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FindProof---0.1.UNS-Prf.s

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%------------------------------------------------------------------------------
% File     : FindProof---0.1
% Problem  : SYN269-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300

% Computer : n009.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 03:34:13 PM UTC 2026

% Result   : Unsatisfiable 6.59s 1.32s
% Output   : Proof 6.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  139 (  75 unt;   0 def)
%            Number of atoms       :  255 (  43 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  238 ( 122   ~; 116   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   19 (  17 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-4 aty)
%            Number of variables   :  220 (  53 sgn  86   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
cnf(f162,axiom,
    ( ~ p0(I,I)
    | s1(I) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_125) ).

fof(f162_nnf,plain,
    ! [I] :
      ( ~ p0(I,I)
      | s1(I) ),
    inference(nnf_transformation,[status(thm)],[f162]) ).

fof(f162_sk,plain,
    ! [I] :
      ( ~ p0(I,I)
      | s1(I) ),
    inference(skolemisation,[status(esa)],[f162_nnf]) ).

cnf(c162,plain,
    ( ~ p0(X0,X0)
    | s1(X0) ),
    inference(cnf_transformation,[status(esa)],[f162_sk]) ).

cnf(hi160,axiom,
    ifeq(p0(X0,X0),true,s1(X0),true) = true,
    inference(equality_encoding,[status(esa)],[c162]) ).

cnf(f13,axiom,
    p0(b,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).

fof(f13_nnf,plain,
    ! [X] : p0(b,X),
    inference(nnf_transformation,[status(thm)],[f13]) ).

fof(f13_sk,plain,
    ! [X] : p0(b,X),
    inference(skolemisation,[status(esa)],[f13_nnf]) ).

cnf(c13,plain,
    p0(b,X0),
    inference(cnf_transformation,[status(esa)],[f13_sk]) ).

cnf(hi13,axiom,
    p0(b,X0) = true,
    inference(equality_encoding,[status(esa)],[c13]) ).

cnf(h26,plain,
    s1(b) = true,
    inference(hyper_resolution,[status(thm)],[hi160,hi13]) ).

cnf(f163,axiom,
    ( ~ s1(H)
    | ~ q0(F,G)
    | s1(F) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_126) ).

fof(f163_nnf,plain,
    ! [F,G,H] :
      ( ~ s1(H)
      | ~ q0(F,G)
      | s1(F) ),
    inference(nnf_transformation,[status(thm)],[f163]) ).

fof(f163_sk,plain,
    ! [F,G,H] :
      ( ~ s1(H)
      | ~ q0(F,G)
      | s1(F) ),
    inference(skolemisation,[status(esa)],[f163_nnf]) ).

cnf(c163,plain,
    ( ~ s1(X2)
    | ~ q0(X0,X1)
    | s1(X0) ),
    inference(cnf_transformation,[status(esa)],[f163_sk]) ).

cnf(hi161,axiom,
    ifeq(q0(X0,X1),true,ifeq(s1(X2),true,s1(X0),true),true) = true,
    inference(equality_encoding,[status(esa)],[c163]) ).

cnf(f35,axiom,
    q0(a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).

fof(f35_nnf,plain,
    q0(a,b),
    inference(nnf_transformation,[status(thm)],[f35]) ).

cnf(c35,plain,
    q0(a,b),
    inference(cnf_transformation,[status(esa)],[f35_nnf]) ).

cnf(hi35,axiom,
    q0(a,b) = true,
    inference(equality_encoding,[status(esa)],[c35]) ).

cnf(h115,plain,
    s1(a) = true,
    inference(hyper_resolution,[status(thm)],[hi161,hi35,h26]) ).

cnf(f227,axiom,
    ( ~ s0(d)
    | ~ s1(a)
    | s2(d) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_190) ).

fof(f227_nnf,plain,
    ( ~ s0(d)
    | ~ s1(a)
    | s2(d) ),
    inference(nnf_transformation,[status(thm)],[f227]) ).

fof(f227_sk,plain,
    ( ~ s0(d)
    | ~ s1(a)
    | s2(d) ),
    inference(skolemisation,[status(esa)],[f227_nnf]) ).

cnf(c227,plain,
    ( ~ s0(d)
    | ~ s1(a)
    | s2(d) ),
    inference(cnf_transformation,[status(esa)],[f227_sk]) ).

cnf(hi224,axiom,
    ifeq(s1(a),true,ifeq(s0(d),true,s2(d),true),true) = true,
    inference(equality_encoding,[status(esa)],[c227]) ).

cnf(f0,axiom,
    s0(d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).

fof(f0_nnf,plain,
    s0(d),
    inference(nnf_transformation,[status(thm)],[f0]) ).

cnf(c0,plain,
    s0(d),
    inference(cnf_transformation,[status(esa)],[f0_nnf]) ).

cnf(hi0,axiom,
    s0(d) = true,
    inference(equality_encoding,[status(esa)],[c0]) ).

cnf(h160,plain,
    s2(d) = true,
    inference(hyper_resolution,[status(thm)],[hi224,h115,hi0]) ).

cnf(f170,axiom,
    ( ~ m0(C,B,J)
    | ~ s1(B)
    | ~ p0(A,A)
    | l2(J,J) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_133) ).

fof(f170_nnf,plain,
    ! [J,A,B,C] :
      ( ~ m0(C,B,J)
      | ~ s1(B)
      | ~ p0(A,A)
      | l2(J,J) ),
    inference(nnf_transformation,[status(thm)],[f170]) ).

fof(f170_sk,plain,
    ! [J,A,B,C] :
      ( ~ m0(C,B,J)
      | ~ s1(B)
      | ~ p0(A,A)
      | l2(J,J) ),
    inference(skolemisation,[status(esa)],[f170_nnf]) ).

cnf(c170,plain,
    ( ~ m0(X3,X2,X0)
    | ~ s1(X2)
    | ~ p0(X1,X1)
    | l2(X0,X0) ),
    inference(cnf_transformation,[status(esa)],[f170_sk]) ).

cnf(hi167,axiom,
    ifeq(p0(X0,X0),true,ifeq(s1(X1),true,ifeq(m0(X2,X1,X3),true,l2(X3,X3),true),true),true) = true,
    inference(equality_encoding,[status(esa)],[c170]) ).

cnf(f15,axiom,
    m0(c,b,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).

fof(f15_nnf,plain,
    m0(c,b,a),
    inference(nnf_transformation,[status(thm)],[f15]) ).

cnf(c15,plain,
    m0(c,b,a),
    inference(cnf_transformation,[status(esa)],[f15_nnf]) ).

cnf(hi15,axiom,
    m0(c,b,a) = true,
    inference(equality_encoding,[status(esa)],[c15]) ).

cnf(h114,plain,
    l2(a,a) = true,
    inference(hyper_resolution,[status(thm)],[hi167,hi13,h26,hi15]) ).

cnf(f262,axiom,
    ( ~ s2(B)
    | ~ m0(J,C,C)
    | ~ l2(C,J)
    | ~ m0(B,B,A)
    | m3(J,A,J) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_225) ).

fof(f262_nnf,plain,
    ! [J,A,B,C] :
      ( ~ s2(B)
      | ~ m0(J,C,C)
      | ~ l2(C,J)
      | ~ m0(B,B,A)
      | m3(J,A,J) ),
    inference(nnf_transformation,[status(thm)],[f262]) ).

fof(f262_sk,plain,
    ! [J,A,B,C] :
      ( ~ s2(B)
      | ~ m0(J,C,C)
      | ~ l2(C,J)
      | ~ m0(B,B,A)
      | m3(J,A,J) ),
    inference(skolemisation,[status(esa)],[f262_nnf]) ).

cnf(c262,plain,
    ( ~ s2(X2)
    | ~ m0(X0,X3,X3)
    | ~ l2(X3,X0)
    | ~ m0(X2,X2,X1)
    | m3(X0,X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f262_sk]) ).

cnf(hi257,axiom,
    ifeq(m0(X0,X0,X1),true,ifeq(l2(X2,X3),true,ifeq(m0(X3,X2,X2),true,ifeq(s2(X0),true,m3(X3,X1,X3),true),true),true),true) = true,
    inference(equality_encoding,[status(esa)],[c262]) ).

cnf(f18,axiom,
    m0(X,d,Y),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).

fof(f18_nnf,plain,
    ! [X,Y] : m0(X,d,Y),
    inference(nnf_transformation,[status(thm)],[f18]) ).

fof(f18_sk,plain,
    ! [X,Y] : m0(X,d,Y),
    inference(skolemisation,[status(esa)],[f18_nnf]) ).

cnf(c18,plain,
    m0(X0,d,X1),
    inference(cnf_transformation,[status(esa)],[f18_sk]) ).

cnf(hi18,axiom,
    m0(X0,d,X1) = true,
    inference(equality_encoding,[status(esa)],[c18]) ).

cnf(f11,axiom,
    m0(a,X,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).

fof(f11_nnf,plain,
    ! [X] : m0(a,X,a),
    inference(nnf_transformation,[status(thm)],[f11]) ).

fof(f11_sk,plain,
    ! [X] : m0(a,X,a),
    inference(skolemisation,[status(esa)],[f11_nnf]) ).

cnf(c11,plain,
    m0(a,X0,a),
    inference(cnf_transformation,[status(esa)],[f11_sk]) ).

cnf(hi11,axiom,
    m0(a,X0,a) = true,
    inference(equality_encoding,[status(esa)],[c11]) ).

cnf(h269,plain,
    m3(a,V0,a) = true,
    inference(hyper_resolution,[status(thm)],[hi257,hi18,h114,hi11,h160]) ).

cnf(f122,axiom,
    ( ~ p0(C,B)
    | p1(B,B,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_085) ).

fof(f122_nnf,plain,
    ! [B,C] :
      ( ~ p0(C,B)
      | p1(B,B,B) ),
    inference(nnf_transformation,[status(thm)],[f122]) ).

fof(f122_sk,plain,
    ! [B,C] :
      ( ~ p0(C,B)
      | p1(B,B,B) ),
    inference(skolemisation,[status(esa)],[f122_nnf]) ).

cnf(c122,plain,
    ( ~ p0(X1,X0)
    | p1(X0,X0,X0) ),
    inference(cnf_transformation,[status(esa)],[f122_sk]) ).

cnf(hi120,axiom,
    ifeq(p0(X0,X1),true,p1(X1,X1,X1),true) = true,
    inference(equality_encoding,[status(esa)],[c122]) ).

cnf(h30,plain,
    p1(V0,V0,V0) = true,
    inference(hyper_resolution,[status(thm)],[hi120,hi13]) ).

cnf(f129,axiom,
    ( ~ p0(C,J)
    | ~ n0(B,A)
    | q1(J,A,J) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_092) ).

fof(f129_nnf,plain,
    ! [J,A,B,C] :
      ( ~ p0(C,J)
      | ~ n0(B,A)
      | q1(J,A,J) ),
    inference(nnf_transformation,[status(thm)],[f129]) ).

fof(f129_sk,plain,
    ! [J,A,B,C] :
      ( ~ p0(C,J)
      | ~ n0(B,A)
      | q1(J,A,J) ),
    inference(skolemisation,[status(esa)],[f129_nnf]) ).

cnf(c129,plain,
    ( ~ p0(X3,X0)
    | ~ n0(X2,X1)
    | q1(X0,X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f129_sk]) ).

cnf(hi127,axiom,
    ifeq(n0(X0,X1),true,ifeq(p0(X2,X3),true,q1(X3,X1,X3),true),true) = true,
    inference(equality_encoding,[status(esa)],[c129]) ).

cnf(f2,axiom,
    n0(d,e),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).

fof(f2_nnf,plain,
    n0(d,e),
    inference(nnf_transformation,[status(thm)],[f2]) ).

cnf(c2,plain,
    n0(d,e),
    inference(cnf_transformation,[status(esa)],[f2_nnf]) ).

cnf(hi2,axiom,
    n0(d,e) = true,
    inference(equality_encoding,[status(esa)],[c2]) ).

cnf(h29,plain,
    q1(V0,e,V0) = true,
    inference(hyper_resolution,[status(thm)],[hi127,hi2,hi13]) ).

cnf(f206,axiom,
    ( ~ p1(D,F,D)
    | ~ q1(E,E,E)
    | p2(D,D,D) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_169) ).

fof(f206_nnf,plain,
    ! [D,E,F] :
      ( ~ p1(D,F,D)
      | ~ q1(E,E,E)
      | p2(D,D,D) ),
    inference(nnf_transformation,[status(thm)],[f206]) ).

fof(f206_sk,plain,
    ! [D,E,F] :
      ( ~ p1(D,F,D)
      | ~ q1(E,E,E)
      | p2(D,D,D) ),
    inference(skolemisation,[status(esa)],[f206_nnf]) ).

cnf(c206,plain,
    ( ~ p1(X0,X2,X0)
    | ~ q1(X1,X1,X1)
    | p2(X0,X0,X0) ),
    inference(cnf_transformation,[status(esa)],[f206_sk]) ).

cnf(hi203,axiom,
    ifeq(q1(X0,X0,X0),true,ifeq(p1(X1,X2,X1),true,p2(X1,X1,X1),true),true) = true,
    inference(equality_encoding,[status(esa)],[c206]) ).

cnf(h173,plain,
    p2(V0,V0,V0) = true,
    inference(hyper_resolution,[status(thm)],[hi203,h29,h30]) ).

cnf(f277,axiom,
    ( ~ p2(E,F,D)
    | n3(D) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_240) ).

fof(f277_nnf,plain,
    ! [D,E,F] :
      ( ~ p2(E,F,D)
      | n3(D) ),
    inference(nnf_transformation,[status(thm)],[f277]) ).

fof(f277_sk,plain,
    ! [D,E,F] :
      ( ~ p2(E,F,D)
      | n3(D) ),
    inference(skolemisation,[status(esa)],[f277_nnf]) ).

cnf(c277,plain,
    ( ~ p2(X1,X2,X0)
    | n3(X0) ),
    inference(cnf_transformation,[status(esa)],[f277_sk]) ).

cnf(hi272,axiom,
    ifeq(p2(X0,X1,X2),true,n3(X2),true) = true,
    inference(equality_encoding,[status(esa)],[c277]) ).

cnf(h339,plain,
    n3(V0) = true,
    inference(hyper_resolution,[status(thm)],[hi272,h173]) ).

cnf(f331,axiom,
    ( ~ m3(B,c,a)
    | ~ n3(a)
    | p4(c,c,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_294) ).

fof(f331_nnf,plain,
    ! [B] :
      ( ~ m3(B,c,a)
      | ~ n3(a)
      | p4(c,c,B) ),
    inference(nnf_transformation,[status(thm)],[f331]) ).

fof(f331_sk,plain,
    ! [B] :
      ( ~ m3(B,c,a)
      | ~ n3(a)
      | p4(c,c,B) ),
    inference(skolemisation,[status(esa)],[f331_nnf]) ).

cnf(c331,plain,
    ( ~ m3(X0,c,a)
    | ~ n3(a)
    | p4(c,c,X0) ),
    inference(cnf_transformation,[status(esa)],[f331_sk]) ).

cnf(hi324,axiom,
    ifeq(n3(a),true,ifeq(m3(X0,c,a),true,p4(c,c,X0),true),true) = true,
    inference(equality_encoding,[status(esa)],[c331]) ).

cnf(h536,plain,
    p4(c,c,a) = true,
    inference(hyper_resolution,[status(thm)],[hi324,h339,h269]) ).

cnf(f38,axiom,
    ( ~ n0(J,I)
    | k1(I) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_001) ).

fof(f38_nnf,plain,
    ! [I,J] :
      ( ~ n0(J,I)
      | k1(I) ),
    inference(nnf_transformation,[status(thm)],[f38]) ).

fof(f38_sk,plain,
    ! [I,J] :
      ( ~ n0(J,I)
      | k1(I) ),
    inference(skolemisation,[status(esa)],[f38_nnf]) ).

cnf(c38,plain,
    ( ~ n0(X1,X0)
    | k1(X0) ),
    inference(cnf_transformation,[status(esa)],[f38_sk]) ).

cnf(hi38,axiom,
    ifeq(n0(X0,X1),true,k1(X1),true) = true,
    inference(equality_encoding,[status(esa)],[c38]) ).

cnf(f6,axiom,
    n0(d,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).

fof(f6_nnf,plain,
    n0(d,b),
    inference(nnf_transformation,[status(thm)],[f6]) ).

cnf(c6,plain,
    n0(d,b),
    inference(cnf_transformation,[status(esa)],[f6_nnf]) ).

cnf(hi6,axiom,
    n0(d,b) = true,
    inference(equality_encoding,[status(esa)],[c6]) ).

cnf(h14,plain,
    k1(b) = true,
    inference(hyper_resolution,[status(thm)],[hi38,hi6]) ).

cnf(f196,axiom,
    ( ~ k1(A)
    | p2(A,A,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_159) ).

fof(f196_nnf,plain,
    ! [A] :
      ( ~ k1(A)
      | p2(A,A,A) ),
    inference(nnf_transformation,[status(thm)],[f196]) ).

fof(f196_sk,plain,
    ! [A] :
      ( ~ k1(A)
      | p2(A,A,A) ),
    inference(skolemisation,[status(esa)],[f196_nnf]) ).

cnf(c196,plain,
    ( ~ k1(X0)
    | p2(X0,X0,X0) ),
    inference(cnf_transformation,[status(esa)],[f196_sk]) ).

cnf(hi193,axiom,
    ifeq(k1(X0),true,p2(X0,X0,X0),true) = true,
    inference(equality_encoding,[status(esa)],[c196]) ).

cnf(h100,plain,
    p2(b,b,b) = true,
    inference(hyper_resolution,[status(thm)],[hi193,h14]) ).

cnf(f304,axiom,
    ( ~ p2(B,D,C)
    | r3(B,C,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_267) ).

fof(f304_nnf,plain,
    ! [B,C,D] :
      ( ~ p2(B,D,C)
      | r3(B,C,B) ),
    inference(nnf_transformation,[status(thm)],[f304]) ).

fof(f304_sk,plain,
    ! [B,C,D] :
      ( ~ p2(B,D,C)
      | r3(B,C,B) ),
    inference(skolemisation,[status(esa)],[f304_nnf]) ).

cnf(c304,plain,
    ( ~ p2(X0,X2,X1)
    | r3(X0,X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f304_sk]) ).

cnf(hi299,axiom,
    ifeq(p2(X0,X1,X2),true,r3(X0,X2,X0),true) = true,
    inference(equality_encoding,[status(esa)],[c304]) ).

cnf(h264,plain,
    r3(b,b,b) = true,
    inference(hyper_resolution,[status(thm)],[hi299,h100]) ).

cnf(f173,axiom,
    ( ~ k1(b)
    | m2(b) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_136) ).

fof(f173_nnf,plain,
    ( ~ k1(b)
    | m2(b) ),
    inference(nnf_transformation,[status(thm)],[f173]) ).

fof(f173_sk,plain,
    ( ~ k1(b)
    | m2(b) ),
    inference(skolemisation,[status(esa)],[f173_nnf]) ).

cnf(c173,plain,
    ( ~ k1(b)
    | m2(b) ),
    inference(cnf_transformation,[status(esa)],[f173_sk]) ).

cnf(hi170,axiom,
    ifeq(k1(b),true,m2(b),true) = true,
    inference(equality_encoding,[status(esa)],[c173]) ).

cnf(h101,plain,
    m2(b) = true,
    inference(hyper_resolution,[status(thm)],[hi170,h14]) ).

cnf(f305,axiom,
    ( ~ r3(I,A,A)
    | ~ m3(J,b,H)
    | ~ m2(I)
    | r3(H,H,I) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_268) ).

fof(f305_nnf,plain,
    ! [H,I,J,A] :
      ( ~ r3(I,A,A)
      | ~ m3(J,b,H)
      | ~ m2(I)
      | r3(H,H,I) ),
    inference(nnf_transformation,[status(thm)],[f305]) ).

fof(f305_sk,plain,
    ! [H,I,J,A] :
      ( ~ r3(I,A,A)
      | ~ m3(J,b,H)
      | ~ m2(I)
      | r3(H,H,I) ),
    inference(skolemisation,[status(esa)],[f305_nnf]) ).

cnf(c305,plain,
    ( ~ r3(X1,X3,X3)
    | ~ m3(X2,b,X0)
    | ~ m2(X1)
    | r3(X0,X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f305_sk]) ).

cnf(hi300,axiom,
    ifeq(m2(X0),true,ifeq(m3(X1,b,X2),true,ifeq(r3(X0,X3,X3),true,r3(X2,X2,X0),true),true),true) = true,
    inference(equality_encoding,[status(esa)],[c305]) ).

cnf(h538,plain,
    r3(a,a,b) = true,
    inference(hyper_resolution,[status(thm)],[hi300,h101,h269,h264]) ).

cnf(f325,axiom,
    ( ~ p4(J,J,A)
    | ~ r3(I,I,H)
    | p4(H,I,I) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_288) ).

fof(f325_nnf,plain,
    ! [H,I,J,A] :
      ( ~ p4(J,J,A)
      | ~ r3(I,I,H)
      | p4(H,I,I) ),
    inference(nnf_transformation,[status(thm)],[f325]) ).

fof(f325_sk,plain,
    ! [H,I,J,A] :
      ( ~ p4(J,J,A)
      | ~ r3(I,I,H)
      | p4(H,I,I) ),
    inference(skolemisation,[status(esa)],[f325_nnf]) ).

cnf(c325,plain,
    ( ~ p4(X2,X2,X3)
    | ~ r3(X1,X1,X0)
    | p4(X0,X1,X1) ),
    inference(cnf_transformation,[status(esa)],[f325_sk]) ).

cnf(hi318,axiom,
    ifeq(r3(X0,X0,X1),true,ifeq(p4(X2,X2,X3),true,p4(X1,X0,X0),true),true) = true,
    inference(equality_encoding,[status(esa)],[c325]) ).

cnf(t69,plain,
    p4(b,a,a) = true,
    inference(hyper_resolution,[status(thm)],[hi318,h538,h536]) ).

cnf(t89,plain,
    p4(b,a,a) = true,
    inference(orient,[status(thm)],[t69]) ).

cnf(f368,negated_conjecture,
    ~ p4(b,a,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

fof(f368_nnf,plain,
    ~ p4(b,a,a),
    inference(nnf_transformation,[status(thm)],[f368]) ).

fof(f368_sk,plain,
    ~ p4(b,a,a),
    inference(skolemisation,[status(esa)],[f368_nnf]) ).

cnf(c368,plain,
    ~ p4(b,a,a),
    inference(cnf_transformation,[status(esa)],[f368_sk]) ).

cnf(goal_0,negated_conjecture,
    p4(b,a,a) != true,
    inference(equality_encoding,[status(esa)],[c368]) ).

cnf(g0_0,plain,
    true != true,
    inference(rw,[status(thm)],[goal_0,t89]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SYN269-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04  % Command  : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37  % Computer : n009.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Fri Sep 25 00:41:14 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 0.10/0.37  Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.59/1.32  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.59/1.32  % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------