%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO543+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 : n008.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 01:18:07 PM UTC 2026
% Result : Theorem 131.04s 18.71s
% Output : Proof 131.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 19
% Syntax : Number of formulae : 234 ( 162 unt; 0 def)
% Number of atoms : 390 ( 158 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 246 ( 90 ~; 84 |; 53 &)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-4 aty)
% Number of variables : 658 ( 78 sgn 257 !; 10 ?)
% 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/sandbox2/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(t232,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)],[t232]) ).
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(t101,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t336,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t101]) ).
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(t218,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(t333,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)],[t218]) ).
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(t174,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)],[t174]) ).
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(t111,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)],[t111]) ).
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(t161,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)],[t161]) ).
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/sandbox2/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(t143,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)],[t143]) ).
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/sandbox2/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(t166,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t308,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(orient,[status(thm)],[t166]) ).
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(t144,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t346,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t144]) ).
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(t142,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(t359,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t142]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,H,A1,P,Q] :
( ( midp(Q,F,C)
& midp(P,E,B)
& midp(A1,C,B)
& coll(H,C,F)
& coll(H,B,E)
& coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(P,Q,H,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL012003) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,H,A1,P,Q] :
( ( midp(Q,F,C)
& midp(P,E,B)
& midp(A1,C,B)
& coll(H,C,F)
& coll(H,B,E)
& coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) )
=> cyclic(P,Q,H,D) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,H,A1,P,Q] :
( ~ cyclic(P,Q,H,D)
& midp(Q,F,C)
& midp(P,E,B)
& midp(A1,C,B)
& coll(H,C,F)
& coll(H,B,E)
& coll(F,A,B)
& perp(F,C,A,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,B,C)
& perp(D,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cyclic(sk28,sk29,sk26,sk23)
& midp(sk29,sk25,sk22)
& midp(sk28,sk24,sk21)
& midp(sk27,sk22,sk21)
& coll(sk26,sk22,sk25)
& coll(sk26,sk21,sk24)
& coll(sk25,sk20,sk21)
& perp(sk25,sk22,sk20,sk21)
& coll(sk24,sk20,sk22)
& perp(sk24,sk21,sk20,sk22)
& 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])],[f94_nnf]) ).
cnf(c121,plain,
midp(sk27,sk22,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi121,negated_conjecture,
midp(sk27,sk22,sk21) = true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(h26,plain,
cong(sk27,sk22,sk27,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi68,hi121]) ).
cnf(hi12,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(cong(X0,X1,X0,X3),true,ifeq(cong(X0,X1,X0,X4),true,cyclic(X1,X2,X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h165,plain,
cyclic(sk22,sk21,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi12,h26,h26,h26]) ).
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/sandbox2/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(t32,plain,
cyclic(sk21,sk21,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi16,h165,h165]) ).
cnf(t3124,plain,
cyclic(sk21,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(t3125,plain,
true = ifeq(true,true,eqangle(sk21,sk21,sk21,sk21,sk21,sk21,sk21,sk21),true),
inference(cp,[status(thm)],[t359,t3124]) ).
cnf(t40,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t40]) ).
cnf(t19962,plain,
true = eqangle(sk21,sk21,sk21,sk21,sk21,sk21,sk21,sk21),
inference(step,[status(thm)],[t3125,t256]) ).
cnf(t6976,plain,
eqangle(sk21,sk21,sk21,sk21,sk21,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t19962]) ).
cnf(t6978,plain,
true = ifeq(true,true,para(sk21,sk21,sk21,sk21),true),
inference(cp,[status(thm)],[t314,t6976]) ).
cnf(t19963,plain,
true = para(sk21,sk21,sk21,sk21),
inference(step,[status(thm)],[t6978,t256]) ).
cnf(t6999,plain,
para(sk21,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t19963]) ).
cnf(t7001,plain,
true = ifeq(true,true,eqangle(sk21,sk21,X1,X2,sk21,sk21,X1,X2),true),
inference(cp,[status(thm)],[t346,t6999]) ).
cnf(t20090,plain,
true = eqangle(sk21,sk21,X1,X2,sk21,sk21,X1,X2),
inference(step,[status(thm)],[t7001,t256]) ).
cnf(t9089,plain,
eqangle(sk21,sk21,X1,X2,sk21,sk21,X1,X2) = true,
inference(orient,[status(thm)],[t20090]) ).
cnf(t9093,plain,
true = ifeq(true,true,eqangle(X1,X2,sk21,sk21,X1,X2,sk21,sk21),true),
inference(cp,[status(thm)],[t308,t9089]) ).
cnf(t20230,plain,
true = eqangle(X1,X2,sk21,sk21,X1,X2,sk21,sk21),
inference(step,[status(thm)],[t9093,t256]) ).
cnf(t10704,plain,
eqangle(X1,X2,sk21,sk21,X1,X2,sk21,sk21) = true,
inference(orient,[status(thm)],[t20230]) ).
cnf(t10705,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t314,t10704]) ).
cnf(t20231,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t10705,t256]) ).
cnf(t10727,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t20231]) ).
cnf(t10744,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)],[t333,t10727]) ).
cnf(t21071,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)],[t10744,t256]) ).
cnf(t21072,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t21071,t10727]) ).
cnf(t21073,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t21072,t256]) ).
cnf(t18293,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t21073]) ).
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(t152,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)],[t152]) ).
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(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(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(t106,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)],[t106]) ).
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(t107,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)],[t107]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD11) ).
fof(f10_nnf,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [M,B,A] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( midp(X2,X0,X1)
| ~ midp(X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(midp(X0,X1,X2),true,midp(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(c122,plain,
midp(sk28,sk24,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi122,negated_conjecture,
midp(sk28,sk24,sk21) = true,
inference(equality_encoding,[status(esa)],[c122]) ).
cnf(h46,plain,
midp(sk28,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi122]) ).
cnf(h267,plain,
cong(sk28,sk21,sk28,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi68,h46]) ).
cnf(t35,plain,
cyclic(sk21,sk24,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi12,h267,h267,h267]) ).
cnf(t3169,plain,
cyclic(sk21,sk24,sk24,sk24) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t3170,plain,
true = ifeq(true,true,cyclic(sk24,sk21,sk24,sk24),true),
inference(cp,[status(thm)],[t360,t3169]) ).
cnf(t19914,plain,
true = cyclic(sk24,sk21,sk24,sk24),
inference(step,[status(thm)],[t3170,t256]) ).
cnf(t5995,plain,
cyclic(sk24,sk21,sk24,sk24) = true,
inference(orient,[status(thm)],[t19914]) ).
cnf(t5996,plain,
true = ifeq(true,true,cyclic(sk24,sk24,sk21,sk24),true),
inference(cp,[status(thm)],[t362,t5995]) ).
cnf(t19931,plain,
true = cyclic(sk24,sk24,sk21,sk24),
inference(step,[status(thm)],[t5996,t256]) ).
cnf(t6363,plain,
cyclic(sk24,sk24,sk21,sk24) = true,
inference(orient,[status(thm)],[t19931]) ).
cnf(t6366,plain,
true = ifeq(true,true,eqangle(sk21,sk24,sk21,sk24,sk24,sk24,sk24,sk24),true),
inference(cp,[status(thm)],[t359,t6363]) ).
cnf(t20073,plain,
true = eqangle(sk21,sk24,sk21,sk24,sk24,sk24,sk24,sk24),
inference(step,[status(thm)],[t6366,t256]) ).
cnf(t8940,plain,
eqangle(sk21,sk24,sk21,sk24,sk24,sk24,sk24,sk24) = true,
inference(orient,[status(thm)],[t20073]) ).
cnf(t8953,plain,
true = ifeq(cyclic(sk24,sk24,sk21,sk24),true,ifeq(cyclic(sk24,sk24,sk21,sk24),true,ifeq(cyclic(sk24,sk24,sk21,sk24),true,ifeq(true,true,cong(sk24,sk24,sk24,sk24),true),true),true),true),
inference(cp,[status(thm)],[t357,t8940]) ).
cnf(t20074,plain,
true = ifeq(true,true,ifeq(cyclic(sk24,sk24,sk21,sk24),true,ifeq(cyclic(sk24,sk24,sk21,sk24),true,ifeq(true,true,cong(sk24,sk24,sk24,sk24),true),true),true),true),
inference(step,[status(thm)],[t8953,t6363]) ).
cnf(t20075,plain,
true = ifeq(cyclic(sk24,sk24,sk21,sk24),true,ifeq(cyclic(sk24,sk24,sk21,sk24),true,ifeq(true,true,cong(sk24,sk24,sk24,sk24),true),true),true),
inference(step,[status(thm)],[t20074,t256]) ).
cnf(t20076,plain,
true = ifeq(true,true,ifeq(cyclic(sk24,sk24,sk21,sk24),true,ifeq(true,true,cong(sk24,sk24,sk24,sk24),true),true),true),
inference(step,[status(thm)],[t20075,t6363]) ).
cnf(t20077,plain,
true = ifeq(cyclic(sk24,sk24,sk21,sk24),true,ifeq(true,true,cong(sk24,sk24,sk24,sk24),true),true),
inference(step,[status(thm)],[t20076,t256]) ).
cnf(t20078,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk24,sk24,sk24,sk24),true),true),
inference(step,[status(thm)],[t20077,t6363]) ).
cnf(t20079,plain,
true = ifeq(true,true,cong(sk24,sk24,sk24,sk24),true),
inference(step,[status(thm)],[t20078,t256]) ).
cnf(t20080,plain,
true = cong(sk24,sk24,sk24,sk24),
inference(step,[status(thm)],[t20079,t256]) ).
cnf(t8954,plain,
cong(sk24,sk24,sk24,sk24) = true,
inference(orient,[status(thm)],[t20080]) ).
cnf(t8964,plain,
true = ifeq(true,true,ifeq(coll(sk24,sk24,sk24),true,midp(sk24,sk24,sk24),true),true),
inference(cp,[status(thm)],[t272,t8954]) ).
cnf(t20081,plain,
true = ifeq(coll(sk24,sk24,sk24),true,midp(sk24,sk24,sk24),true),
inference(step,[status(thm)],[t8964,t256]) ).
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(t102,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t353,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t102]) ).
cnf(t5998,plain,
true = ifeq(true,true,eqangle(sk24,sk24,sk24,sk21,sk24,sk24,sk24,sk21),true),
inference(cp,[status(thm)],[t359,t5995]) ).
cnf(t20053,plain,
true = eqangle(sk24,sk24,sk24,sk21,sk24,sk24,sk24,sk21),
inference(step,[status(thm)],[t5998,t256]) ).
cnf(t8727,plain,
eqangle(sk24,sk24,sk24,sk21,sk24,sk24,sk24,sk21) = true,
inference(orient,[status(thm)],[t20053]) ).
cnf(t8729,plain,
true = ifeq(true,true,para(sk24,sk24,sk24,sk24),true),
inference(cp,[status(thm)],[t314,t8727]) ).
cnf(t20054,plain,
true = para(sk24,sk24,sk24,sk24),
inference(step,[status(thm)],[t8729,t256]) ).
cnf(t8741,plain,
para(sk24,sk24,sk24,sk24) = true,
inference(orient,[status(thm)],[t20054]) ).
cnf(t8742,plain,
true = ifeq(true,true,coll(sk24,sk24,sk24),true),
inference(cp,[status(thm)],[t353,t8741]) ).
cnf(t20055,plain,
true = coll(sk24,sk24,sk24),
inference(step,[status(thm)],[t8742,t256]) ).
cnf(t8761,plain,
coll(sk24,sk24,sk24) = true,
inference(orient,[status(thm)],[t20055]) ).
cnf(t20082,plain,
true = ifeq(true,true,midp(sk24,sk24,sk24),true),
inference(step,[status(thm)],[t20081,t8761]) ).
cnf(t20083,plain,
true = midp(sk24,sk24,sk24),
inference(step,[status(thm)],[t20082,t256]) ).
cnf(t8992,plain,
midp(sk24,sk24,sk24) = true,
inference(orient,[status(thm)],[t20083]) ).
cnf(t18294,plain,
true = ifeq(true,true,midp(sk24,X1,X1),true),
inference(cp,[status(thm)],[t18293,t8992]) ).
cnf(t21074,plain,
true = midp(sk24,X1,X1),
inference(step,[status(thm)],[t18294,t256]) ).
cnf(t18297,plain,
midp(sk24,X1,X1) = true,
inference(orient,[status(thm)],[t21074]) ).
cnf(t18298,plain,
true = ifeq(true,true,cong(sk24,X1,sk24,X1),true),
inference(cp,[status(thm)],[t336,t18297]) ).
cnf(t21077,plain,
true = cong(sk24,X1,sk24,X1),
inference(step,[status(thm)],[t18298,t256]) ).
cnf(t18357,plain,
cong(sk24,X1,sk24,X1) = true,
inference(orient,[status(thm)],[t21077]) ).
cnf(t18370,plain,
true = ifeq(true,true,ifeq(cong(sk24,X1,sk24,X1),true,perp(sk24,sk24,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t18357]) ).
cnf(t21081,plain,
true = ifeq(cong(sk24,X1,sk24,X1),true,perp(sk24,sk24,X2,X1),true),
inference(step,[status(thm)],[t18370,t256]) ).
cnf(t21082,plain,
true = ifeq(true,true,perp(sk24,sk24,X2,X1),true),
inference(step,[status(thm)],[t21081,t18357]) ).
cnf(t21083,plain,
true = perp(sk24,sk24,X2,X1),
inference(step,[status(thm)],[t21082,t256]) ).
cnf(t18483,plain,
perp(sk24,sk24,X1,X2) = true,
inference(orient,[status(thm)],[t21083]) ).
cnf(t18484,plain,
true = ifeq(true,true,perp(X1,X2,sk24,sk24),true),
inference(cp,[status(thm)],[t292,t18483]) ).
cnf(t21093,plain,
true = perp(X1,X2,sk24,sk24),
inference(step,[status(thm)],[t18484,t256]) ).
cnf(t18638,plain,
perp(X1,X2,sk24,sk24) = true,
inference(orient,[status(thm)],[t21093]) ).
cnf(t18645,plain,
true = ifeq(true,true,ifeq(perp(sk24,sk24,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t18638]) ).
cnf(t21099,plain,
true = ifeq(perp(sk24,sk24,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t18645,t256]) ).
cnf(t21100,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t21099,t18483]) ).
cnf(t21101,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t21100,t256]) ).
cnf(t18792,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t21101]) ).
cnf(t21113,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)],[t333,t18792]) ).
cnf(t21114,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)],[t21113,t256]) ).
cnf(t21115,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t21114,t18792]) ).
cnf(t21116,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t21115,t256]) ).
cnf(t18799,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t21116]) ).
cnf(t19555,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t18799]) ).
cnf(t6998,plain,
true = ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),true),
inference(cp,[status(thm)],[t357,t6976]) ).
cnf(t19965,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),true),
inference(step,[status(thm)],[t6998,t3124]) ).
cnf(t19966,plain,
true = ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),
inference(step,[status(thm)],[t19965,t256]) ).
cnf(t19967,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),
inference(step,[status(thm)],[t19966,t3124]) ).
cnf(t19968,plain,
true = ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),
inference(step,[status(thm)],[t19967,t256]) ).
cnf(t19969,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),
inference(step,[status(thm)],[t19968,t3124]) ).
cnf(t19970,plain,
true = ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),
inference(step,[status(thm)],[t19969,t256]) ).
cnf(t19971,plain,
true = cong(sk21,sk21,sk21,sk21),
inference(step,[status(thm)],[t19970,t256]) ).
cnf(t7047,plain,
cong(sk21,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t19971]) ).
cnf(t7057,plain,
true = ifeq(true,true,ifeq(coll(sk21,sk21,sk21),true,midp(sk21,sk21,sk21),true),true),
inference(cp,[status(thm)],[t272,t7047]) ).
cnf(t19972,plain,
true = ifeq(coll(sk21,sk21,sk21),true,midp(sk21,sk21,sk21),true),
inference(step,[status(thm)],[t7057,t256]) ).
cnf(t7000,plain,
true = ifeq(true,true,coll(sk21,sk21,sk21),true),
inference(cp,[status(thm)],[t353,t6999]) ).
cnf(t19964,plain,
true = coll(sk21,sk21,sk21),
inference(step,[status(thm)],[t7000,t256]) ).
cnf(t7020,plain,
coll(sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t19964]) ).
cnf(t19973,plain,
true = ifeq(true,true,midp(sk21,sk21,sk21),true),
inference(step,[status(thm)],[t19972,t7020]) ).
cnf(t19974,plain,
true = midp(sk21,sk21,sk21),
inference(step,[status(thm)],[t19973,t256]) ).
cnf(t7085,plain,
midp(sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t19974]) ).
cnf(t18296,plain,
true = ifeq(true,true,midp(sk21,X1,X1),true),
inference(cp,[status(thm)],[t18293,t7085]) ).
cnf(t21076,plain,
true = midp(sk21,X1,X1),
inference(step,[status(thm)],[t18296,t256]) ).
cnf(t18337,plain,
midp(sk21,X1,X1) = true,
inference(orient,[status(thm)],[t21076]) ).
cnf(t19556,plain,
true = ifeq(true,true,midp(sk21,X1,X2),true),
inference(cp,[status(thm)],[t19555,t18337]) ).
cnf(t21208,plain,
true = midp(sk21,X1,X2),
inference(step,[status(thm)],[t19556,t256]) ).
cnf(t19581,plain,
midp(sk21,X1,X2) = true,
inference(orient,[status(thm)],[t21208]) ).
cnf(t19582,plain,
true = ifeq(true,true,cong(sk21,X1,sk21,X2),true),
inference(cp,[status(thm)],[t336,t19581]) ).
cnf(t21214,plain,
true = cong(sk21,X1,sk21,X2),
inference(step,[status(thm)],[t19582,t256]) ).
cnf(t19640,plain,
cong(sk21,X1,sk21,X2) = true,
inference(orient,[status(thm)],[t21214]) ).
cnf(t19658,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X2),true,ifeq(cong(sk21,X1,sk21,X3),true,cyclic(X1,X4,X2,X3),true),true),true),
inference(cp,[status(thm)],[t273,t19640]) ).
cnf(t21225,plain,
true = ifeq(cong(sk21,X1,sk21,X2),true,ifeq(cong(sk21,X1,sk21,X3),true,cyclic(X1,X4,X2,X3),true),true),
inference(step,[status(thm)],[t19658,t256]) ).
cnf(t21226,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X3),true,cyclic(X1,X4,X2,X3),true),true),
inference(step,[status(thm)],[t21225,t19640]) ).
cnf(t21227,plain,
true = ifeq(cong(sk21,X1,sk21,X3),true,cyclic(X1,X4,X2,X3),true),
inference(step,[status(thm)],[t21226,t256]) ).
cnf(t21228,plain,
true = ifeq(true,true,cyclic(X1,X4,X2,X3),true),
inference(step,[status(thm)],[t21227,t19640]) ).
cnf(t21229,plain,
true = cyclic(X1,X4,X2,X3),
inference(step,[status(thm)],[t21228,t256]) ).
cnf(t19828,plain,
cyclic(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t21229]) ).
cnf(c124,plain,
~ cyclic(sk28,sk29,sk26,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
cyclic(sk28,sk29,sk26,sk23) != true,
inference(equality_encoding,[status(esa)],[c124]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t19828]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO543+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.44 % Computer : n008.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Wed Sep 23 12:21:55 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 131.04/18.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 131.04/18.71 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------