transformation,[status(thm)],[f19]) ).

cnf(c19,plain,
    between(u1,v1,w),
    inference(cnf_transformation,[status(esa)],[f19_nnf]) ).

cnf(t10,plain,
    between(u1,v1,w) = true,
    inference(equality_encoding,[status(esa)],[c19]) ).

cnf(t44,plain,
    between(u1,v1,w) = true,
    inference(orient,[status(thm)],[t10]) ).

cnf(t51,plain,
    true = ifeq(between(X1,X2,w),true,ifeq(true,true,between(v1,inner_pasch(X1,X2,w,v1,u1),X1),true),true),
    inference(cp,[status(thm)],[t45,t44]) ).

cnf(t30483,plain,
    true = ifeq(between(X1,X2,w),true,between(v1,inner_pasch(X1,X2,w,v1,u1),X1),true),
    inference(step,[status(thm)],[t51,t35]) ).

cnf(t703,plain,
    ifeq(between(X1,X2,w),true,between(v1,inner_pasch(X1,X2,w,v1,u1),X1),true) = true,
    inference(orient,[status(thm)],[t30483]) ).

cnf(t704,plain,
    true = ifeq(true,true,between(v1,inner_pasch(X1,w,w,v1,u1),X1),true),
    inference(cp,[status(thm)],[t703,t287]) ).

cnf(t30484,plain,
    true = between(v1,inner_pasch(X1,w,w,v1,u1),X1),
    inference(step,[status(thm)],[t704,t35]) ).

cnf(t708,plain,
    between(v1,inner_pasch(X1,w,w,v1,u1),X1) = true,
    inference(orient,[status(thm)],[t30484]) ).

cnf(t709,plain,
    inner_pasch(v1,w,w,v1,u1) = ifeq(true,true,v1,inner_pasch(v1,w,w,v1,u1)),
    inference(cp,[status(thm)],[t36,t708]) ).

cnf(t30485,plain,
    inner_pasch(v1,w,w,v1,u1) = v1,
    inference(step,[status(thm)],[t709,t35]) ).

cnf(t734,plain,
    inner_pasch(v1,w,w,v1,u1) = v1,
    inference(orient,[status(thm)],[t30485]) ).

cnf(t735,plain,
    true = ifeq(between(v1,w,w),true,ifeq(between(u1,v1,w),true,between(w,v1,u1),true),true),
    inference(cp,[status(thm)],[t54,t734]) ).

cnf(t30486,plain,
    true = ifeq(true,true,ifeq(between(u1,v1,w),true,between(w,v1,u1),true),true),
    inference(step,[status(thm)],[t735,t287]) ).

cnf(t30487,plain,
    true = ifeq(between(u1,v1,w),true,between(w,v1,u1),true),
    inference(step,[status(thm)],[t30486,t35]) ).

cnf(t30488,plain,
    true = ifeq(true,true,between(w,v1,u1),true),
    inference(step,[status(thm)],[t30487,t44]) ).

cnf(t30489,plain,
    true = between(w,v1,u1),
    inference(step,[status(thm)],[t30488,t35]) ).

cnf(t736,plain,
    between(w,v1,u1) = true,
    inference(orient,[status(thm)],[t30489]) ).

cnf(t737,plain,
    true = ifeq(true,true,between(v1,inner_pasch(u,x,u1,v1,w),u),true),
    inference(cp,[status(thm)],[t655,t736]) ).

cnf(t30490,plain,
    true = between(v1,inner_pasch(u,x,u1,v1,w),u),
    inference(step,[status(thm)],[t737,t35]) ).

cnf(t757,plain,
    between(v1,inner_pasch(u,x,u1,v1,w),u) = true,
    inference(orient,[status(thm)],[t30490]) ).

cnf(t30287,plain,
    true = ifeq(true,true,between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),true),
    inference(cp,[status(thm)],[t30092,t757]) ).

cnf(t31792,plain,
    true = between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
    inference(step,[status(thm)],[t30287,t35]) ).

cnf(f22,negated_conjecture,
    ~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_conclusion2) ).

fof(f22_nnf,plain,
    ~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
    inference(nnf_transformation,[status(thm)],[f22]) ).

fof(f22_sk,plain,
    ~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
    inference(skolemisation,[status(esa)],[f22_nnf]) ).

cnf(c22,plain,
    ~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
    inference(cnf_transformation,[status(esa)],[f22_sk]) ).

cnf(t21,plain,
    between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1) = false,
    inference(equality_encoding,[status(esa)],[c22]) ).

cnf(t178,plain,
    between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1) = false,
    inference(orient,[status(thm)],[t21]) ).

cnf(t31793,plain,
    true = false,
    inference(step,[status(thm)],[t31792,t178]) ).

cnf(t30421,plain,
    false = true,
    inference(orient,[status(thm)],[t31793]) ).

cnf(f9,axiom,
    ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).

fof(f9_nnf,plain,
    ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    inference(nnf_transformation,[status(thm)],[f9]) ).

fof(f9_sk,plain,
    ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    inference(skolemisation,[status(esa)],[f9_nnf]) ).

cnf(c9,plain,
    ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    inference(cnf_transformation,[status(esa)],[f9_sk]) ).

cnf(f10,axiom,
    ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).

fof(f10_nnf,plain,
    ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
    inference(nnf_transformation,[status(thm)],[f10]) ).

fof(f10_sk,plain,
    ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
    inference(skolemisation,[status(esa)],[f10_nnf]) ).

cnf(c10,plain,
    ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
    inference(cnf_transformation,[status(esa)],[f10_sk]) ).

cnf(f11,axiom,
    ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).

fof(f11_nnf,plain,
    ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
    inference(nnf_transformation,[status(thm)],[f11]) ).

fof(f11_sk,plain,
    ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
    inference(skolemisation,[status(esa)],[f11_nnf]) ).

cnf(c11,plain,
    ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
    inference(cnf_transformation,[status(esa)],[f11_sk]) ).

cnf(f21,negated_conjecture,
    ~ between(x,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),w),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_conclusion1) ).

fof(f21_nnf,plain,
    ~ between(x,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),w),
    inference(nnf_transformation,[status(thm)],[f21]) ).

fof(f21_sk,plain,
    ~ between(x,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),w),
    inference(skolemisation,[status(esa)],[f21_nnf]) ).

cnf(c21,plain,
    ~ between(x,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),w),
    inference(cnf_transformation,[status(esa)],[f21_sk]) ).

cnf(goal_0,negated_conjecture,
    true != false,
    inference(equality_encoding,[status(esa)],[c9,c10,c11,c21,c22]) ).

cnf(g0_0,plain,
    true != true,
    inference(rw,[status(thm)],[goal_0,t30421]) ).

cnf(contradiction_0,plain,
    $false,
    inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : GEO048-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04  % Command  : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37  % Computer : n007.cluster.edu
% 0.11/0.37  % Model    : x86_64 x86_64
% 0.11/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37  % Memory   : 8046.5625MB
% 0.11/0.37  % OS       : Linux 6.8.0-71-generic
% 0.11/0.37  % CPULimit : 300
% 0.11/0.37  % WCLimit  : 300
% 0.11/0.37  % DateTime : Wed Sep 23 10:32:22 UTC 2026
% 0.11/0.37  % CPUTime  : 
% 0.11/0.38  Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 45.16/6.30  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.16/6.30  % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------