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FindProof---0.1.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : FindProof---0.1
% Problem  : GEO631+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300

% Computer : n013.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 01:18:20 PM UTC 2026

% Result   : Theorem 32.94s 9.84s
% Output   : Proof 32.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  107 (  59 unt;   0 def)
%            Number of atoms       :  219 (  54 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  163 (  51   ~;  45   |;  54   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-8 aty)
%            Number of functors    :   15 (  15 usr;  14 con; 0-4 aty)
%            Number of variables   :  271 (   0 sgn 164   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B,C] :
      ( coll(A,B,C)
     => coll(B,A,C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD2) ).

fof(f1_nnf,plain,
    ! [A,B,C] :
      ( coll(B,A,C)
      | ~ coll(A,B,C) ),
    inference(nnf_transformation,[status(thm)],[f1]) ).

fof(f1_sk,plain,
    ! [A,B,C] :
      ( coll(B,A,C)
      | ~ coll(A,B,C) ),
    inference(skolemisation,[status(esa)],[f1_nnf]) ).

cnf(c1,plain,
    ( coll(X1,X0,X2)
    | ~ coll(X0,X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f1_sk]) ).

cnf(hi1,axiom,
    ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
    inference(equality_encoding,[status(esa)],[c1]) ).

fof(f94,conjecture,
    ! [A,B,C,O,D,P,F,G,H,E,I,NWPNT1,NWPNT2] :
      ( ( coll(I,H,E)
        & coll(I,F,G)
        & coll(E,C,D)
        & perp(E,P,C,D)
        & coll(H,B,C)
        & perp(H,P,B,C)
        & coll(G,A,B)
        & perp(G,P,A,B)
        & coll(F,A,D)
        & perp(F,P,A,D)
        & circle(O,A,P,NWPNT2)
        & circle(O,A,D,NWPNT1)
        & circle(O,A,B,C) )
     => cyclic(P,G,I,H) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL8110994) ).

fof(f94_neg,negated_conjecture,
    ~ ! [A,B,C,O,D,P,F,G,H,E,I,NWPNT1,NWPNT2] :
        ( ( coll(I,H,E)
          & coll(I,F,G)
          & coll(E,C,D)
          & perp(E,P,C,D)
          & coll(H,B,C)
          & perp(H,P,B,C)
          & coll(G,A,B)
          & perp(G,P,A,B)
          & coll(F,A,D)
          & perp(F,P,A,D)
          & circle(O,A,P,NWPNT2)
          & circle(O,A,D,NWPNT1)
          & circle(O,A,B,C) )
       => cyclic(P,G,I,H) ),
    inference(negated_conjecture,[status(cth)],[f94]) ).

fof(f94_nnf,plain,
    ? [A,B,C,O,D,P,F,G,H,E,I,NWPNT1,NWPNT2] :
      ( ~ cyclic(P,G,I,H)
      & coll(I,H,E)
      & coll(I,F,G)
      & coll(E,C,D)
      & perp(E,P,C,D)
      & coll(H,B,C)
      & perp(H,P,B,C)
      & coll(G,A,B)
      & perp(G,P,A,B)
      & coll(F,A,D)
      & perp(F,P,A,D)
      & circle(O,A,P,NWPNT2)
      & circle(O,A,D,NWPNT1)
      & circle(O,A,B,C) ),
    inference(nnf_transformation,[status(thm)],[f94_neg]) ).

fof(f94_sk,plain,
    ( ~ cyclic(sk25,sk27,sk30,sk28)
    & coll(sk30,sk28,sk29)
    & coll(sk30,sk26,sk27)
    & coll(sk29,sk22,sk24)
    & perp(sk29,sk25,sk22,sk24)
    & coll(sk28,sk21,sk22)
    & perp(sk28,sk25,sk21,sk22)
    & coll(sk27,sk20,sk21)
    & perp(sk27,sk25,sk20,sk21)
    & coll(sk26,sk20,sk24)
    & perp(sk26,sk25,sk20,sk24)
    & circle(sk23,sk20,sk25,sk32)
    & circle(sk23,sk20,sk24,sk31)
    & circle(sk23,sk20,sk21,sk22) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30,sk31,sk32])],[f94_nnf]) ).

cnf(c124,plain,
    coll(sk30,sk26,sk27),
    inference(cnf_transformation,[status(esa)],[f94_sk]) ).

cnf(hi124,negated_conjecture,
    coll(sk30,sk26,sk27) = true,
    inference(equality_encoding,[status(esa)],[c124]) ).

cnf(h13,plain,
    coll(sk26,sk30,sk27) = true,
    inference(hyper_resolution,[status(thm)],[hi1,hi124]) ).

fof(f0,axiom,
    ! [A,B,C] :
      ( coll(A,B,C)
     => coll(A,C,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD1) ).

fof(f0_nnf,plain,
    ! [A,B,C] :
      ( coll(A,C,B)
      | ~ coll(A,B,C) ),
    inference(nnf_transformation,[status(thm)],[f0]) ).

fof(f0_sk,plain,
    ! [A,B,C] :
      ( coll(A,C,B)
      | ~ coll(A,B,C) ),
    inference(skolemisation,[status(esa)],[f0_nnf]) ).

cnf(c0,plain,
    ( coll(X0,X2,X1)
    | ~ coll(X0,X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f0_sk]) ).

cnf(hi0,axiom,
    ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
    inference(equality_encoding,[status(esa)],[c0]) ).

cnf(h47,plain,
    coll(sk26,sk27,sk30) = true,
    inference(hyper_resolution,[status(thm)],[hi0,h13]) ).

fof(f2,axiom,
    ! [A,B,C,D] :
      ( ( coll(A,B,D)
        & coll(A,B,C) )
     => coll(C,D,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD3) ).

fof(f2_nnf,plain,
    ! [A,B,C,D] :
      ( coll(C,D,A)
      | ~ coll(A,B,D)
      | ~ coll(A,B,C) ),
    inference(nnf_transformation,[status(thm)],[f2]) ).

fof(f2_sk,plain,
    ! [A,B,C,D] :
      ( coll(C,D,A)
      | ~ coll(A,B,D)
      | ~ coll(A,B,C) ),
    inference(skolemisation,[status(esa)],[f2_nnf]) ).

cnf(c2,plain,
    ( coll(X2,X3,X0)
    | ~ coll(X0,X1,X3)
    | ~ coll(X0,X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(hi2,axiom,
    ifeq(coll(X0,X1,X2),true,ifeq(coll(X0,X1,X3),true,coll(X2,X3,X0),true),true) = true,
    inference(equality_encoding,[status(esa)],[c2]) ).

cnf(h120,plain,
    coll(sk30,sk30,sk26) = true,
    inference(hyper_resolution,[status(thm)],[hi2,h47,h47]) ).

cnf(c125,plain,
    coll(sk30,sk28,sk29),
    inference(cnf_transformation,[status(esa)],[f94_sk]) ).

cnf(hi125,negated_conjecture,
    coll(sk30,sk28,sk29) = true,
    inference(equality_encoding,[status(esa)],[c125]) ).

cnf(h16,plain,
    coll(sk28,sk30,sk29) = true,
    inference(hyper_resolution,[status(thm)],[hi1,hi125]) ).

cnf(h53,plain,
    coll(sk28,sk29,sk30) = true,
    inference(hyper_resolution,[status(thm)],[hi0,h16]) ).

cnf(h135,plain,
    coll(sk30,sk30,sk28) = true,
    inference(hyper_resolution,[status(thm)],[hi2,h53,h53]) ).

cnf(h253,plain,
    coll(sk28,sk26,sk30) = true,
    inference(hyper_resolution,[status(thm)],[hi2,h135,h120]) ).

cnf(h449,plain,
    coll(sk28,sk30,sk26) = true,
    inference(hyper_resolution,[status(thm)],[hi0,h253]) ).

cnf(h684,plain,
    coll(sk26,sk26,sk28) = true,
    inference(hyper_resolution,[status(thm)],[hi2,h449,h449]) ).

fof(f7,axiom,
    ! [A,B,C,D] :
      ( perp(A,B,C,D)
     => perp(C,D,A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD8) ).

fof(f7_nnf,plain,
    ! [A,B,C,D] :
      ( perp(C,D,A,B)
      | ~ perp(A,B,C,D) ),
    inference(nnf_transformation,[status(thm)],[f7]) ).

fof(f7_sk,plain,
    ! [A,B,C,D] :
      ( perp(C,D,A,B)
      | ~ perp(A,B,C,D) ),
    inference(skolemisation,[status(esa)],[f7_nnf]) ).

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

cnf(hi7,axiom,
    ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
    inference(equality_encoding,[status(esa)],[c7]) ).

cnf(c116,plain,
    perp(sk26,sk25,sk20,sk24),
    inference(cnf_transformation,[status(esa)],[f94_sk]) ).

cnf(hi116,negated_conjecture,
    perp(sk26,sk25,sk20,sk24) = true,
    inference(equality_encoding,[status(esa)],[c116]) ).

cnf(h723,plain,
    perp(sk20,sk24,sk26,sk25) = true,
    inference(hyper_resolution,[status(thm)],[hi7,hi116]) ).

fof(f8,axiom,
    ! [A,B,C,D,E,F] :
      ( ( perp(C,D,E,F)
        & perp(A,B,C,D) )
     => para(A,B,E,F) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD9) ).

fof(f8_nnf,plain,
    ! [A,B,C,D,E,F] :
      ( para(A,B,E,F)
      | ~ perp(C,D,E,F)
      | ~ perp(A,B,C,D) ),
    inference(nnf_transformation,[status(thm)],[f8]) ).

fof(f8_sk,plain,
    ! [A,B,C,D,E,F] :
      ( para(A,B,E,F)
      | ~ perp(C,D,E,F)
      | ~ perp(A,B,C,D) ),
    inference(skolemisation,[status(esa)],[f8_nnf]) ).

cnf(c8,plain,
    ( para(X0,X1,X4,X5)
    | ~ perp(X2,X3,X4,X5)
    | ~ perp(X0,X1,X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f8_sk]) ).

cnf(hi8,axiom,
    ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X3,X4,X5),true,para(X0,X1,X4,X5),true),true) = true,
    inference(equality_encoding,[status(esa)],[c8]) ).

cnf(h731,plain,
    para(sk26,sk25,sk26,sk25) = true,
    inference(hyper_resolution,[status(thm)],[hi8,hi116,h723]) ).

fof(f39,axiom,
    ! [A,B,C,D,P,Q] :
      ( para(A,B,C,D)
     => eqangle(A,B,P,Q,C,D,P,Q) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD40) ).

fof(f39_nnf,plain,
    ! [A,B,C,D,P,Q] :
      ( eqangle(A,B,P,Q,C,D,P,Q)
      | ~ para(A,B,C,D) ),
    inference(nnf_transformation,[status(thm)],[f39]) ).

fof(f39_sk,plain,
    ! [A,B,C,D,P,Q] :
      ( eqangle(A,B,P,Q,C,D,P,Q)
      | ~ para(A,B,C,D) ),
    inference(skolemisation,[status(esa)],[f39_nnf]) ).

cnf(c39,plain,
    ( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
    | ~ para(X0,X1,X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f39_sk]) ).

cnf(hi39,axiom,
    ifeq(para(X0,X1,X2,X3),true,eqangle(X0,X1,X4,X5,X2,X3,X4,X5),true) = true,
    inference(equality_encoding,[status(esa)],[c39]) ).

cnf(h1267,plain,
    eqangle(sk26,sk25,V0,V1,sk26,sk25,V0,V1) = true,
    inference(hyper_resolution,[status(thm)],[hi39,h731]) ).

fof(f42,axiom,
    ! [A,B,P,Q] :
      ( ( coll(P,Q,B)
        & eqangle(P,A,P,B,Q,A,Q,B) )
     => cyclic(A,B,P,Q) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD42b) ).

fof(f42_nnf,plain,
    ! [A,B,P,Q] :
      ( cyclic(A,B,P,Q)
      | ~ coll(P,Q,B)
      | ~ eqangle(P,A,P,B,Q,A,Q,B) ),
    inference(nnf_transformation,[status(thm)],[f42]) ).

fof(f42_sk,plain,
    ! [P,A,B,Q] :
      ( cyclic(A,B,P,Q)
      | ~ coll(P,Q,B)
      | ~ eqangle(P,A,P,B,Q,A,Q,B) ),
    inference(skolemisation,[status(esa)],[f42_nnf]) ).

cnf(c42,plain,
    ( cyclic(X0,X1,X2,X3)
    | ~ coll(X2,X3,X1)
    | ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
    inference(cnf_transformation,[status(esa)],[f42_sk]) ).

cnf(hi42,axiom,
    ifeq(eqangle(X0,X1,X0,X2,X3,X1,X3,X2),true,ifeq(coll(X0,X3,X2),true,cyclic(X1,X2,X0,X3),true),true) = true,
    inference(equality_encoding,[status(esa)],[c42]) ).

cnf(h7847,plain,
    cyclic(sk25,sk28,sk26,sk26) = true,
    inference(hyper_resolution,[status(thm)],[hi42,h1267,h684]) ).

fof(f14,axiom,
    ! [A,B,C,D] :
      ( cyclic(A,B,C,D)
     => cyclic(A,C,B,D) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD15) ).

fof(f14_nnf,plain,
    ! [A,B,C,D] :
      ( cyclic(A,C,B,D)
      | ~ cyclic(A,B,C,D) ),
    inference(nnf_transformation,[status(thm)],[f14]) ).

fof(f14_sk,plain,
    ! [A,B,C,D] :
      ( cyclic(A,C,B,D)
      | ~ cyclic(A,B,C,D) ),
    inference(skolemisation,[status(esa)],[f14_nnf]) ).

cnf(c14,plain,
    ( cyclic(X0,X2,X1,X3)
    | ~ cyclic(X0,X1,X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f14_sk]) ).

cnf(hi14,axiom,
    ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X2,X1,X3),true) = true,
    inference(equality_encoding,[status(esa)],[c14]) ).

cnf(h7862,plain,
    cyclic(sk25,sk26,sk28,sk26) = true,
    inference(hyper_resolution,[status(thm)],[hi14,h7847]) ).

fof(f13,axiom,
    ! [A,B,C,D] :
      ( cyclic(A,B,C,D)
     => cyclic(A,B,D,C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD14) ).

fof(f13_nnf,plain,
    ! [A,B,C,D] :
      ( cyclic(A,B,D,C)
      | ~ cyclic(A,B,C,D) ),
    inference(nnf_transformation,[status(thm)],[f13]) ).

fof(f13_sk,plain,
    ! [A,B,C,D] :
      ( cyclic(A,B,D,C)
      | ~ cyclic(A,B,C,D) ),
    inference(skolemisation,[status(esa)],[f13_nnf]) ).

cnf(c13,plain,
    ( cyclic(X0,X1,X3,X2)
    | ~ cyclic(X0,X1,X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f13_sk]) ).

cnf(hi13,axiom,
    ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X1,X3,X2),true) = true,
    inference(equality_encoding,[status(esa)],[c13]) ).

cnf(h7894,plain,
    cyclic(sk25,sk26,sk26,sk28) = true,
    inference(hyper_resolution,[status(thm)],[hi13,h7862]) ).

fof(f66,axiom,
    ! [A,B,C] :
      ( para(A,B,A,C)
     => coll(A,B,C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD66) ).

fof(f66_nnf,plain,
    ! [A,B,C] :
      ( coll(A,B,C)
      | ~ para(A,B,A,C) ),
    inference(nnf_transformation,[status(thm)],[f66]) ).

fof(f66_sk,plain,
    ! [A,B,C] :
      ( coll(A,B,C)
      | ~ para(A,B,A,C) ),
    inference(skolemisation,[status(esa)],[f66_nnf]) ).

cnf(c66,plain,
    ( coll(X0,X1,X2)
    | ~ para(X0,X1,X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f66_sk]) ).

cnf(hi66,axiom,
    ifeq(para(X0,X1,X0,X2),true,coll(X0,X1,X2),true) = true,
    inference(equality_encoding,[status(esa)],[c66]) ).

cnf(h751,plain,
    coll(sk26,sk25,sk25) = true,
    inference(hyper_resolution,[status(thm)],[hi66,h731]) ).

cnf(h753,plain,
    coll(sk25,sk25,sk26) = true,
    inference(hyper_resolution,[status(thm)],[hi2,h751,h751]) ).

cnf(h755,plain,
    coll(sk26,sk26,sk25) = true,
    inference(hyper_resolution,[status(thm)],[hi2,h753,h753]) ).

cnf(h7846,plain,
    cyclic(sk25,sk25,sk26,sk26) = true,
    inference(hyper_resolution,[status(thm)],[hi42,h1267,h755]) ).

cnf(h7859,plain,
    cyclic(sk25,sk26,sk25,sk26) = true,
    inference(hyper_resolution,[status(thm)],[hi14,h7846]) ).

cnf(h7888,plain,
    cyclic(sk25,sk26,sk26,sk25) = true,
    inference(hyper_resolution,[status(thm)],[hi13,h7859]) ).

fof(f16,axiom,
    ! [A,B,C,D,E] :
      ( ( cyclic(A,B,C,E)
        & cyclic(A,B,C,D) )
     => cyclic(B,C,D,E) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD17) ).

fof(f16_nnf,plain,
    ! [A,B,C,D,E] :
      ( cyclic(B,C,D,E)
      | ~ cyclic(A,B,C,E)
      | ~ cyclic(A,B,C,D) ),
    inference(nnf_transformation,[status(thm)],[f16]) ).

fof(f16_sk,plain,
    ! [A,B,C,D,E] :
      ( cyclic(B,C,D,E)
      | ~ cyclic(A,B,C,E)
      | ~ cyclic(A,B,C,D) ),
    inference(skolemisation,[status(esa)],[f16_nnf]) ).

cnf(c16,plain,
    ( cyclic(X1,X2,X3,X4)
    | ~ cyclic(X0,X1,X2,X4)
    | ~ cyclic(X0,X1,X2,X3) ),
    inference(cnf_transformation,[status(esa)],[f16_sk]) ).

cnf(hi16,axiom,
    ifeq(cyclic(X0,X1,X2,X3),true,ifeq(cyclic(X0,X1,X2,X4),true,cyclic(X1,X2,X3,X4),true),true) = true,
    inference(equality_encoding,[status(esa)],[c16]) ).

cnf(h7956,plain,
    cyclic(sk26,sk26,sk25,sk28) = true,
    inference(hyper_resolution,[status(thm)],[hi16,h7888,h7894]) ).

cnf(h46,plain,
    coll(sk27,sk27,sk26) = true,
    inference(hyper_resolution,[status(thm)],[hi2,h13,h13]) ).

cnf(h116,plain,
    coll(sk26,sk26,sk27) = true,
    inference(hyper_resolution,[status(thm)],[hi2,h46,h46]) ).

cnf(h7852,plain,
    cyclic(sk25,sk27,sk26,sk26) = true,
    inference(hyper_resolution,[status(thm)],[hi42,h1267,h116]) ).

cnf(h7876,plain,
    cyclic(sk25,sk26,sk27,sk26) = true,
    inference(hyper_resolution,[status(thm)],[hi14,h7852]) ).

cnf(h7920,plain,
    cyclic(sk25,sk26,sk26,sk27) = true,
    inference(hyper_resolution,[status(thm)],[hi13,h7876]) ).

cnf(h8021,plain,
    cyclic(sk26,sk26,sk25,sk27) = true,
    inference(hyper_resolution,[status(thm)],[hi16,h7888,h7920]) ).

cnf(h9309,plain,
    cyclic(sk26,sk25,sk27,sk28) = true,
    inference(hyper_resolution,[status(thm)],[hi16,h8021,h7956]) ).

cnf(h14,plain,
    coll(sk30,sk27,sk26) = true,
    inference(hyper_resolution,[status(thm)],[hi0,hi124]) ).

cnf(h48,plain,
    coll(sk26,sk26,sk30) = true,
    inference(hyper_resolution,[status(thm)],[hi2,h14,h14]) ).

cnf(h7854,plain,
    cyclic(sk25,sk30,sk26,sk26) = true,
    inference(hyper_resolution,[status(thm)],[hi42,h1267,h48]) ).

cnf(h7882,plain,
    cyclic(sk25,sk26,sk30,sk26) = true,
    inference(hyper_resolution,[status(thm)],[hi14,h7854]) ).

cnf(h7932,plain,
    cyclic(sk25,sk26,sk26,sk30) = true,
    inference(hyper_resolution,[status(thm)],[hi13,h7882]) ).

cnf(h8065,plain,
    cyclic(sk26,sk26,sk25,sk30) = true,
    inference(hyper_resolution,[status(thm)],[hi16,h7888,h7932]) ).

cnf(h9676,plain,
    cyclic(sk26,sk25,sk27,sk30) = true,
    inference(hyper_resolution,[status(thm)],[hi16,h8021,h8065]) ).

cnf(t39,plain,
    cyclic(sk25,sk27,sk30,sk28) = true,
    inference(hyper_resolution,[status(thm)],[hi16,h9676,h9309]) ).

cnf(t3063,plain,
    cyclic(sk25,sk27,sk30,sk28) = true,
    inference(orient,[status(thm)],[t39]) ).

cnf(c126,plain,
    ~ cyclic(sk25,sk27,sk30,sk28),
    inference(cnf_transformation,[status(esa)],[f94_sk]) ).

cnf(goal_0,negated_conjecture,
    cyclic(sk25,sk27,sk30,sk28) != true,
    inference(equality_encoding,[status(esa)],[c126]) ).

cnf(g0_0,plain,
    true != true,
    inference(rw,[status(thm)],[goal_0,t3063]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : GEO631+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04  % Command  : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.57  % Computer : n013.cluster.edu
% 0.09/5.57  % Model    : x86_64 x86_64
% 0.09/5.57  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.57  % Memory   : 8046.5625MB
% 0.09/5.57  % OS       : Linux 6.8.0-71-generic
% 0.09/5.57  % CPULimit : 300
% 0.09/5.57  % WCLimit  : 300
% 0.09/5.57  % DateTime : Wed Sep 23 12:36:17 UTC 2026
% 0.09/5.58  % CPUTime  : 
% 0.09/5.58  Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 32.94/9.84  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.94/9.84  % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------