%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO595+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 : n004.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 01:18:14 PM UTC 2026
% Result : Theorem 192.42s 24.89s
% Output : Proof 192.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 79
% Number of leaves : 24
% Syntax : Number of formulae : 282 ( 190 unt; 0 def)
% Number of atoms : 450 ( 185 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 276 ( 108 ~; 102 |; 42 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-4 aty)
% Number of variables : 872 ( 113 sgn 325 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD13) ).
fof(f12_nnf,plain,
! [A,B,C,D,O] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [O,A,B,C,D] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( cyclic(X0,X1,X2,X3)
| ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t236,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(cong(X1,X2,X1,X4),true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t273,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(cong(X1,X2,X1,X4),true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t236]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD68) ).
fof(f68_nnf,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(t93,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t351,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t93]) ).
fof(f64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD64) ).
fof(f64_nnf,plain,
! [A,B,C,D,M] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [M,A,B,C,D] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c64,plain,
( midp(X4,X2,X3)
| ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(t228,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t341,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t228]) ).
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(t169,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t285,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t169]) ).
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(t104,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t292,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t104]) ).
fof(f56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD56) ).
fof(f56_nnf,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [A,P,B,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
( perp(X0,X1,X2,X3)
| ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(t156,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(t271,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(orient,[status(thm)],[t156]) ).
fof(f38,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD39) ).
fof(f38_nnf,plain,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A,B,P,Q,C,D] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( para(X0,X1,X2,X3)
| ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(t134,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t314,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t134]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
fof(f94,conjecture,
! [A,B,C,D,O,E,F,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ( circle(O,D,F,NWPNT4)
& coll(F,A,C)
& circle(O,D,E,NWPNT3)
& coll(E,A,B)
& circle(O,D,NWPNT1,NWPNT2)
& midp(O,A,D)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(B,C,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL416057) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,O,E,F,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ( circle(O,D,F,NWPNT4)
& coll(F,A,C)
& circle(O,D,E,NWPNT3)
& coll(E,A,B)
& circle(O,D,NWPNT1,NWPNT2)
& midp(O,A,D)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(B,C,E,F) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,O,E,F,NWPNT1,NWPNT2,NWPNT3,NWPNT4] :
( ~ cyclic(B,C,E,F)
& circle(O,D,F,NWPNT4)
& coll(F,A,C)
& circle(O,D,E,NWPNT3)
& coll(E,A,B)
& circle(O,D,NWPNT1,NWPNT2)
& midp(O,A,D)
& coll(D,B,C)
& perp(D,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cyclic(sk21,sk22,sk25,sk26)
& circle(sk24,sk23,sk26,sk30)
& coll(sk26,sk20,sk22)
& circle(sk24,sk23,sk25,sk29)
& coll(sk25,sk20,sk21)
& circle(sk24,sk23,sk27,sk28)
& midp(sk24,sk20,sk23)
& coll(sk23,sk21,sk22)
& perp(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30])],[f94_nnf]) ).
cnf(c113,plain,
perp(sk23,sk20,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
perp(sk23,sk20,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h0,plain,
perp(sk21,sk22,sk23,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi113]) ).
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(h24,plain,
para(sk21,sk22,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,h0,hi113]) ).
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(h132,plain,
eqangle(sk21,sk22,V0,V1,sk21,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h24]) ).
fof(f18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD19) ).
fof(f18_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X2,X3,X0,X1,X6,X7,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t35,plain,
eqangle(X1,X2,sk21,sk22,X1,X2,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi18,h132]) ).
cnf(t1858,plain,
eqangle(X1,X2,sk21,sk22,X1,X2,sk21,sk22) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t1862,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t314,t1858]) ).
cnf(t21,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t21]) ).
cnf(t29263,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t1862,t256]) ).
cnf(t4499,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t29263]) ).
cnf(t4518,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),true),
inference(cp,[status(thm)],[t341,t4499]) ).
cnf(t31069,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t4518,t256]) ).
cnf(t31070,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t31069,t4499]) ).
cnf(t31071,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t31070,t256]) ).
cnf(t20571,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t31071]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD67) ).
fof(f67_nnf,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,plain,
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(t147,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t272,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(orient,[status(thm)],[t147]) ).
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(t139,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t260,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(orient,[status(thm)],[t139]) ).
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(t77,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t263,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t77]) ).
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(t78,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t261,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t78]) ).
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(t94,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t337,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t94]) ).
cnf(t4500,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t337,t4499]) ).
cnf(t29264,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t4500,t256]) ).
cnf(t4528,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t29264]) ).
cnf(t4530,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t261,t4528]) ).
cnf(t29265,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t4530,t256]) ).
cnf(t4572,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t29265]) ).
cnf(t4575,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t263,t4572]) ).
cnf(t29266,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t4575,t256]) ).
cnf(t4604,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t29266]) ).
cnf(t4607,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t260,t4604]) ).
cnf(t29267,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t4607,t256]) ).
cnf(t29268,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t29267,t4604]) ).
cnf(t29269,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t29268,t256]) ).
cnf(t4639,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t29269]) ).
cnf(t29280,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(true,true,midp(X1,X2,X3),true),true) = true,
inference(step,[status(thm)],[t272,t4639]) ).
cnf(t29281,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t29280,t256]) ).
cnf(t4646,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[t29281]) ).
cnf(t23426,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t4646]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD23) ).
fof(f22_nnf,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t96,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t268,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t96]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD24) ).
fof(f23_nnf,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t97,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t266,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t97]) ).
fof(f43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD43) ).
fof(f43_nnf,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(t253,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t357,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(orient,[status(thm)],[t253]) ).
fof(f17,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(B,A,C,D,P,Q,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD18) ).
fof(f17_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( eqangle(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t160,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X2,X1,X3,X4,X5,X6,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t310,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X2,X1,X3,X4,X5,X6,X7,X8),true) = true,
inference(orient,[status(thm)],[t160]) ).
cnf(t1865,plain,
true = ifeq(true,true,eqangle(X1,X2,sk21,sk22,X2,X1,sk21,sk22),true),
inference(cp,[status(thm)],[t310,t1858]) ).
cnf(t29405,plain,
true = eqangle(X1,X2,sk21,sk22,X2,X1,sk21,sk22),
inference(step,[status(thm)],[t1865,t256]) ).
cnf(t5643,plain,
eqangle(X1,X2,sk21,sk22,X2,X1,sk21,sk22) = true,
inference(orient,[status(thm)],[t29405]) ).
cnf(t5656,plain,
true = ifeq(cyclic(sk21,sk22,sk21,sk21),true,ifeq(cyclic(sk21,sk22,sk21,sk22),true,ifeq(cyclic(sk21,sk22,sk21,sk21),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),true),
inference(cp,[status(thm)],[t357,t5643]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD16) ).
fof(f15_nnf,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t100,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t360,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t100]) ).
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(c117,plain,
coll(sk25,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
coll(sk25,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h15,plain,
coll(sk21,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi117,hi117]) ).
cnf(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h94,plain,
coll(sk21,sk25,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h15]) ).
cnf(h195,plain,
coll(sk21,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h94,h94]) ).
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(t16,plain,
cyclic(sk22,sk21,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi42,h132,h195]) ).
cnf(t3054,plain,
cyclic(sk22,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t3055,plain,
true = ifeq(true,true,cyclic(sk21,sk22,sk21,sk21),true),
inference(cp,[status(thm)],[t360,t3054]) ).
cnf(t29347,plain,
true = cyclic(sk21,sk22,sk21,sk21),
inference(step,[status(thm)],[t3055,t256]) ).
cnf(t4803,plain,
cyclic(sk21,sk22,sk21,sk21) = true,
inference(orient,[status(thm)],[t29347]) ).
cnf(t29406,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk22,sk21,sk22),true,ifeq(cyclic(sk21,sk22,sk21,sk21),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),true),
inference(step,[status(thm)],[t5656,t4803]) ).
cnf(t29407,plain,
true = ifeq(cyclic(sk21,sk22,sk21,sk22),true,ifeq(cyclic(sk21,sk22,sk21,sk21),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),
inference(step,[status(thm)],[t29406,t256]) ).
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(t98,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t364,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t98]) ).
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(t99,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t362,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t99]) ).
cnf(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c114,plain,
coll(sk23,sk21,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
coll(sk23,sk21,sk22) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h3,plain,
coll(sk21,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi114]) ).
cnf(h30,plain,
coll(sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h3,h3]) ).
cnf(h143,plain,
coll(sk21,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h30,h30]) ).
cnf(t17,plain,
cyclic(sk22,sk22,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi42,h132,h143]) ).
cnf(t3038,plain,
cyclic(sk22,sk22,sk21,sk21) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(t3039,plain,
true = ifeq(true,true,cyclic(sk22,sk21,sk22,sk21),true),
inference(cp,[status(thm)],[t362,t3038]) ).
cnf(t29346,plain,
true = cyclic(sk22,sk21,sk22,sk21),
inference(step,[status(thm)],[t3039,t256]) ).
cnf(t4787,plain,
cyclic(sk22,sk21,sk22,sk21) = true,
inference(orient,[status(thm)],[t29346]) ).
cnf(t4788,plain,
true = ifeq(true,true,cyclic(sk22,sk21,sk21,sk22),true),
inference(cp,[status(thm)],[t364,t4787]) ).
cnf(t29361,plain,
true = cyclic(sk22,sk21,sk21,sk22),
inference(step,[status(thm)],[t4788,t256]) ).
cnf(t5012,plain,
cyclic(sk22,sk21,sk21,sk22) = true,
inference(orient,[status(thm)],[t29361]) ).
cnf(t5013,plain,
true = ifeq(true,true,cyclic(sk21,sk22,sk21,sk22),true),
inference(cp,[status(thm)],[t360,t5012]) ).
cnf(t29378,plain,
true = cyclic(sk21,sk22,sk21,sk22),
inference(step,[status(thm)],[t5013,t256]) ).
cnf(t5263,plain,
cyclic(sk21,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t29378]) ).
cnf(t29408,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk22,sk21,sk21),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),true),
inference(step,[status(thm)],[t29407,t5263]) ).
cnf(t29409,plain,
true = ifeq(cyclic(sk21,sk22,sk21,sk21),true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),
inference(step,[status(thm)],[t29408,t256]) ).
cnf(t29410,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),true),
inference(step,[status(thm)],[t29409,t4803]) ).
cnf(t29411,plain,
true = ifeq(true,true,cong(sk21,sk22,sk21,sk22),true),
inference(step,[status(thm)],[t29410,t256]) ).
cnf(t29412,plain,
true = cong(sk21,sk22,sk21,sk22),
inference(step,[status(thm)],[t29411,t256]) ).
cnf(t5657,plain,
cong(sk21,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t29412]) ).
cnf(t5660,plain,
true = ifeq(true,true,cong(sk21,sk22,sk22,sk21),true),
inference(cp,[status(thm)],[t268,t5657]) ).
cnf(t29413,plain,
true = cong(sk21,sk22,sk22,sk21),
inference(step,[status(thm)],[t5660,t256]) ).
cnf(t5688,plain,
cong(sk21,sk22,sk22,sk21) = true,
inference(orient,[status(thm)],[t29413]) ).
cnf(t5690,plain,
true = ifeq(true,true,cong(sk22,sk21,sk21,sk22),true),
inference(cp,[status(thm)],[t266,t5688]) ).
cnf(t29414,plain,
true = cong(sk22,sk21,sk21,sk22),
inference(step,[status(thm)],[t5690,t256]) ).
cnf(t5698,plain,
cong(sk22,sk21,sk21,sk22) = true,
inference(orient,[status(thm)],[t29414]) ).
cnf(t5700,plain,
true = ifeq(true,true,cong(sk22,sk21,sk22,sk21),true),
inference(cp,[status(thm)],[t268,t5698]) ).
cnf(t29415,plain,
true = cong(sk22,sk21,sk22,sk21),
inference(step,[status(thm)],[t5700,t256]) ).
cnf(t5707,plain,
cong(sk22,sk21,sk22,sk21) = true,
inference(orient,[status(thm)],[t29415]) ).
cnf(t23432,plain,
true = ifeq(true,true,midp(sk22,sk21,sk21),true),
inference(cp,[status(thm)],[t23426,t5707]) ).
cnf(t31382,plain,
true = midp(sk22,sk21,sk21),
inference(step,[status(thm)],[t23432,t256]) ).
cnf(t23609,plain,
midp(sk22,sk21,sk21) = true,
inference(orient,[status(thm)],[t31382]) ).
cnf(t23611,plain,
true = ifeq(true,true,midp(sk22,X1,X1),true),
inference(cp,[status(thm)],[t20571,t23609]) ).
cnf(t31413,plain,
true = midp(sk22,X1,X1),
inference(step,[status(thm)],[t23611,t256]) ).
cnf(t24224,plain,
midp(sk22,X1,X1) = true,
inference(orient,[status(thm)],[t31413]) ).
cnf(t24229,plain,
true = ifeq(true,true,cong(sk22,X1,sk22,X1),true),
inference(cp,[status(thm)],[t351,t24224]) ).
cnf(t31457,plain,
true = cong(sk22,X1,sk22,X1),
inference(step,[status(thm)],[t24229,t256]) ).
cnf(t25252,plain,
cong(sk22,X1,sk22,X1) = true,
inference(orient,[status(thm)],[t31457]) ).
cnf(t25263,plain,
true = ifeq(true,true,ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t25252]) ).
cnf(t31505,plain,
true = ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t25263,t256]) ).
cnf(t31506,plain,
true = ifeq(true,true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t31505,t25252]) ).
cnf(t31507,plain,
true = perp(sk22,sk22,X2,X1),
inference(step,[status(thm)],[t31506,t256]) ).
cnf(t26192,plain,
perp(sk22,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t31507]) ).
cnf(t26193,plain,
true = ifeq(true,true,perp(X1,X2,sk22,sk22),true),
inference(cp,[status(thm)],[t292,t26192]) ).
cnf(t31563,plain,
true = perp(X1,X2,sk22,sk22),
inference(step,[status(thm)],[t26193,t256]) ).
cnf(t26986,plain,
perp(X1,X2,sk22,sk22) = true,
inference(orient,[status(thm)],[t31563]) ).
cnf(t26993,plain,
true = ifeq(true,true,ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t26986]) ).
cnf(t31606,plain,
true = ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t26993,t256]) ).
cnf(t31607,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t31606,t26192]) ).
cnf(t31608,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t31607,t256]) ).
cnf(t27509,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t31608]) ).
cnf(t31620,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(step,[status(thm)],[t341,t27509]) ).
cnf(t31621,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t31620,t256]) ).
cnf(t31622,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t31621,t27509]) ).
cnf(t31623,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t31622,t256]) ).
cnf(t27516,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t31623]) ).
cnf(t29016,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t27516]) ).
cnf(t25255,plain,
true = ifeq(true,true,cong(sk22,X1,X1,sk22),true),
inference(cp,[status(thm)],[t268,t25252]) ).
cnf(t31504,plain,
true = cong(sk22,X1,X1,sk22),
inference(step,[status(thm)],[t25255,t256]) ).
cnf(t26160,plain,
cong(sk22,X1,X1,sk22) = true,
inference(orient,[status(thm)],[t31504]) ).
cnf(t26162,plain,
true = ifeq(true,true,cong(X1,sk22,sk22,X1),true),
inference(cp,[status(thm)],[t266,t26160]) ).
cnf(t31562,plain,
true = cong(X1,sk22,sk22,X1),
inference(step,[status(thm)],[t26162,t256]) ).
cnf(t26958,plain,
cong(X1,sk22,sk22,X1) = true,
inference(orient,[status(thm)],[t31562]) ).
cnf(t26960,plain,
true = ifeq(true,true,cong(X1,sk22,X1,sk22),true),
inference(cp,[status(thm)],[t268,t26958]) ).
cnf(t31578,plain,
true = cong(X1,sk22,X1,sk22),
inference(step,[status(thm)],[t26960,t256]) ).
cnf(t27370,plain,
cong(X1,sk22,X1,sk22) = true,
inference(orient,[status(thm)],[t31578]) ).
cnf(t27371,plain,
true = ifeq(true,true,midp(X1,sk22,sk22),true),
inference(cp,[status(thm)],[t23426,t27370]) ).
cnf(t31579,plain,
true = midp(X1,sk22,sk22),
inference(step,[status(thm)],[t27371,t256]) ).
cnf(t27402,plain,
midp(X1,sk22,sk22) = true,
inference(orient,[status(thm)],[t31579]) ).
cnf(t27403,plain,
true = ifeq(true,true,midp(X1,X2,X2),true),
inference(cp,[status(thm)],[t20571,t27402]) ).
cnf(t31584,plain,
true = midp(X1,X2,X2),
inference(step,[status(thm)],[t27403,t256]) ).
cnf(t27423,plain,
midp(X1,X2,X2) = true,
inference(orient,[status(thm)],[t31584]) ).
cnf(t29017,plain,
true = ifeq(true,true,midp(X1,X2,X3),true),
inference(cp,[status(thm)],[t29016,t27423]) ).
cnf(t31743,plain,
true = midp(X1,X2,X3),
inference(step,[status(thm)],[t29017,t256]) ).
cnf(t29042,plain,
midp(X1,X2,X3) = true,
inference(orient,[status(thm)],[t31743]) ).
cnf(t31752,plain,
ifeq(true,true,cong(X1,X2,X1,X3),true) = true,
inference(step,[status(thm)],[t351,t29042]) ).
cnf(t31753,plain,
cong(X1,X2,X1,X3) = true,
inference(step,[status(thm)],[t31752,t256]) ).
cnf(t29047,plain,
cong(X1,X2,X1,X3) = true,
inference(rw,[status(thm)],[t31753]) ).
cnf(t29171,plain,
cong(X1,X2,X1,X3) = true,
inference(orient,[status(thm)],[t29047]) ).
cnf(t31782,plain,
ifeq(true,true,ifeq(cong(X1,X2,X1,X4),true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true),true) = true,
inference(step,[status(thm)],[t273,t29171]) ).
cnf(t31783,plain,
ifeq(cong(X1,X2,X1,X4),true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true) = true,
inference(step,[status(thm)],[t31782,t256]) ).
cnf(t31784,plain,
ifeq(true,true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true) = true,
inference(step,[status(thm)],[t31783,t29171]) ).
cnf(t31785,plain,
ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true) = true,
inference(step,[status(thm)],[t31784,t256]) ).
cnf(t31786,plain,
ifeq(true,true,cyclic(X2,X3,X4,X5),true) = true,
inference(step,[status(thm)],[t31785,t29171]) ).
cnf(t31787,plain,
cyclic(X2,X3,X4,X5) = true,
inference(step,[status(thm)],[t31786,t256]) ).
cnf(t29192,plain,
cyclic(X2,X3,X4,X5) = true,
inference(rw,[status(thm)],[t31787]) ).
cnf(t29225,plain,
cyclic(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t29192]) ).
cnf(c121,plain,
~ cyclic(sk21,sk22,sk25,sk26),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
cyclic(sk21,sk22,sk25,sk26) != true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t29225]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO595+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.04/0.36 % CPULimit : 300
% 0.04/0.36 % WCLimit : 300
% 0.04/0.36 % DateTime : Wed Sep 23 12:30:05 UTC 2026
% 0.04/0.36 % CPUTime :
% 0.04/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 192.42/24.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 192.42/24.89 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------