0.05/0.10	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.05/0.11	% Command  : /export/starexec/sandbox2/solver/bin/run_iprover 120 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
0.11/0.31	% Computer : n010.cluster.edu
0.11/0.31	% Model    : x86_64 x86_64
0.11/0.31	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.31	% Memory   : 8042.1875MB
0.11/0.31	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.31	% CPULimit : 960
0.11/0.31	% WCLimit  : 120
0.11/0.31	% DateTime : Wed Jul 30 16:30:49 EDT 2025
0.11/0.32	% CPUTime  : 
0.16/0.44	Running TFA theorem proving
0.16/0.44	Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core-casc.sh -l tptp -s tfa_schedule -t 120 /export/starexec/sandbox2/benchmark/theBenchmark.p
0.16/0.44	
0.16/0.44	% ======== iProver multi-core TPTP/SMT =========
0.16/0.44	
0.16/0.44	% Detected problem language: tptp
0.16/0.45	% Checking...
0.52/1.15	% Proving...
3.66/1.92	% SZS status Started for theBenchmark.p
3.66/1.92	% SZS status Theorem for theBenchmark.p
3.66/1.92	
3.66/1.92	%---------------- iProver v3.9.3 (pre CASC 2025/SMT-COMP 2025) ----------------%
3.66/1.92	
3.66/1.92	% ------  iProver source info
3.66/1.92	
3.66/1.92	% git: date: 2025-07-21 10:15:00 +0000
3.66/1.92	% git: sha1: d7ebeb21b290b8724a1e08b4c4a533d26e8c009f
3.66/1.92	% git: non_committed_changes: true
3.66/1.92	
3.66/1.92	% ------ Parsing...
3.66/1.92	% ------ Clausification by vclausify_rel  & Parsing by iProver...% 
3.66/1.92	
3.66/1.92	% ------ Preprocessing...% 
3.66/1.92	
3.66/1.92	% SZS status Theorem for theBenchmark.p
3.66/1.92	
3.66/1.92	% % SZS output start CNFRefutation for theBenchmark.p
3.66/1.92	
3.66/1.92	tff(func_def_0, type, witness1: ty > uni).
3.66/1.92	tff(pred_def_1, type, sort1: (ty * uni) > $o).
3.66/1.92	tff(pred_def_2, type, repr1: (uf_pure1 * $int * $int) > $o).
3.66/1.92	tff(pred_def_3, type, same1: (uf_pure1 * $int * $int) > $o).
3.66/1.92	tff(pred_def_4, type, same_reprs1: (uf_pure1 * uf_pure1) > $o).
3.66/1.92	tff(pred_def_5, type, path1: (graph1 * $int * $int) > $o).
3.66/1.92	tff(func_def_6, type, match_bool1: (ty * bool1 * uni * uni) > uni).
3.66/1.92	tff(func_def_7, type, tuple0: ty).
3.66/1.92	tff(pred_def_8, type, sP0: (graph1 * $int * $int) > $o).
3.66/1.92	tff(pred_def_9, type, sP1: (graph1 * $int * $int) > $o).
3.66/1.92	tff(func_def_10, type, ref: ty > ty).
3.66/1.92	tff(func_def_11, type, mk_ref: (ty * uni) > uni).
3.66/1.92	tff(func_def_12, type, contents: (ty * uni) > uni).
3.66/1.92	tff(func_def_13, type, uf_pure: ty).
3.66/1.92	tff(func_def_14, type, size1: uf_pure1 > $int).
3.66/1.92	tff(func_def_15, type, num1: uf_pure1 > $int).
3.66/1.92	tff(func_def_16, type, uf: ty).
3.66/1.92	tff(func_def_17, type, mk_uf1: uf_pure1 > uf1).
3.66/1.92	tff(func_def_18, type, state1: uf1 > uf_pure1).
3.66/1.92	tff(func_def_19, type, graph: ty).
3.66/1.92	tff(func_def_25, type, sK2: $int).
3.66/1.92	tff(func_def_26, type, sK3: $int).
3.66/1.92	tff(func_def_27, type, sK4: $int).
3.66/1.92	tff(func_def_28, type, sK5: (uf_pure1 * $int) > $int).
3.66/1.92	tff(func_def_29, type, sK6: (graph1 * $int * $int) > graph1).
3.66/1.92	tff(func_def_30, type, sK7: (graph1 * $int * $int) > $int).
3.66/1.92	tff(func_def_31, type, sK8: (graph1 * $int * $int) > $int).
3.66/1.92	tff(func_def_32, type, sK9: (graph1 * $int * $int) > graph1).
3.66/1.92	tff(func_def_33, type, sK10: (graph1 * $int * $int) > $int).
3.66/1.92	tff(func_def_34, type, sK11: (graph1 * $int * $int) > $int).
3.66/1.92	tff(func_def_35, type, sK12: (graph1 * $int * $int) > $int).
3.66/1.92	tff(func_def_36, type, sK13: (graph1 * $int * $int) > graph1).
3.66/1.92	tff(func_def_37, type, sK14: (graph1 * $int * $int) > $int).
3.66/1.92	tff(f2,axiom,(
3.66/1.92	  ! [X3 : ty,X1 : uni] : sort1(X3,contents(X3,X1))),
3.66/1.92	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contents_sort1)).
3.66/1.92	
3.66/1.92	tff(f3,conjecture,(
3.66/1.92	  ! [X4 : $int,X1 : $int,X2 : $int] : ($lesseq(0,X4) => (($less(X1,X4) & $lesseq(0,X1)) => (($less(X2,X4) & $lesseq(0,X2)) => $less($sum($product(X1,X4),X2),$product(X4,X4)))))),
3.66/1.92	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ineq1)).
3.66/1.92	
3.66/1.92	tff(f4,negated_conjecture,(
3.66/1.92	  ~! [X4 : $int,X1 : $int,X2 : $int] : ($lesseq(0,X4) => (($less(X1,X4) & $lesseq(0,X1)) => (($less(X2,X4) & $lesseq(0,X2)) => $less($sum($product(X1,X4),X2),$product(X4,X4)))))),
3.66/1.92	inference(negated_conjecture,[status(cth)],[f3])).
3.66/1.92	
3.66/1.92	tff(f6,axiom,(
3.66/1.92	  ! [X0 : uf1] : mk_uf1(state1(X0)) = X0),
3.66/1.92	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uf_inversion1)).
3.66/1.92	
3.66/1.92	tff(f8,axiom,(
3.66/1.92	  ! [X0 : tuple02] : tuple03 = X0),
3.66/1.92	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tuple0_inversion)).
3.66/1.92	
3.66/1.92	tff(f9,axiom,(
3.66/1.92	  ! [X3 : ty] : sort1(X3,witness1(X3))),
3.66/1.92	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',witness_sort1)).
3.66/1.92	
3.66/1.92	tff(f12,axiom,(
3.66/1.92	  true1 != false1),
3.66/1.92	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',true_False)).
3.66/1.92	
3.66/1.92	tff(f15,axiom,(
3.66/1.92	  ! [X3 : ty,X1 : uni] : sort1(ref(X3),mk_ref(X3,X1))),
3.66/1.92	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mk_ref_sort1)).
3.66/1.92	
3.66/1.92	tff(f17,axiom,(
3.66/1.92	  ! [X3 : ty,X1 : bool1,X11 : uni,X12 : uni] : sort1(X3,match_bool1(X3,X1,X11,X12))),
3.66/1.92	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',match_bool_sort1)).
3.66/1.92	
3.66/1.92	tff(f19,axiom,(
3.66/1.92	  ! [X5 : graph1,X1 : $int] : path1(X5,X1,X1)),
3.66/1.92	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_refl)).
3.66/1.92	
3.66/1.92	tff(f21,axiom,(
3.66/1.92	  ! [X0 : bool1] : (true1 = X0 | false1 = X0)),
3.66/1.92	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bool_inversion)).
3.66/1.92	
3.66/1.92	tff(f23,axiom,(
3.66/1.92	  ! [X0 : uf_pure1] : state1(mk_uf1(X0)) = X0),
3.66/1.92	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',state_def1)).
3.66/1.92	
3.66/1.92	tff(f24,axiom,(
3.66/1.92	  ! [X5 : graph1,X1 : $int,X2 : $int] : (path1(X5,X1,X2) => path1(X5,X2,X1))),
3.66/1.92	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_sym)).
3.66/1.92	
3.66/1.92	tff(f27,plain,(
3.66/1.92	  ~! [X4 : $int,X1 : $int,X2 : $int] : (~$less(X4,0) => (($less(X1,X4) & ~$less(X1,0)) => (($less(X2,X4) & ~$less(X2,0)) => $less($sum($product(X1,X4),X2),$product(X4,X4)))))),
3.66/1.92	  inference(theory_normalization,[],[f4])).
3.66/1.92	
3.66/1.92	tff(f31,plain,(
3.66/1.92	  ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
3.66/1.92	  introduced(theory_axiom_138,[])).
3.66/1.92	
3.66/1.92	tff(f33,plain,(
3.66/1.92	  ( ! [X0 : $int] : ($sum(X0,0) = X0) )),
3.66/1.92	  introduced(theory_axiom_140,[])).
3.66/1.92	
3.66/1.92	tff(f35,plain,(
3.66/1.92	  ( ! [X0 : $int] : (0 = $sum(X0,$uminus(X0))) )),
3.66/1.92	  introduced(theory_axiom_143,[])).
3.66/1.92	
3.66/1.92	tff(f36,plain,(
3.66/1.92	  ( ! [X0 : $int] : (~$less(X0,X0)) )),
3.66/1.92	  introduced(theory_axiom_145,[])).
3.66/1.92	
3.66/1.92	tff(f40,plain,(
3.66/1.92	  ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less(X1,$sum(X0,1))) )),
3.66/1.92	  introduced(theory_axiom_150,[])).
3.66/1.92	
3.66/1.92	tff(f41,plain,(
3.66/1.92	  ( ! [X0 : $int] : ($uminus($uminus(X0)) = X0) )),
3.66/1.92	  introduced(theory_axiom_151,[])).
3.66/1.92	
3.66/1.92	tff(f42,plain,(
3.66/1.92	  ( ! [X0 : $int,X1 : $int] : ($product(X0,X1) = $product(X1,X0)) )),
3.66/1.92	  introduced(theory_axiom_138,[])).
3.66/1.92	
3.66/1.92	tff(f44,plain,(
3.66/1.92	  ( ! [X0 : $int] : ($product(X0,1) = X0) )),
3.66/1.92	  introduced(theory_axiom_140,[])).
3.66/1.92	
3.66/1.92	tff(f45,plain,(
3.66/1.92	  ( ! [X0 : $int] : (0 = $product(X0,0)) )),
3.66/1.92	  introduced(theory_axiom_152,[])).
3.66/1.92	
3.66/1.92	tff(f49,plain,(
3.66/1.92	  ! [X0 : ty,X1 : uni] : sort1(X0,contents(X0,X1))),
3.66/1.92	  inference(rectify,[],[f2])).
3.66/1.92	
3.66/1.92	tff(f50,plain,(
3.66/1.92	  ~! [X0 : $int,X1 : $int,X2 : $int] : (~$less(X0,0) => (($less(X1,X0) & ~$less(X1,0)) => (($less(X2,X0) & ~$less(X2,0)) => $less($sum($product(X1,X0),X2),$product(X0,X0)))))),
3.66/1.92	  inference(rectify,[],[f27])).
3.66/1.92	
3.66/1.92	tff(f53,plain,(
3.66/1.92	  ! [X0 : ty] : sort1(X0,witness1(X0))),
3.66/1.92	  inference(rectify,[],[f9])).
3.66/1.92	
3.66/1.92	tff(f57,plain,(
3.66/1.92	  ! [X0 : ty,X1 : uni] : sort1(ref(X0),mk_ref(X0,X1))),
3.66/1.92	  inference(rectify,[],[f15])).
3.66/1.92	
3.66/1.92	tff(f59,plain,(
3.66/1.92	  ! [X0 : ty,X1 : bool1,X2 : uni,X3 : uni] : sort1(X0,match_bool1(X0,X1,X2,X3))),
3.66/1.92	  inference(rectify,[],[f17])).
3.66/1.92	
3.66/1.92	tff(f61,plain,(
3.66/1.92	  ! [X0 : graph1,X1 : $int] : path1(X0,X1,X1)),
3.66/1.92	  inference(rectify,[],[f19])).
3.66/1.92	
3.66/1.92	tff(f64,plain,(
3.66/1.92	  ! [X0 : graph1,X1 : $int,X2 : $int] : (path1(X0,X1,X2) => path1(X0,X2,X1))),
3.66/1.92	  inference(rectify,[],[f24])).
3.66/1.92	
3.66/1.92	tff(f69,plain,(
3.66/1.92	  ? [X0 : $int,X1 : $int,X2 : $int] : (((~$less($sum($product(X1,X0),X2),$product(X0,X0)) & ($less(X2,X0) & ~$less(X2,0))) & ($less(X1,X0) & ~$less(X1,0))) & ~$less(X0,0))),
3.66/1.92	  inference(ennf_transformation,[],[f50])).
3.66/1.92	
3.66/1.92	tff(f70,plain,(
3.66/1.92	  ? [X0 : $int,X1 : $int,X2 : $int] : (~$less($sum($product(X1,X0),X2),$product(X0,X0)) & $less(X2,X0) & ~$less(X2,0) & $less(X1,X0) & ~$less(X1,0) & ~$less(X0,0))),
3.66/1.92	  inference(flattening,[],[f69])).
3.66/1.92	
3.66/1.92	tff(f84,plain,(
3.66/1.92	  ! [X0 : graph1,X1 : $int,X2 : $int] : (path1(X0,X2,X1) | ~path1(X0,X1,X2))),
3.66/1.92	  inference(ennf_transformation,[],[f64])).
3.66/1.92	
3.66/1.92	tff(f90,plain,(
3.66/1.92	  ? [X0 : $int,X1 : $int,X2 : $int] : (~$less($sum($product(X1,X0),X2),$product(X0,X0)) & $less(X2,X0) & ~$less(X2,0) & $less(X1,X0) & ~$less(X1,0) & ~$less(X0,0)) => (~$less($sum($product(sK3,sK2),sK4),$product(sK2,sK2)) & $less(sK4,sK2) & ~$less(sK4,0) & $less(sK3,sK2) & ~$less(sK3,0) & ~$less(sK2,0))),
3.66/1.92	  introduced(choice_axiom,[])).
3.66/1.92	
3.66/1.92	tff(f91,plain,(
3.66/1.92	  ~$less($sum($product(sK3,sK2),sK4),$product(sK2,sK2)) & $less(sK4,sK2) & ~$less(sK4,0) & $less(sK3,sK2) & ~$less(sK3,0) & ~$less(sK2,0)),
3.66/1.92	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f70,f90])).
3.66/1.92	
3.66/1.92	tff(f106,plain,(
3.66/1.92	  ( ! [X0 : ty,X1 : uni] : (sort1(X0,contents(X0,X1))) )),
3.66/1.92	  inference(cnf_transformation,[],[f49])).
3.66/1.92	
3.66/1.92	tff(f107,plain,(
3.66/1.92	  ~$less(sK2,0)),
3.66/1.92	  inference(cnf_transformation,[],[f91])).
3.66/1.92	
3.66/1.92	tff(f108,plain,(
3.66/1.92	  ~$less(sK3,0)),
3.66/1.92	  inference(cnf_transformation,[],[f91])).
3.66/1.92	
3.66/1.92	tff(f109,plain,(
3.66/1.92	  $less(sK3,sK2)),
3.66/1.92	  inference(cnf_transformation,[],[f91])).
3.66/1.92	
3.66/1.92	tff(f110,plain,(
3.66/1.92	  ~$less(sK4,0)),
3.66/1.92	  inference(cnf_transformation,[],[f91])).
3.66/1.92	
3.66/1.92	tff(f111,plain,(
3.66/1.92	  $less(sK4,sK2)),
3.66/1.92	  inference(cnf_transformation,[],[f91])).
3.66/1.92	
3.66/1.92	tff(f114,plain,(
3.66/1.92	  ( ! [X0 : uf1] : (mk_uf1(state1(X0)) = X0) )),
3.66/1.92	  inference(cnf_transformation,[],[f6])).
3.66/1.92	
3.66/1.92	tff(f115,plain,(
3.66/1.92	  ( ! [X0 : tuple02] : (tuple03 = X0) )),
3.66/1.92	  inference(cnf_transformation,[],[f8])).
3.66/1.92	
3.66/1.92	tff(f116,plain,(
3.66/1.92	  ( ! [X0 : ty] : (sort1(X0,witness1(X0))) )),
3.66/1.92	  inference(cnf_transformation,[],[f53])).
3.66/1.92	
3.66/1.92	tff(f120,plain,(
3.66/1.92	  true1 != false1),
3.66/1.92	  inference(cnf_transformation,[],[f12])).
3.66/1.92	
3.66/1.92	tff(f125,plain,(
3.66/1.92	  ( ! [X0 : ty,X1 : uni] : (sort1(ref(X0),mk_ref(X0,X1))) )),
3.66/1.92	  inference(cnf_transformation,[],[f57])).
3.66/1.92	
3.66/1.92	tff(f127,plain,(
3.66/1.92	  ( ! [X2 : uni,X3 : uni,X0 : ty,X1 : bool1] : (sort1(X0,match_bool1(X0,X1,X2,X3))) )),
3.66/1.92	  inference(cnf_transformation,[],[f59])).
3.66/1.92	
3.66/1.92	tff(f129,plain,(
3.66/1.92	  ( ! [X0 : graph1,X1 : $int] : (path1(X0,X1,X1)) )),
3.66/1.92	  inference(cnf_transformation,[],[f61])).
3.66/1.92	
3.66/1.92	tff(f131,plain,(
3.66/1.92	  ( ! [X0 : bool1] : (true1 = X0 | false1 = X0) )),
3.66/1.92	  inference(cnf_transformation,[],[f21])).
3.66/1.92	
3.66/1.92	tff(f144,plain,(
3.66/1.92	  ( ! [X0 : uf_pure1] : (state1(mk_uf1(X0)) = X0) )),
3.66/1.92	  inference(cnf_transformation,[],[f23])).
3.66/1.92	
3.66/1.92	tff(f145,plain,(
3.66/1.92	  ( ! [X2 : $int,X0 : graph1,X1 : $int] : (path1(X0,X2,X1) | ~path1(X0,X1,X2)) )),
3.66/1.92	  inference(cnf_transformation,[],[f84])).
3.66/1.92	
3.66/1.92	tcf(c_52,plain,![X0_int:$int]:  
3.66/1.92	    ($product(X0_int,0) = 0),
3.66/1.92	    inference(cnf_transformation,[],[f45])).
3.66/1.92	
3.66/1.92	tcf(c_53,plain,![X0_int:$int]:  
3.66/1.92	    ($product(X0_int,1) = X0_int),
3.66/1.92	    inference(cnf_transformation,[],[f44])).
3.66/1.92	
3.66/1.92	tcf(c_55,plain,![X0_int:$int,X1_int:$int]:  
3.66/1.92	    ($product(X0_int,X1_int) = $product(X1_int,X0_int)),
3.66/1.92	    inference(cnf_transformation,[],[f42])).
3.66/1.92	
3.66/1.92	tcf(c_56,plain,![X0_int:$int]:  
3.66/1.92	    ($uminus($uminus(X0_int)) = X0_int),
3.66/1.92	    inference(cnf_transformation,[],[f41])).
3.66/1.92	
3.66/1.92	tcf(c_57,plain,![X0_int:$int,X1_int:$int]:  
3.66/1.92	    ($less(X0_int,$sum(X1_int,1))|$less(X1_int,X0_int)),
3.66/1.92	    inference(cnf_transformation,[],[f40])).
3.66/1.92	
3.66/1.92	tcf(c_61,plain,![X0_int:$int]:  
3.66/1.92	    (~$less(X0_int,X0_int)),
3.66/1.92	    inference(cnf_transformation,[],[f36])).
3.66/1.92	
3.66/1.92	tcf(c_62,plain,![X0_int:$int]:  
3.66/1.92	    ($sum(X0_int,$uminus(X0_int)) = 0),
3.66/1.92	    inference(cnf_transformation,[],[f35])).
3.66/1.92	
3.66/1.92	tcf(c_64,plain,![X0_int:$int]:  
3.66/1.92	    ($sum(X0_int,0) = X0_int),
3.66/1.92	    inference(cnf_transformation,[],[f33])).
3.66/1.92	
3.66/1.92	tcf(c_66,plain,![X0_int:$int,X1_int:$int]:  
3.66/1.92	    ($sum(X0_int,X1_int) = $sum(X1_int,X0_int)),
3.66/1.92	    inference(cnf_transformation,[],[f31])).
3.66/1.92	
3.66/1.92	tcf(c_68,plain,![X0_uni:uni,X0_ty:ty]:  
3.66/1.92	    (sort1(X0_ty,contents(X0_ty,X0_uni))),
3.66/1.92	    inference(cnf_transformation,[],[f106])).
3.66/1.92	
3.66/1.92	tcf(c_70,plain, ($less(sK4,sK2)),inference(cnf_transformation,[],[f111])).
3.66/1.92	
3.66/1.92	tcf(c_71,plain, (~$less(sK4,0)),inference(cnf_transformation,[],[f110])).
3.66/1.92	
3.66/1.92	tcf(c_72,plain, ($less(sK3,sK2)),inference(cnf_transformation,[],[f109])).
3.66/1.92	
3.66/1.92	tcf(c_73,plain, (~$less(sK3,0)),inference(cnf_transformation,[],[f108])).
3.66/1.92	
3.66/1.92	tcf(c_74,plain, (~$less(sK2,0)),inference(cnf_transformation,[],[f107])).
3.66/1.92	
3.66/1.92	tcf(c_76,plain,![X0_uf1:uf1]:  
3.66/1.92	    (mk_uf1(state1(X0_uf1)) = X0_uf1),
3.66/1.92	    inference(cnf_transformation,[],[f114])).
3.66/1.92	
3.66/1.92	tcf(c_77,plain,![X0_tuple02:tuple02]:  
3.66/1.92	    (X0_tuple02 = tuple03),
3.66/1.92	    inference(cnf_transformation,[],[f115])).
3.66/1.92	
3.66/1.92	tcf(c_78,plain,![X0_ty:ty]:  
3.66/1.92	    (sort1(X0_ty,witness1(X0_ty))),
3.66/1.92	    inference(cnf_transformation,[],[f116])).
3.66/1.92	
3.66/1.92	tcf(c_82,plain, (true1 != false1),inference(cnf_transformation,[],[f120])).
3.66/1.92	
3.66/1.92	tcf(c_87,plain,![X0_uni:uni,X0_ty:ty]:  
3.66/1.92	    (sort1(ref(X0_ty),mk_ref(X0_ty,X0_uni))),
3.66/1.92	    inference(cnf_transformation,[],[f125])).
3.66/1.92	
3.66/1.92	tcf(c_89,plain,![X0_uni:uni,X0_ty:ty,X0_bool1:bool1,X1_uni:uni]:  
3.66/1.92	    (sort1(X0_ty,match_bool1(X0_ty,X0_bool1,X0_uni,X1_uni))),
3.66/1.92	    inference(cnf_transformation,[],[f127])).
3.66/1.92	
3.66/1.92	tcf(c_91,plain,![X0_int:$int,X0_graph1:graph1]:  
3.66/1.92	    (path1(X0_graph1,X0_int,X0_int)),
3.66/1.92	    inference(cnf_transformation,[],[f129])).
3.66/1.92	
3.66/1.92	tcf(c_93,plain,![X0_bool1:bool1]:  
3.66/1.92	    (X0_bool1 = true1|X0_bool1 = false1),
3.66/1.92	    inference(cnf_transformation,[],[f131])).
3.66/1.92	
3.66/1.92	tcf(c_106,plain,![X0_uf_pure1:uf_pure1]:  
3.66/1.92	    (state1(mk_uf1(X0_uf_pure1)) = X0_uf_pure1),
3.66/1.92	    inference(cnf_transformation,[],[f144])).
3.66/1.92	
3.66/1.92	tcf(c_107,plain,![X0_int:$int,X0_graph1:graph1,X1_int:$int]:  
3.66/1.92	    (~path1(X0_graph1,X0_int,X1_int)|path1(X0_graph1,X1_int,X0_int)),
3.66/1.92	    inference(cnf_transformation,[],[f145])).
3.66/1.92	
3.66/1.92	tcf(c_109,plain, ($less(0,1)),theory(arith)).
3.66/1.92	
3.66/1.92	tcf(c_157,plain,![X0_int:$int,X1_int:$int]:  
3.66/1.93	    ($less(X1_int,X0_int)|$less(X0_int,$sum(X1_int,1))),
3.66/1.93	    inference(prop_impl_just,[status(thm)],[c_57])).
3.66/1.93	
3.66/1.93	tcf(c_158,plain,![X0_int:$int,X1_int:$int]:  
3.66/1.93	    ($less(X0_int,$sum(X1_int,1))|$less(X1_int,X0_int)),
3.66/1.93	    inference(renaming,[status(thm)],[c_157])).
3.66/1.93	
3.66/1.93	tcf(c_161,plain,![X0_int:$int,X0_graph1:graph1,X1_int:$int]:  
3.66/1.93	    (path1(X0_graph1,X1_int,X0_int)|~path1(X0_graph1,X0_int,X1_int)),
3.66/1.93	    inference(prop_impl_just,[status(thm)],[c_107])).
3.66/1.93	
3.66/1.93	tcf(c_162,plain,![X0_int:$int,X0_graph1:graph1,X1_int:$int]:  
3.66/1.93	    (~path1(X0_graph1,X0_int,X1_int)|path1(X0_graph1,X1_int,X0_int)),
3.66/1.93	    inference(renaming,[status(thm)],[c_161])).
3.66/1.93	
3.66/1.93	tcf(c_191,plain,![X0_bool1:bool1]:  
3.66/1.93	    (X0_bool1 = true1|X0_bool1 = false1),
3.66/1.93	    inference(prop_impl_just,[status(thm)],[c_93])).
3.66/1.93	
3.66/1.93	tcf(c_547,plain, 
3.66/1.93	    ($false),
3.66/1.93	    inference(smt_impl_just,
3.66/1.93	              [status(thm)],
3.66/1.93	              [c_109,c_162,c_106,c_191,c_91,c_89,c_87,c_82,c_78,c_77,
3.66/1.93	               c_76,c_74,c_73,c_72,c_71,c_70,c_68,c_66,c_64,c_62,c_61,
3.66/1.93	               c_158,c_56,c_55,c_53,c_52])).
3.66/1.93	
3.66/1.93	
3.66/1.93	% % SZS output end CNFRefutation for theBenchmark.p
3.66/1.93	
3.66/1.93	
3.66/2.02	EOF