%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO653+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 01:18:24 PM UTC 2026
% Result : Theorem 187.87s 25.33s
% Output : Proof 187.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 25
% Syntax : Number of formulae : 270 ( 174 unt; 0 def)
% Number of atoms : 446 ( 166 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 287 ( 111 ~; 105 |; 46 &)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-4 aty)
% Number of variables : 809 ( 52 sgn 358 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/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(t193,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(t276,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)],[t193]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox2/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(t157,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t285,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t157]) ).
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/sandbox2/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(t180,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(t326,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)],[t180]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox2/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(t147,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t375,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t147]) ).
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/sandbox2/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(t364,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(f73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD73) ).
fof(f73_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(t212,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t296,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t212]) ).
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/sandbox2/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]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G,H] :
( ( coll(H,C,F)
& coll(H,B,E)
& coll(G,A,E)
& coll(G,D,F)
& coll(F,A,B)
& para(A,D,F,E)
& coll(E,C,D)
& para(A,C,B,D)
& para(A,B,C,D) )
=> para(G,H,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULLmoreE0227) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H] :
( ( coll(H,C,F)
& coll(H,B,E)
& coll(G,A,E)
& coll(G,D,F)
& coll(F,A,B)
& para(A,D,F,E)
& coll(E,C,D)
& para(A,C,B,D)
& para(A,B,C,D) )
=> para(G,H,A,B) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G,H] :
( ~ para(G,H,A,B)
& coll(H,C,F)
& coll(H,B,E)
& coll(G,A,E)
& coll(G,D,F)
& coll(F,A,B)
& para(A,D,F,E)
& coll(E,C,D)
& para(A,C,B,D)
& para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk26,sk27,sk20,sk21)
& coll(sk27,sk22,sk25)
& coll(sk27,sk21,sk24)
& coll(sk26,sk20,sk24)
& coll(sk26,sk23,sk25)
& coll(sk25,sk20,sk21)
& para(sk20,sk23,sk25,sk24)
& coll(sk24,sk22,sk23)
& para(sk20,sk22,sk21,sk23)
& para(sk20,sk21,sk22,sk23) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27])],[f94_nnf]) ).
cnf(c113,plain,
para(sk20,sk21,sk22,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
para(sk20,sk21,sk22,sk23) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h0,plain,
eqangle(sk20,sk21,V0,V1,sk22,sk23,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,hi113]) ).
fof(f20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD21) ).
fof(f20_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi20,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X0,X1,X4,X5,X2,X3,X6,X7),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h27,plain,
eqangle(sk20,sk21,sk22,sk23,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h0]) ).
fof(f19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD20) ).
fof(f19_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X4,X5,X6,X7,X0,X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t64,plain,
eqangle(X1,X2,X1,X2,sk20,sk21,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi19,h27]) ).
cnf(t1926,plain,
eqangle(X1,X2,X1,X2,sk20,sk21,sk22,sk23) = true,
inference(orient,[status(thm)],[t64]) ).
cnf(t1939,plain,
true = ifeq(true,true,ifeq(para(sk20,sk21,sk22,sk23),true,para(X1,X2,X1,X2),true),true),
inference(cp,[status(thm)],[t296,t1926]) ).
cnf(t39,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t39]) ).
cnf(t25706,plain,
true = ifeq(para(sk20,sk21,sk22,sk23),true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t1939,t256]) ).
cnf(t42,plain,
para(sk20,sk21,sk22,sk23) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(t1566,plain,
para(sk20,sk21,sk22,sk23) = true,
inference(orient,[status(thm)],[t42]) ).
cnf(t25707,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t25706,t1566]) ).
cnf(t25708,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t25707,t256]) ).
cnf(t4231,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t25708]) ).
cnf(t4251,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)],[t364,t4231]) ).
cnf(t27937,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)],[t4251,t256]) ).
cnf(t27938,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t27937,t4231]) ).
cnf(t27939,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t27938,t256]) ).
cnf(t23714,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t27939]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox2/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(t171,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(t327,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)],[t171]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox2/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(t170,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)],[t170]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/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(t123,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)],[t123]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/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(t124,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)],[t124]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/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(t148,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t275,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t148]) ).
cnf(t4233,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t275,t4231]) ).
cnf(t25709,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t4233,t256]) ).
cnf(t4260,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t25709]) ).
cnf(t4262,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t261,t4260]) ).
cnf(t25710,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t4262,t256]) ).
cnf(t4304,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t25710]) ).
cnf(t4307,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t263,t4304]) ).
cnf(t25711,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t4307,t256]) ).
cnf(t4336,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t25711]) ).
cnf(t4339,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t260,t4336]) ).
cnf(t25712,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t4339,t256]) ).
cnf(t25713,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t25712,t4336]) ).
cnf(t25714,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t25713,t256]) ).
cnf(t4371,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t25714]) ).
cnf(t25719,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(true,true,midp(X1,X2,X3),true),true) = true,
inference(step,[status(thm)],[t327,t4371]) ).
cnf(t25720,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(step,[status(thm)],[t25719,t256]) ).
cnf(t4375,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(rw,[status(thm)],[t25720]) ).
cnf(t24096,plain,
ifeq(cong(X1,X2,X1,X3),true,midp(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t4375]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox2/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(t149,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t323,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t149]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox2/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(t150,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t321,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t150]) ).
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/sandbox2/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(t341,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(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD41) ).
fof(f40_nnf,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(t164,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t343,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t164]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox2/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(t151,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t348,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t151]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox2/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(t152,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t346,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t152]) ).
cnf(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(c120,plain,
coll(sk27,sk21,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi120,negated_conjecture,
coll(sk27,sk21,sk24) = true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(h23,plain,
coll(sk27,sk24,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi120]) ).
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(c119,plain,
coll(sk26,sk20,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi119,negated_conjecture,
coll(sk26,sk20,sk24) = true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(h18,plain,
coll(sk24,sk24,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi119,hi119]) ).
cnf(h21,plain,
coll(sk24,sk24,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi120,hi120]) ).
cnf(h84,plain,
coll(sk27,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,h21,h18]) ).
cnf(h320,plain,
coll(sk27,sk24,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi0,h84]) ).
cnf(h1947,plain,
coll(sk26,sk21,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi2,h320,h23]) ).
cnf(h101,plain,
eqangle(V0,V1,V0,V1,sk20,sk21,sk22,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi19,h27]) ).
fof(f21,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD22) ).
fof(f21_nnf,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi21,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,ifeq(eqangle(X4,X5,X6,X7,X8,X9,X10,X11),true,eqangle(X0,X1,X2,X3,X8,X9,X10,X11),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(h393,plain,
eqangle(V0,V1,V0,V1,V2,V3,V2,V3) = true,
inference(hyper_resolution,[status(thm)],[hi21,h101,h27]) ).
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/sandbox2/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(t38,plain,
cyclic(sk27,sk27,sk26,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi42,h393,h1947]) ).
cnf(t2582,plain,
cyclic(sk27,sk27,sk26,sk21) = true,
inference(orient,[status(thm)],[t38]) ).
cnf(t2583,plain,
true = ifeq(true,true,cyclic(sk27,sk26,sk27,sk21),true),
inference(cp,[status(thm)],[t346,t2582]) ).
cnf(t25806,plain,
true = cyclic(sk27,sk26,sk27,sk21),
inference(step,[status(thm)],[t2583,t256]) ).
cnf(t4712,plain,
cyclic(sk27,sk26,sk27,sk21) = true,
inference(orient,[status(thm)],[t25806]) ).
cnf(t4713,plain,
true = ifeq(true,true,cyclic(sk27,sk26,sk21,sk27),true),
inference(cp,[status(thm)],[t348,t4712]) ).
cnf(t25838,plain,
true = cyclic(sk27,sk26,sk21,sk27),
inference(step,[status(thm)],[t4713,t256]) ).
cnf(t5222,plain,
cyclic(sk27,sk26,sk21,sk27) = true,
inference(orient,[status(thm)],[t25838]) ).
cnf(t5225,plain,
true = ifeq(true,true,eqangle(sk21,sk27,sk21,sk26,sk27,sk27,sk27,sk26),true),
inference(cp,[status(thm)],[t343,t5222]) ).
cnf(t26126,plain,
true = eqangle(sk21,sk27,sk21,sk26,sk27,sk27,sk27,sk26),
inference(step,[status(thm)],[t5225,t256]) ).
cnf(t8552,plain,
eqangle(sk21,sk27,sk21,sk26,sk27,sk27,sk27,sk26) = true,
inference(orient,[status(thm)],[t26126]) ).
cnf(t8565,plain,
true = ifeq(cyclic(sk27,sk26,sk21,sk27),true,ifeq(cyclic(sk27,sk26,sk21,sk26),true,ifeq(cyclic(sk27,sk26,sk21,sk27),true,ifeq(true,true,cong(sk27,sk26,sk27,sk26),true),true),true),true),
inference(cp,[status(thm)],[t341,t8552]) ).
cnf(t26127,plain,
true = ifeq(true,true,ifeq(cyclic(sk27,sk26,sk21,sk26),true,ifeq(cyclic(sk27,sk26,sk21,sk27),true,ifeq(true,true,cong(sk27,sk26,sk27,sk26),true),true),true),true),
inference(step,[status(thm)],[t8565,t5222]) ).
cnf(t26128,plain,
true = ifeq(cyclic(sk27,sk26,sk21,sk26),true,ifeq(cyclic(sk27,sk26,sk21,sk27),true,ifeq(true,true,cong(sk27,sk26,sk27,sk26),true),true),true),
inference(step,[status(thm)],[t26127,t256]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox2/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(t153,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t344,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t153]) ).
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(h12,plain,
coll(sk21,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi117,hi117]) ).
cnf(h53,plain,
coll(sk25,sk25,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h12,h12]) ).
cnf(c118,plain,
coll(sk26,sk23,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
coll(sk26,sk23,sk25) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h15,plain,
coll(sk25,sk25,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi118,hi118]) ).
cnf(h191,plain,
coll(sk26,sk21,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h15,h53]) ).
cnf(h752,plain,
coll(sk26,sk25,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h191]) ).
cnf(c121,plain,
coll(sk27,sk22,sk25),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi121,negated_conjecture,
coll(sk27,sk22,sk25) = true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(h24,plain,
coll(sk25,sk25,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi121,hi121]) ).
cnf(h91,plain,
coll(sk26,sk27,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h15,h24]) ).
cnf(h341,plain,
coll(sk26,sk25,sk27) = true,
inference(hyper_resolution,[status(thm)],[hi0,h91]) ).
cnf(h3479,plain,
coll(sk27,sk21,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h341,h752]) ).
cnf(t35,plain,
cyclic(sk26,sk26,sk27,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi42,h393,h3479]) ).
cnf(t2690,plain,
cyclic(sk26,sk26,sk27,sk21) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t2691,plain,
true = ifeq(true,true,cyclic(sk26,sk27,sk26,sk21),true),
inference(cp,[status(thm)],[t346,t2690]) ).
cnf(t25812,plain,
true = cyclic(sk26,sk27,sk26,sk21),
inference(step,[status(thm)],[t2691,t256]) ).
cnf(t4814,plain,
cyclic(sk26,sk27,sk26,sk21) = true,
inference(orient,[status(thm)],[t25812]) ).
cnf(t4815,plain,
true = ifeq(true,true,cyclic(sk26,sk27,sk21,sk26),true),
inference(cp,[status(thm)],[t348,t4814]) ).
cnf(t25848,plain,
true = cyclic(sk26,sk27,sk21,sk26),
inference(step,[status(thm)],[t4815,t256]) ).
cnf(t5378,plain,
cyclic(sk26,sk27,sk21,sk26) = true,
inference(orient,[status(thm)],[t25848]) ).
cnf(t5379,plain,
true = ifeq(true,true,cyclic(sk27,sk26,sk21,sk26),true),
inference(cp,[status(thm)],[t344,t5378]) ).
cnf(t25872,plain,
true = cyclic(sk27,sk26,sk21,sk26),
inference(step,[status(thm)],[t5379,t256]) ).
cnf(t5734,plain,
cyclic(sk27,sk26,sk21,sk26) = true,
inference(orient,[status(thm)],[t25872]) ).
cnf(t26129,plain,
true = ifeq(true,true,ifeq(cyclic(sk27,sk26,sk21,sk27),true,ifeq(true,true,cong(sk27,sk26,sk27,sk26),true),true),true),
inference(step,[status(thm)],[t26128,t5734]) ).
cnf(t26130,plain,
true = ifeq(cyclic(sk27,sk26,sk21,sk27),true,ifeq(true,true,cong(sk27,sk26,sk27,sk26),true),true),
inference(step,[status(thm)],[t26129,t256]) ).
cnf(t26131,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk27,sk26,sk27,sk26),true),true),
inference(step,[status(thm)],[t26130,t5222]) ).
cnf(t26132,plain,
true = ifeq(true,true,cong(sk27,sk26,sk27,sk26),true),
inference(step,[status(thm)],[t26131,t256]) ).
cnf(t26133,plain,
true = cong(sk27,sk26,sk27,sk26),
inference(step,[status(thm)],[t26132,t256]) ).
cnf(t8566,plain,
cong(sk27,sk26,sk27,sk26) = true,
inference(orient,[status(thm)],[t26133]) ).
cnf(t8569,plain,
true = ifeq(true,true,cong(sk27,sk26,sk26,sk27),true),
inference(cp,[status(thm)],[t323,t8566]) ).
cnf(t26134,plain,
true = cong(sk27,sk26,sk26,sk27),
inference(step,[status(thm)],[t8569,t256]) ).
cnf(t8597,plain,
cong(sk27,sk26,sk26,sk27) = true,
inference(orient,[status(thm)],[t26134]) ).
cnf(t8599,plain,
true = ifeq(true,true,cong(sk26,sk27,sk27,sk26),true),
inference(cp,[status(thm)],[t321,t8597]) ).
cnf(t26135,plain,
true = cong(sk26,sk27,sk27,sk26),
inference(step,[status(thm)],[t8599,t256]) ).
cnf(t8607,plain,
cong(sk26,sk27,sk27,sk26) = true,
inference(orient,[status(thm)],[t26135]) ).
cnf(t8609,plain,
true = ifeq(true,true,cong(sk26,sk27,sk26,sk27),true),
inference(cp,[status(thm)],[t323,t8607]) ).
cnf(t26136,plain,
true = cong(sk26,sk27,sk26,sk27),
inference(step,[status(thm)],[t8609,t256]) ).
cnf(t8616,plain,
cong(sk26,sk27,sk26,sk27) = true,
inference(orient,[status(thm)],[t26136]) ).
cnf(t24097,plain,
true = ifeq(true,true,midp(sk26,sk27,sk27),true),
inference(cp,[status(thm)],[t24096,t8616]) ).
cnf(t28042,plain,
true = midp(sk26,sk27,sk27),
inference(step,[status(thm)],[t24097,t256]) ).
cnf(t24117,plain,
midp(sk26,sk27,sk27) = true,
inference(orient,[status(thm)],[t28042]) ).
cnf(t24118,plain,
true = ifeq(true,true,midp(sk26,X1,X1),true),
inference(cp,[status(thm)],[t23714,t24117]) ).
cnf(t28062,plain,
true = midp(sk26,X1,X1),
inference(step,[status(thm)],[t24118,t256]) ).
cnf(t24519,plain,
midp(sk26,X1,X1) = true,
inference(orient,[status(thm)],[t28062]) ).
cnf(t24520,plain,
true = ifeq(true,true,cong(sk26,X1,sk26,X1),true),
inference(cp,[status(thm)],[t375,t24519]) ).
cnf(t28070,plain,
true = cong(sk26,X1,sk26,X1),
inference(step,[status(thm)],[t24520,t256]) ).
cnf(t24660,plain,
cong(sk26,X1,sk26,X1) = true,
inference(orient,[status(thm)],[t28070]) ).
cnf(t24671,plain,
true = ifeq(true,true,ifeq(cong(sk26,X1,sk26,X1),true,perp(sk26,sk26,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t24660]) ).
cnf(t28078,plain,
true = ifeq(cong(sk26,X1,sk26,X1),true,perp(sk26,sk26,X2,X1),true),
inference(step,[status(thm)],[t24671,t256]) ).
cnf(t28079,plain,
true = ifeq(true,true,perp(sk26,sk26,X2,X1),true),
inference(step,[status(thm)],[t28078,t24660]) ).
cnf(t28080,plain,
true = perp(sk26,sk26,X2,X1),
inference(step,[status(thm)],[t28079,t256]) ).
cnf(t24898,plain,
perp(sk26,sk26,X1,X2) = true,
inference(orient,[status(thm)],[t28080]) ).
cnf(t24899,plain,
true = ifeq(true,true,perp(X1,X2,sk26,sk26),true),
inference(cp,[status(thm)],[t285,t24898]) ).
cnf(t28106,plain,
true = perp(X1,X2,sk26,sk26),
inference(step,[status(thm)],[t24899,t256]) ).
cnf(t25267,plain,
perp(X1,X2,sk26,sk26) = true,
inference(orient,[status(thm)],[t28106]) ).
cnf(t25275,plain,
true = ifeq(true,true,ifeq(perp(sk26,sk26,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t276,t25267]) ).
cnf(t28122,plain,
true = ifeq(perp(sk26,sk26,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t25275,t256]) ).
cnf(t28123,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t28122,t24898]) ).
cnf(t28124,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t28123,t256]) ).
cnf(t25647,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t28124]) ).
cnf(c122,plain,
~ para(sk26,sk27,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
para(sk26,sk27,sk20,sk21) != true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t25647]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO653+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n007.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 12:38:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 187.87/25.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 187.87/25.33 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------