%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWX187+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:32:46 PM UTC 2026
% Result : Theorem 4.35s 1.08s
% Output : CNFRefutation 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 67 ( 45 unt; 1 def)
% Number of atoms : 171 ( 90 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 126 ( 57 ~; 57 |; 1 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 162 ( 0 sgn 154 !; 8 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : head(cons(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
fof(f3,axiom,
! [X0,X1] : nil != cons(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
fof(f5,axiom,
! [X0] : s(X0) != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
fof(f6,axiom,
length(nil) = z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
fof(f7,axiom,
! [X0,X1] : length(cons(X0,X1)) = s(length(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
fof(f8,axiom,
! [X0,X1] :
( x2(s(X0),s(X1))
<=> x2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
fof(f10,axiom,
! [X0] : x2(z,s(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
fof(f12,axiom,
! [X0] : x(nil,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
fof(f13,axiom,
! [X0,X1,X2] : x(cons(X1,X2),X0) = cons(X1,x(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
fof(f15,axiom,
! [X0,X1,X2] : rotate(s(X0),cons(X1,X2)) = rotate(X0,x(X2,cons(X1,nil))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
fof(f16,axiom,
! [X0] : rotate(z,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
fof(f17,conjecture,
? [X0,X1,X2,X3] :
~ ( x2(X0,length(X3))
=> ( x2(X1,length(X2))
=> ( X3 = X2
=> ( rotate(s(z),X3) != X3
=> ( rotate(X0,X3) = rotate(X1,X2)
=> X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_017) ).
fof(f18,negated_conjecture,
~ ? [X0,X1,X2,X3] :
~ ( x2(X0,length(X3))
=> ( x2(X1,length(X2))
=> ( X3 = X2
=> ( rotate(s(z),X3) != X3
=> ( rotate(X0,X3) = rotate(X1,X2)
=> X0 = X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( ~ x2(X0,length(X3))
| ~ x2(X1,length(X2))
| X2 != X3
| rotate(s(z),X3) = X3
| rotate(X0,X3) != rotate(X1,X2)
| X0 = X1 ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( ~ x2(X0,length(X3))
| ~ x2(X1,length(X2))
| X2 != X3
| rotate(s(z),X3) = X3
| rotate(X0,X3) != rotate(X1,X2)
| X0 = X1 ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ x2(s(X0),s(X1))
| x2(X0,X1) )
& ( ~ x2(X0,X1)
| x2(s(X0),s(X1)) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f22,plain,
! [X0,X1] : head(cons(X0,X1)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f24,plain,
! [X0,X1] : cons(X0,X1) != nil,
inference(cnf_transformation,[],[f3]) ).
fof(f26,plain,
! [X0] : s(X0) != z,
inference(cnf_transformation,[],[f5]) ).
fof(f27,plain,
z = length(nil),
inference(cnf_transformation,[],[f6]) ).
fof(f28,plain,
! [X0,X1] : length(cons(X0,X1)) = s(length(X1)),
inference(cnf_transformation,[],[f7]) ).
fof(f30,plain,
! [X0,X1] :
( ~ x2(X0,X1)
| x2(s(X0),s(X1)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f32,plain,
! [X0] : x2(z,s(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f34,plain,
! [X0] : x(nil,X0) = X0,
inference(cnf_transformation,[],[f12]) ).
fof(f35,plain,
! [X2,X0,X1] : x(cons(X1,X2),X0) = cons(X1,x(X2,X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f37,plain,
! [X2,X0,X1] : rotate(s(X0),cons(X1,X2)) = rotate(X0,x(X2,cons(X1,nil))),
inference(cnf_transformation,[],[f15]) ).
fof(f38,plain,
! [X0] : rotate(z,X0) = X0,
inference(cnf_transformation,[],[f16]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( ~ x2(X0,length(X3))
| ~ x2(X1,length(X2))
| X2 != X3
| rotate(s(z),X3) = X3
| rotate(X0,X3) != rotate(X1,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
! [X3,X0,X1] :
( ~ x2(X0,length(X3))
| ~ x2(X1,length(X3))
| rotate(s(z),X3) = X3
| rotate(X0,X3) != rotate(X1,X3)
| X0 = X1 ),
inference(equality_resolution,[],[f39]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : head(cons(X0,X1)) = X0,
inference(cnf_transformation,[],[f22]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : cons(X0,X1) != nil,
inference(cnf_transformation,[],[f24]) ).
tcf(c_53,plain,
! [X0: $i] : s(X0) != z,
inference(cnf_transformation,[],[f26]) ).
tcf(c_54,plain,
length(nil) = z,
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : length(cons(X0,X1)) = s(length(X1)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( x2(s(X0),s(X1))
| ~ x2(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_59,plain,
! [X0: $i] : x2(z,s(X0)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_61,plain,
! [X0: $i] : x(nil,X0) = X0,
inference(cnf_transformation,[],[f34]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : cons(X0,x(X1,X2)) = x(cons(X0,X1),X2),
inference(cnf_transformation,[],[f35]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] : rotate(X0,x(X1,cons(X2,nil))) = rotate(s(X0),cons(X2,X1)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_65,plain,
! [X0: $i] : rotate(z,X0) = X0,
inference(cnf_transformation,[],[f38]) ).
tcf(c_66,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( rotate(s(z),X1) = X1 )
| ~ x2(X2,length(X1))
| ~ x2(X0,length(X1))
| ( rotate(X0,X1) != rotate(X2,X1) ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_188,definition,
iPr_def_10 = s(z),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_189,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( rotate(iPr_def_10,X1) = X1 )
| ~ x2(X2,length(X1))
| ~ x2(X0,length(X1))
| ( rotate(X0,X1) != rotate(X2,X1) ) ),
inference(demodulation,[status(thm)],[c_66,c_188]) ).
tcf(c_598,plain,
! [X0: $i] :
( x2(iPr_def_10,s(X0))
| ~ x2(z,X0) ),
inference(superposition,[status(thm)],[c_188,c_56]) ).
tcf(c_637,plain,
! [X0: $i,X1: $i] : rotate(s(z),cons(X0,X1)) = x(X1,cons(X0,nil)),
inference(superposition,[status(thm)],[c_64,c_65]) ).
tcf(c_641,plain,
! [X0: $i,X1: $i] : x(X0,cons(X1,nil)) = rotate(iPr_def_10,cons(X1,X0)),
inference(light_normalisation,[status(thm)],[c_637,c_188]) ).
tcf(c_653,plain,
! [X0: $i,X1: $i,X2: $i] : rotate(X0,rotate(iPr_def_10,cons(X1,X2))) = rotate(s(X0),cons(X1,X2)),
inference(demodulation,[status(thm)],[c_64,c_641]) ).
tcf(c_666,plain,
! [X0: $i] : rotate(iPr_def_10,cons(X0,nil)) = cons(X0,nil),
inference(superposition,[status(thm)],[c_641,c_61]) ).
tcf(c_667,plain,
! [X0: $i,X1: $i,X2: $i] : cons(X0,x(X1,cons(X2,nil))) = rotate(iPr_def_10,cons(X2,cons(X0,X1))),
inference(superposition,[status(thm)],[c_641,c_62]) ).
tcf(c_738,plain,
! [X0: $i,X1: $i,X2: $i] : cons(X0,rotate(iPr_def_10,cons(X1,X2))) = rotate(iPr_def_10,cons(X1,cons(X0,X2))),
inference(demodulation,[status(thm)],[c_667,c_641]) ).
tcf(c_742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : rotate(X0,cons(X1,rotate(iPr_def_10,cons(X2,X3)))) = rotate(s(X0),cons(X2,cons(X1,X3))),
inference(superposition,[status(thm)],[c_738,c_653]) ).
tcf(c_771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : rotate(X0,cons(X1,cons(X2,rotate(iPr_def_10,cons(X3,X4))))) = rotate(s(X0),cons(X3,cons(X1,cons(X2,X4)))),
inference(superposition,[status(thm)],[c_738,c_742]) ).
tcf(c_998,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : rotate(X0,cons(X1,cons(X2,cons(X3,rotate(iPr_def_10,cons(X4,X5)))))) = rotate(s(X0),cons(X4,cons(X1,cons(X2,cons(X3,X5))))),
inference(superposition,[status(thm)],[c_738,c_771]) ).
tcf(c_1924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : rotate(s(X0),cons(X1,cons(X2,cons(X3,cons(X4,nil))))) = rotate(X0,cons(X2,cons(X3,cons(X4,cons(X1,nil))))),
inference(superposition,[status(thm)],[c_666,c_998]) ).
tcf(c_2574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( s(X5) = X0 )
| ( rotate(iPr_def_10,cons(X1,cons(X2,cons(X3,cons(X4,nil))))) = cons(X1,cons(X2,cons(X3,cons(X4,nil)))) )
| ~ x2(X0,length(cons(X1,cons(X2,cons(X3,cons(X4,nil))))))
| ~ x2(s(X5),length(cons(X1,cons(X2,cons(X3,cons(X4,nil))))))
| ( rotate(X0,cons(X1,cons(X2,cons(X3,cons(X4,nil))))) != rotate(X5,cons(X2,cons(X3,cons(X4,cons(X1,nil))))) ) ),
inference(superposition,[status(thm)],[c_1924,c_189]) ).
tcf(c_2753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( s(X5) = X0 )
| ( cons(X1,cons(X2,cons(X3,cons(X4,nil)))) = cons(X2,cons(X3,cons(X4,cons(X1,nil)))) )
| ~ x2(X0,s(s(s(iPr_def_10))))
| ~ x2(s(X5),s(s(s(iPr_def_10))))
| ( rotate(X0,cons(X1,cons(X2,cons(X3,cons(X4,nil))))) != rotate(X5,cons(X2,cons(X3,cons(X4,cons(X1,nil))))) ) ),
inference(demodulation,[status(thm)],[c_2574,c_54,c_55,c_188,c_666,c_738]) ).
tcf(c_2774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( s(iPr_def_10) = X0 )
| ( cons(X1,cons(X2,cons(X3,cons(X4,nil)))) = cons(X2,cons(X3,cons(X4,cons(X1,nil)))) )
| ~ x2(X0,s(s(s(iPr_def_10))))
| ~ x2(s(iPr_def_10),s(s(s(iPr_def_10))))
| ( rotate(X0,cons(X1,cons(X2,cons(X3,cons(X4,nil))))) != cons(X3,rotate(iPr_def_10,cons(X2,cons(X4,cons(X1,nil))))) ) ),
inference(superposition,[status(thm)],[c_738,c_2753]) ).
tcf(c_3602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( s(iPr_def_10) = X0 )
| ( cons(X1,cons(X2,cons(X3,cons(X4,nil)))) = cons(X2,cons(X3,cons(X4,cons(X1,nil)))) )
| ~ x2(X0,s(s(s(iPr_def_10))))
| ~ x2(s(iPr_def_10),s(s(s(iPr_def_10))))
| ( rotate(X0,cons(X1,cons(X2,cons(X3,cons(X4,nil))))) != cons(X3,cons(X4,cons(X1,cons(X2,nil)))) ) ),
inference(demodulation,[status(thm)],[c_2774,c_666,c_738]) ).
tcf(c_3618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( s(iPr_def_10) = z )
| ( cons(X0,cons(X1,cons(X2,cons(X3,nil)))) = cons(X1,cons(X2,cons(X3,cons(X0,nil)))) )
| ~ x2(z,s(s(s(iPr_def_10))))
| ~ x2(s(iPr_def_10),s(s(s(iPr_def_10))))
| ( cons(X0,cons(X1,cons(X2,cons(X3,nil)))) != cons(X2,cons(X3,cons(X0,cons(X1,nil)))) ) ),
inference(superposition,[status(thm)],[c_65,c_3602]) ).
tcf(c_3622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cons(X0,cons(X1,cons(X2,cons(X3,nil)))) = cons(X1,cons(X2,cons(X3,cons(X0,nil)))) )
| ~ x2(s(iPr_def_10),s(s(s(iPr_def_10))))
| ( cons(X0,cons(X1,cons(X2,cons(X3,nil)))) != cons(X2,cons(X3,cons(X0,cons(X1,nil)))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3618,c_53,c_59]) ).
tcf(c_3913,plain,
! [X0: $i,X1: $i] :
( ( cons(X0,cons(X1,cons(X0,cons(X1,nil)))) = cons(X1,cons(X0,cons(X1,cons(X0,nil)))) )
| ~ x2(s(iPr_def_10),s(s(s(iPr_def_10)))) ),
inference(equality_resolution,[status(thm)],[c_3622]) ).
tcf(c_3929,plain,
! [X0: $i,X1: $i] :
( ( cons(X0,cons(X1,cons(X0,cons(X1,nil)))) = cons(X1,cons(X0,cons(X1,cons(X0,nil)))) )
| ~ x2(iPr_def_10,s(s(iPr_def_10))) ),
inference(superposition,[status(thm)],[c_56,c_3913]) ).
tcf(c_3937,plain,
! [X0: $i,X1: $i] :
( ( cons(X0,cons(X1,cons(X0,cons(X1,nil)))) = cons(X1,cons(X0,cons(X1,cons(X0,nil)))) )
| ~ x2(z,s(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_598,c_3929]) ).
tcf(c_3938,plain,
! [X0: $i,X1: $i] : cons(X0,cons(X1,cons(X0,cons(X1,nil)))) = cons(X1,cons(X0,cons(X1,cons(X0,nil)))),
inference(forward_subsumption_resolution,[status(thm)],[c_3937,c_59]) ).
tcf(c_4048,plain,
! [X0: $i,X1: $i] : head(cons(X0,cons(X1,cons(X0,cons(X1,nil))))) = X1,
inference(superposition,[status(thm)],[c_3938,c_49]) ).
tcf(c_4660,plain,
! [X0: $i,X1: $i] : X0 = X1,
inference(demodulation,[status(thm)],[c_4048,c_49]) ).
tcf(c_4662,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_51,c_4660]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWX187+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Thu Sep 24 23:32:21 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.31 Running first-order theorem proving
% 0.03/0.31 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.32
% 0.03/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.32
% 0.03/0.32 % Detected problem language: tptp
% 0.06/0.32 % Proving...
% 4.35/1.08 % SZS status Started for theBenchmark.p
% 4.35/1.08 % SZS status Theorem for theBenchmark.p
% 4.35/1.08
% 4.35/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.35/1.08
% 4.35/1.08 % ------ iProver source info
% 4.35/1.08
% 4.35/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 4.35/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.35/1.08 % git: non_committed_changes: false
% 4.35/1.08
% 4.35/1.08 % ------ Parsing...
% 4.35/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.35/1.08
% 4.35/1.08 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.35/1.08
% 4.35/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.35/1.08
% 4.35/1.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.35/1.08 % ------ Proving...
% 4.35/1.08 % ------ Problem Properties
% 4.35/1.08
% 4.35/1.08 %
% 4.35/1.08 % clauses 19
% 4.35/1.08 % conjectures 1
% 4.35/1.08 % EPR 1
% 4.35/1.08 % Horn 18
% 4.35/1.08 % unary 16
% 4.35/1.08 % binary 2
% 4.35/1.08 % lits 25
% 4.35/1.08 % lits eq 16
% 4.35/1.08 % fd_pure 0
% 4.35/1.08 % fd_pseudo 0
% 4.35/1.08 % fd_cond 0
% 4.35/1.08 % fd_pseudo_cond 0
% 4.35/1.08 % AC symbols 0
% 4.35/1.08
% 4.35/1.08 % ------ Schedule dynamic 5 is on
% 4.35/1.08
% 4.35/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.35/1.08
% 4.35/1.08
% 4.35/1.08 % ------
% 4.35/1.08 % Current options:
% 4.35/1.08 % ------
% 4.35/1.08
% 4.35/1.08
% 4.35/1.08 %
% 4.35/1.08
% 4.35/1.08 % ------ Proving...
% 4.35/1.08 %
% 4.35/1.08
% 4.35/1.08 % SZS status Theorem for theBenchmark.p
% 4.35/1.08
% 4.35/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.35/1.09
% 4.35/1.09
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